proposal-origin/PROPOSAL | Year 4 Maths · T2 W11–12

Public educator selection · preserve first work before criteria or later sources. These pages are public; record prior access.

Year4 Mathematics · Resource Weeks11–12 · Days51–60

Written proposal edition1 · 13October2026 · Australian Curriculumv9.0 / Queensland. Choose a paper note, a number puzzle, a game plan or a useful collection problem. Read what each number counts, try a strategy, then give someone a check they can follow. Quiet/private work, usual communication, directing an agreeing helper, switching tasks and stopping are ordinary choices. The activity can be useful without a finished page or a public performance.

This proposal offers ten complete plans and thirty switchable routes, twenty ordinary worked situations, ten home offers, ten larger projects, ten genuinely blank daily sheets, ten original written read-aloud scripts, eight distinct formative sources with32 individual prompt/criterion/worked/full next-teaching chains, twenty future original visual briefs/full alternatives, and a temporary seven-field proposed Working-Notes Bench. The Bench is a place to keep chosen words, not an automatic calculator or judge. No final SVG, narration recording, web interface, print rendering or learner result is claimed.

Begin with actual learning

Resource numbers are identifiers. They do not require a particular school calendar. The fixed predecessor first taught decimal place/equivalence/fraction lines, then parity and algorithms, then multiplication/division/scaling and budget interpretation. They do not guarantee additive regrouping or unknown relationships. The new entry tasks teach missing whole-number joins, tens/ones equivalence and equal-unit roles before large values. Use a smaller complete ordinary model when needed, and name supplied mathematical help.

This deliberately proposes Week11–12 additive strategies/unknown relationships in place of the old map's Week12 multiplication focus, and brings forward part of its later Week15 unknown-equation intention. It fills observed source gaps; it does not silently certify or overwrite the historical map. The exact historical annual document is retained in YEAR-SEQUENCE.md. PREDECESSOR-SCOPE.md names this proposed sequencing shift and the full fixed-source body pins.

Fast start for a beginning teacher

Choose today's complete plan in TEACHING.md. Read its entry check before selecting a route.
Put the ordinary source and a genuinely empty W sheet in the learner's chosen mode. Keep your worked model on separate adult work.
Teach one relationship, guide a different problem, then offer one route. The35-minute rhythm and shorter10–20-minute follow-ups are adjustable and unpiloted.
Receive one available own contribution and its actual support. Use the specific criterion and a new next-teaching lesson rather than an item total or presumed gain.
Use a held source only after its stated relationships have been taught. Public resources are not secure tests: record exposure. If time/access is missing, record not yet observed and offer another sitting.
A busy parent can start with H01–H10 in ORDINARY.md. The home offers contain their own source, numbered steps, small beginning and a separate grown-up possibility. No purchase or device is needed.

Where things live

TEACHING.md: ten complete daily plans, all30 full routes and teacher possibilities.
ORDINARY.md: C01–C20 full practice sources and models, H01–H10 home, X01–X10 projects, W01–W10 true blank specifications and written scripts.
ASSESSMENTS.md: eight complete neutral sources and exposure/eligibility contracts, all32 prompts, criteria, models and full unrelated next lessons. Later source pages must separate own prompts from staff teaching.
TOOL-AND-AIDS.md: complete seven-field temporary Bench and paper contract, initial/failure/no-script states and finite future testing gates.
VISUALS.md: all20 precise original future geometry briefs, full alternatives and48 planned genuinely empty interiors.
CURRICULUM-RIGHTS.md: full138 national meanings are retained and linked; exact national/raw/native witnesses, partial mappings, complete Queensland context, primary facts, reuse and review limits. No full-year, whole-code mastery, independently calibrated progress, state-by-state completion or translated/cultural authority claim follows.

Ten daily plans · complete teacher sources

One route is enough; show the ordinary source before your separate model. Session suggestions are flexible and unpiloted. Learner ownership concerns the mathematics and choices, not a required physical action.

Access: Show, draw, type, sign, use your usual communication or direct an agreeing helper. Choose quiet/private work, switch a route, pause, pass or finish. One useful part is enough. A helper can read the exact words or scribe your choices; supplying an operation, count, regrouping or reason is mathematical help and is named. No speed, neatness, speech, handling or device requirement.

Lessons

A total worth checking

Adult model: 612 + 243 = (600 + 200) + (10 + 40) + (2 + 3) = 800 + 50 + 5 = 855 badges. Say what each part counts. This is joining two collections, not 612 groups of 243.

Child direction: Can we make a stock note that someone else can trust? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: columns are mixed; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 51

Different guided practice: An invented drawing archive has 421 cards plus 136 new cards. Invite the partition before the total: 400 + 100, 20 + 30, 1 + 6, then 557 cards. Ask why units can be joined.

Entry check and teach: Ask for 42 + 15 and a representation of 42 as four tens and two ones. If either is unavailable, count labelled tens/ones, join 2 + 5 ones then 4 + 1 tens. Teach 57 before increasing the number. Earlier fraction, parity or multiplication packs are not an entry guarantee.

Hook: Can we make a stock note that someone else can trust?

Materials: Broad paper, labelled place-value/part-whole/number-line alternatives as suitable; optional familiar safe counters; usual communication. No hundreds of loose marks, purchases or physical handling required. Keep adult model and own work separate.

Next teaching: If columns are mixed, label hundreds/tens/ones on 203 + 124, build 327, then invite 302 + 113 = 415 with labels faded.

Ordinary source: Fictional badge studio: 612 blank badges arrive in one parcel and 243 in another. Every badge is counted once. How many badges are available?

Own exit: For 304 + 152, give a total and one way to check its parts.

Partial codes

AC9M4N06

Purpose: Join like whole counts using place-value partitioning.

Routes

A

Complete task: A fictional game has 42 clue cards, then 15 arrive. Make a total note using tens and ones.

Entry or access: Return to two broad tens and three ones plus one ten if needed.

Id: A

Title: Small card repair

Worked staff: 42 + 15 = 57 cards: 40 + 10 = 50, 2 + 5 = 7.

B

Complete task: Use the 612 and 243 badge parcels. Compare partitioning with adding 200, then 40, then 3 to 612.

Entry or access: Use labels rather than 855 loose marks.

Id: B

Title: Badge maker

Worked staff: 855 badges; 612→812→852→855 keeps the complete second quantity.

C

Complete task: A fictional archive joins 2436 and 1523 cards. Show two compatible partitions.

Entry or access: Check thousands/hundreds entry before this larger route.

Id: C

Title: Archive upgrade

Worked staff: 3959 cards: 2000 + 1000, 400 + 500, 30 + 20, 6 + 3. Or 2436 + 1500 + 23.

Session stages

Meet the job

Instruction: Can we make a stock note that someone else can trust? Read the source. Ask what the numbers count and the wanted quantity. Ask for 42 + 15 and a representation of 42 as four tens and two ones. If either is unavailable, count labelled tens/ones, join 2 + 5 ones then 4 + 1 tens. Teach 57 before increasing the number. Earlier fraction, parity or multiplication packs are not an entry guarantee.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: 612 + 243 = (600 + 200) + (10 + 40) + (2 + 3) = 800 + 50 + 5 = 855 badges. Say what each part counts. This is joining two collections, not 612 groups of 243. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: An invented drawing archive has 421 cards plus 136 new cards. Invite the partition before the total: 400 + 100, 20 + 30, 1 + 6, then 557 cards. Ask why units can be joined. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: For 304 + 152, give a total and one way to check its parts. Receive an available response before staff key. If columns are mixed, label hundreds/tens/ones on 203 + 124, build 327, then invite 302 + 113 = 415 with labels faded.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: The result and a valid like-unit partition agree; a copied total alone is insufficient for the explanation.

Staff key: 456; 300 + 100, 0 + 50, 4 + 2. Check 456 − 152 = 304 or recombine the parts.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: A total worth checking

Ten ones can travel together

Adult model: 364 + 278 = 500 + 130 + 12 = 642. Rename 12 ones as 1 ten 2 ones; 14 tens as 1 hundred 4 tens, with 6 hundreds altogether. Equivalently 364 + 200 = 564, +70 = 634, +8 = 642. No item disappears when regrouped.

Child direction: Make a plan for a collection that crosses a ten or a hundred. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: a carried ten disappears; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 52

Different guided practice: A fictional picture station joins 527 cards and 186 cards: 527 + 100 = 627, +80 = 707, +6 = 713. Ask the learner to show where a hundred boundary was crossed.

Entry check and teach: Check 8 + 7 and explain ten ones = one ten. If needed, show 8 plus 2 fills ten and 5 remains; use 28 + 7 = 35 before hundreds.

Hook: Make a plan for a collection that crosses a ten or a hundred.

Next teaching: If a carried ten disappears, teach 48 + 16 with ten-unit labels: 40 + 10 + 8 + 6 = 64. Then offer 57 + 18 = 75.

Ordinary source: An invented costume cupboard has 364 tags, then receives 278 tags of the same kind. Find the new count.

Own exit: Try 258 + 167. Show the regroup or describe it exactly.

Partial codes

AC9M4N06

Purpose: Regroup an addition without changing its value.

Routes

A

Complete task: There are 28 fictional counters and 17 more. Show what happens to fifteen ones.

Entry or access: Build one ten from ten labelled ones if needed.

Id: A

Title: Game counters

Worked staff: 45 counters: 30 + 15 = 45.

B

Complete task: Use 527 and 186 cards. Make a checkable regrouping note.

Entry or access: Keep each place-value amount visible.

Id: B

Title: Picture station

Worked staff: 713 cards; 600 + 100 + 13 = 713.

C

Complete task: Join 2687 and 1756 imagined sheets. Compare adding chunks with place-value regrouping.

Entry or access: Use this only after thousands can be renamed.

Id: C

Title: Print store

Worked staff: 4443: 3000 + 1300 + 130 + 13 = 4443; chunks +1000,+700,+50,+6.

Session stages

Meet the job

Instruction: Make a plan for a collection that crosses a ten or a hundred. Read the source. Ask what the numbers count and the wanted quantity. Check 8 + 7 and explain ten ones = one ten. If needed, show 8 plus 2 fills ten and 5 remains; use 28 + 7 = 35 before hundreds.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: 364 + 278 = 500 + 130 + 12 = 642. Rename 12 ones as 1 ten 2 ones; 14 tens as 1 hundred 4 tens, with 6 hundreds altogether. Equivalently 364 + 200 = 564, +70 = 634, +8 = 642. No item disappears when regrouped. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: A fictional picture station joins 527 cards and 186 cards: 527 + 100 = 627, +80 = 707, +6 = 713. Ask the learner to show where a hundred boundary was crossed. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: Try 258 + 167. Show the regroup or describe it exactly. Receive an available response before staff key. If a carried ten disappears, teach 48 + 16 with ten-unit labels: 40 + 10 + 8 + 6 = 64. Then offer 57 + 18 = 75.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: Each regroup keeps the quantity, including both parts of the added amount, and yields 425.

Staff key: 425: 300 + 110 + 15 = 425, or 258 + 100 + 60 + 7.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: Ten ones can travel together

Borrow a friendly number, then put it back

Adult model: 398 + 267 = 400 + 267 − 2 = 665. We added two extra in the friendly-number step, so remove two from 667. About 400 + 300 = 700 is an estimate, not this exact calculation.

Child direction: Would moving to a nearby round number make this job easier? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: the adjustment goes the wrong way; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 53

Different guided practice: For fictional prompt cards, 497 + 186 = 500 + 186 − 3 = 683. Contrast the wrong 686: it counts the three extra cards. Invite a different check: 497 + 180 + 6.

Entry check and teach: Ask why 39 + 12 can be worked as 40 + 12 − 1. Model with a labelled extra mark if needed. Teach the compensation before rounding two large inputs.

Hook: Would moving to a nearby round number make this job easier?

Next teaching: If the adjustment goes the wrong way, compare 19 + 6 with 20 + 6 − 1 using marks. Guide 29 + 14, then invite 49 + 17 = 66.

Ordinary source: An invented sticker design has 398 blue stickers and 267 plain stickers. Find the exact total.

Own exit: Work 299 + 146 exactly using a friendly number, and name the adjustment.

Partial codes

AC9M4N06
AC9M4N07 partial

Purpose: Use exact compensation and distinguish it from estimation.

Routes

A

Complete task: An invented puzzle tray joins 49 and 27 pieces. Use fifty carefully.

Entry or access: Draw the one added extra separately.

Id: A

Title: Puzzle pieces

Worked staff: 76: 50 + 27 − 1.

B

Complete task: Find 398 + 267 and compare compensation with chunks.

Entry or access: Explain which quantity was changed.

Id: B

Title: Sticker plan

Worked staff: 665 exactly; 700 is a coarse estimate.

C

Complete task: An imaginary exhibit game counts 1998 + 367 slips. Compare exact compensation and a nearest-hundred estimate.

Entry or access: This fictional game is not a museum programme or attendance fact.

Id: C

Title: Museum-copy game

Worked staff: 2365 exact; 2000 + 400 ≈ 2400, 35 above exact.

Session stages

Meet the job

Instruction: Would moving to a nearby round number make this job easier? Read the source. Ask what the numbers count and the wanted quantity. Ask why 39 + 12 can be worked as 40 + 12 − 1. Model with a labelled extra mark if needed. Teach the compensation before rounding two large inputs.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: 398 + 267 = 400 + 267 − 2 = 665. We added two extra in the friendly-number step, so remove two from 667. About 400 + 300 = 700 is an estimate, not this exact calculation. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: For fictional prompt cards, 497 + 186 = 500 + 186 − 3 = 683. Contrast the wrong 686: it counts the three extra cards. Invite a different check: 497 + 180 + 6. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: Work 299 + 146 exactly using a friendly number, and name the adjustment. Receive an available response before staff key. If the adjustment goes the wrong way, compare 19 + 6 with 20 + 6 − 1 using marks. Guide 29 + 14, then invite 49 + 17 = 66.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: The nearby number, compensating adjustment and exact result are linked; rounding alone is not an exact proof.

Staff key: 445: 300 + 146 − 1; the added extra one is removed.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: Borrow a friendly number, then put it back

Take away without losing the place values

Adult model: 806 = 7 hundreds + 9 tens + 16 ones. Subtract 2 hundreds, 4 tens, 7 ones to leave 5 hundreds 5 tens 9 ones = 559. Check 247 + 559 = 806. A count-up check is 247→250 (+3)→800 (+550)→806 (+6), total 559.

Child direction: Can a repair drawer show what is left clearly? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: 0 tens blocks the subtraction; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 54

Different guided practice: A made-up card store has 704 cards, uses 168. Guide 6 hundreds 9 tens 14 ones minus 1 hundred 6 tens 8 ones = 536. Or subtract 100, 60, 8 in chunks.

Entry check and teach: Ask for 52 − 17 and whether one ten can become ten ones. If not, teach 30 − 8 as 2 tens 10 ones minus 8 = 22; return to 52 − 17 = 35.

Hook: Can a repair drawer show what is left clearly?

Next teaching: If 0 tens blocks the subtraction, teach 102 − 38 by trading one hundred for tens, then one ten for ones. Guide 64; invite 201 − 46 = 155.

Ordinary source: A fictional repair drawer starts with 806 labels. It uses 247 labels once. Find labels left.

Own exit: For 603 − 157, show what remains and a connected check.

Partial codes

AC9M4N06

Purpose: Subtract through regrouping or a connected count-up check.

Routes

A

Complete task: A fictional drawer has 63 labels and uses 28. Find what remains with regrouping.

Entry or access: No actual paint or material handling is needed.

Id: A

Title: Small paint labels

Worked staff: 35 labels; 28 + 35 = 63.

B

Complete task: Use 806 − 247. Make a left-count record with a check.

Entry or access: Describe bundles instead of drawing hundreds of marks.

Id: B

Title: Repair drawer

Worked staff: 559 labels; 247 + 559 = 806.

C

Complete task: An invented archive has 2004 cards and retires 786. Find remaining cards using two approaches.

Entry or access: Check thousands entry and the meaning of retiring a count.

Id: C

Title: Archive use

Worked staff: 1218; 786→800(+14)→2000(+1200)→2004(+4).

Session stages

Meet the job

Instruction: Can a repair drawer show what is left clearly? Read the source. Ask what the numbers count and the wanted quantity. Ask for 52 − 17 and whether one ten can become ten ones. If not, teach 30 − 8 as 2 tens 10 ones minus 8 = 22; return to 52 − 17 = 35.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: 806 = 7 hundreds + 9 tens + 16 ones. Subtract 2 hundreds, 4 tens, 7 ones to leave 5 hundreds 5 tens 9 ones = 559. Check 247 + 559 = 806. A count-up check is 247→250 (+3)→800 (+550)→806 (+6), total 559. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: A made-up card store has 704 cards, uses 168. Guide 6 hundreds 9 tens 14 ones minus 1 hundred 6 tens 8 ones = 536. Or subtract 100, 60, 8 in chunks. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: For 603 − 157, show what remains and a connected check. Receive an available response before staff key. If 0 tens blocks the subtraction, teach 102 − 38 by trading one hundred for tens, then one ten for ones. Guide 64; invite 201 − 46 = 155.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: Renamed values conserve 603; subtraction and inverse agree with 446 labels/items left.

Staff key: 446; 157 + 446 = 603. Regroup 603 as 5 hundreds 9 tens 13 ones.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: Take away without losing the place values

How much more?

Adult model: 987→1000 adds 13; 1000→1200 adds 200; 1200→1203 adds 3. The gap is 216 labels: 987 + 216 = 1203. The difference is a count comparison, not evidence the larger design is preferable.

Child direction: Help two made-up teams compare their counts without calling one better. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: the difference is added to both counts; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 55

Different guided practice: Two invented folders contain 1501 and 1297 cards. Guide +3 to 1300,+200 to 1500,+1 to 1501 =204. Ask whether taking 1297 away from 1501 gives the same difference.

Entry check and teach: Ask how many more 37 is than 29; count 29→30(+1)→37(+7)=8. Both original collections still exist. If comparison is unclear, use 7 and 4 labels side by side.

Hook: Help two made-up teams compare their counts without calling one better.

Next teaching: If the difference is added to both counts, keep a bar for each whole. Teach 46 compared with 39 gives 7, check 39+7=46; invite 81 compared with 68 gives 13.

Ordinary source: Two fictional poster designs require 1203 labels and 987 labels. What is the difference in their requirements? No labels have been removed.

Own exit: A fictional score sheet lists 1002 and 875 points. Find the difference and explain its meaning.

Partial codes

AC9M4N06

Purpose: Find a difference by counting up; distinguish comparison from a removal event.

Routes

A

Complete task: Compare fictional 52 and 38 game points. Show the gap, keeping both scores.

Entry or access: Use a marked line or exact spoken steps.

Id: A

Title: Small score comparison

Worked staff: 14 points; 38 + 14 = 52.

B

Complete task: Compare 1203 and 987 labels needed. Give a gap note that avoids a value judgement.

Entry or access: Use friendly stepping stones.

Id: B

Title: Poster designs

Worked staff: 216 more labels for the first design.

C

Complete task: Two invented game routes are 3502 and 2789 step-cards long. Find the difference, not a real walking distance.

Entry or access: The counts are fictional game units, not travel or fitness advice.

Id: C

Title: Fictional trail game

Worked staff: 713 step-cards; +11 to 2800,+700 to 3500,+2.

Session stages

Meet the job

Instruction: Help two made-up teams compare their counts without calling one better. Read the source. Ask what the numbers count and the wanted quantity. Ask how many more 37 is than 29; count 29→30(+1)→37(+7)=8. Both original collections still exist. If comparison is unclear, use 7 and 4 labels side by side.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: 987→1000 adds 13; 1000→1200 adds 200; 1200→1203 adds 3. The gap is 216 labels: 987 + 216 = 1203. The difference is a count comparison, not evidence the larger design is preferable. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: Two invented folders contain 1501 and 1297 cards. Guide +3 to 1300,+200 to 1500,+1 to 1501 =204. Ask whether taking 1297 away from 1501 gives the same difference. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: A fictional score sheet lists 1002 and 875 points. Find the difference and explain its meaning. Receive an available response before staff key. If the difference is added to both counts, keep a bar for each whole. Teach 46 compared with 39 gives 7, check 39+7=46; invite 81 compared with 68 gives 13.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: The difference and count-up bridge are correct and interpreted as comparison, not a performed removal.

Staff key: 127 points: +25 to 900,+100 to 1000,+2. No claim about real players.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: How much more?

Find the missing part

Adult model: 468→500 adds 32; 500→725 adds 225; missing part 257. Check 468+257=725. The box is a number value, not the total 725; the equation has two equal sides.

Child direction: What needs to join a collection to reach the target? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: the total is placed in the box; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 56

Different guided practice: A fictional badge target is 630 with 275 available. Guide 275+□=630; 275→300(+25)→630(+330)=355. Check 275+355.

Entry check and teach: Check 18 + □ = 31. Show 18 and the target 31, count up 13, then check 18+13. If the box is treated as a decoration, put a temporary question card over one part of a small 4+3=7 model.

Hook: What needs to join a collection to reach the target?

Next teaching: If the total is placed in the box, label whole 54, known part 28, unknown part 26. Guide 28+26=54, then invite 37+□=65. Staff reference: □=28; check 37+28=65.

Ordinary source: An invented card kit needs 725 cards in total. It already has 468. How many more are needed? 468 + □ = 725.

Own exit: Solve 386 + □ = 540, and show the check in the original equation.

Partial codes

AC9M4A01
AC9M4N06

Purpose: Use addition/subtraction relationships for an unknown addend.

Routes

A

Complete task: A made-up game target is 65 points, with 37 already recorded. Find the missing part.

Entry or access: Use two bars for known part and unknown part.

Id: A

Title: Small game target

Worked staff: 28; 37+28=65.

B

Complete task: Use 468+□=725. Tell the next maker how many more cards would be needed.

Entry or access: The future requirement is not a completed supply event.

Id: B

Title: Card kit

Worked staff: 257 cards.

C

Complete task: An invented print target is 2400 sheets; 1587 are already counted. Find the missing part and an exact check.

Entry or access: Choose a thousands representation only if available.

Id: C

Title: Print target

Worked staff: 813; 1587+813=2400.

Session stages

Meet the job

Instruction: What needs to join a collection to reach the target? Read the source. Ask what the numbers count and the wanted quantity. Check 18 + □ = 31. Show 18 and the target 31, count up 13, then check 18+13. If the box is treated as a decoration, put a temporary question card over one part of a small 4+3=7 model.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: 468→500 adds 32; 500→725 adds 225; missing part 257. Check 468+257=725. The box is a number value, not the total 725; the equation has two equal sides. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: A fictional badge target is 630 with 275 available. Guide 275+□=630; 275→300(+25)→630(+330)=355. Check 275+355. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: Solve 386 + □ = 540, and show the check in the original equation. Receive an available response before staff key. If the total is placed in the box, label whole 54, known part 28, unknown part 26. Guide 28+26=54, then invite 37+□=65. Staff reference: □=28; check 37+28=65.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: The missing part 154 and original equality are supported by an inverse or count-up relationship.

Staff key: 154; 386+154=540.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: Find the missing part

Which part is missing?

Adult model: Used tags 930−586=344, check 930−344=586. Starting cards 428+175=603, check 603−175=428. Addition or subtraction is chosen by the unknown role, not by spotting the word left.

Child direction: A missing count can sit at the start or in the amount used. Can your note make that clear? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: all left stories trigger subtraction; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 57

Different guided practice: A fictional game starts with 702 tokens and ends with 459: used 243. A different game uses 126 and ends with 387: start 513. Guide both original-equation checks, one case at a time.

Entry check and teach: Contrast □ − 7 =12 with 19 − □ =12 using an empty part/whole bar. First means start 19; second means used 7. Teach small connected addition if the roles are swapped.

Hook: A missing count can sit at the start or in the amount used. Can your note make that clear?

Next teaching: If all left stories trigger subtraction, teach □−4=9 by joining used 4 and left 9 into 13. Then invite □−8=15. Staff reference: starting value □=23; check 23−8=15.

Ordinary source: A fictional store starts with 930 tags and finishes with 586. How many were used?930−□=586. Separately, a fictional box uses 175 cards and has 428 left. How many did it start with?□−175=428.

Own exit: Solve □ − 148 =367 and explain what the box counts.

Partial codes

AC9M4A01
AC9M4N06

Purpose: Distinguish unknown starting quantity from unknown subtraction amount.

Routes

A

Complete task: A pretend tray starts with 61 cards and ends with 38. Find how many were used.

Entry or access: Keep start/use/left labels visible.

Id: A

Title: Small stock story

Worked staff: 23 used; 61−23=38.

B

Complete task: Work the 930/586 tags and 175/428 cards cases separately. Name each unknown role.

Entry or access: Do not join card and tag quantities.

Id: B

Title: Two store notes

Worked staff: 344 used tags; 603 starting cards.

C

Complete task: A fictional archive has 2001−□=1278; another has□−586=1447. Explain and check both.

Entry or access: Offer just one equation if two cases overload the purpose.

Id: C

Title: Archive puzzles

Worked staff: 723 removed; 2033 starting.

Session stages

Meet the job

Instruction: A missing count can sit at the start or in the amount used. Can your note make that clear? Read the source. Ask what the numbers count and the wanted quantity. Contrast □ − 7 =12 with 19 − □ =12 using an empty part/whole bar. First means start 19; second means used 7. Teach small connected addition if the roles are swapped.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: Used tags 930−586=344, check 930−344=586. Starting cards 428+175=603, check 603−175=428. Addition or subtraction is chosen by the unknown role, not by spotting the word left. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: A fictional game starts with 702 tokens and ends with 459: used 243. A different game uses 126 and ends with 387: start 513. Guide both original-equation checks, one case at a time. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: Solve □ − 148 =367 and explain what the box counts. Receive an available response before staff key. If all left stories trigger subtraction, teach □−4=9 by joining used 4 and left 9 into 13. Then invite □−8=15. Staff reference: starting value □=23; check 23−8=15.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: The box is the starting quantity 515; rebuilding from used 148 and left 367 supports the original equality.

Staff key: 515 starting items; 515−148=367.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: Which part is missing?

Both sides mean the same amount

Adult model: Right side 390+75=465;□=465−245=220. Substitution 245+220=465 and 390+75=465. The box is 220, not 465. Keep each original side intact.

Child direction: Make a puzzle another person can check without guessing what the equals sign means. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: If 465 is entered in the box; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 58

Different guided practice: For a fictional drawer 620−185=□+240: left 435, unknown 195, check 195+240=435. Invite the learner to compute the known side before undoing the other part.

Entry check and teach: Check 12+3=10+5 as equal 15, then 12+□=10+5 gives 3. If = means next answer, use two named equal 15 bars and vary one decomposition.

Hook: Make a puzzle another person can check without guessing what the equals sign means.

Next teaching: If 465 is entered in the box, use 20+□=30+7: known side 37, missing 17. Guide 20+17=37; then invite 14+□=20+8 gives 14.

Ordinary source: An invented display equation is 245+□=390+75. Find the box value and check both sides.

Own exit: Solve 128+□=200+47 and check the two sides.

Partial codes

AC9M4A01
AC9M4N06

Purpose: Find an unknown when each side contains a calculation.

Routes

A

Complete task: Solve 18+□=25+7, preserving both sides.

Entry or access: Represent each entire side as a whole.

Id: A

Title: Small equality puzzle

Worked staff: 14; 18+14=32=25+7.

B

Complete task: Use 245+□=390+75. Create a readable substitution check.

Entry or access: No balance-scale physical claim is needed.

Id: B

Title: Display equation

Worked staff: 220; both sides 465.

C

Complete task: Solve 2000−675=□+486. Show what is known first.

Entry or access: Use a broad labelled two-side diagram.

Id: C

Title: Archive equality

Worked staff: 839; 1325=839+486.

Session stages

Meet the job

Instruction: Make a puzzle another person can check without guessing what the equals sign means. Read the source. Ask what the numbers count and the wanted quantity. Check 12+3=10+5 as equal 15, then 12+□=10+5 gives 3. If = means next answer, use two named equal 15 bars and vary one decomposition.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: Right side 390+75=465;□=465−245=220. Substitution 245+220=465 and 390+75=465. The box is 220, not 465. Keep each original side intact. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: For a fictional drawer 620−185=□+240: left 435, unknown 195, check 195+240=435. Invite the learner to compute the known side before undoing the other part. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: Solve 128+□=200+47 and check the two sides. Receive an available response before staff key. If 465 is entered in the box, use 20+□=30+7: known side 37, missing 17. Guide 20+17=37; then invite 14+□=20+8 gives 14.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: Unknown 119 makes both full sides equal 247; explanation distinguishes box value from whole-side value.

Staff key: 119; 128+119=247 and 200+47=247.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: Both sides mean the same amount

An estimate helps. An exact check decides.

Adult model: Handouts 268+124=392; 485−392=93 more needed. Budget 265+148=413 cost; 450−413=37 left. Nearest-ten estimate 270+150≈420 checks scale but is not the exact 413 or 37. Keep handouts and dollars separate.

Child direction: Pick a made-up supply or budget job. What decision does the arithmetic need to answer? Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: an estimate is treated as exact; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 59

Different guided practice: An imaginary card plan needs 600 cards; 328+195=523 available, gap 77. A separate invented budget $380 costs $197+$186=$383, $3 over. A rough $200+$190≈$390 suggests close but exact arithmetic settles it.

Entry check and teach: Check sum/difference role and nearest-ten rounding. Show 265 rounds 270 and 148 rounds 150; nearest-ten rough cost 420 differs from exact 413. No cents, retail price or family-finance knowledge assumed.

Hook: Pick a made-up supply or budget job. What decision does the arithmetic need to answer?

Next teaching: If an estimate is treated as exact, compare 49+52≈50+50=100 with exact 101 and target 100. Guide it is 1 over; then invite 98+103 with target 200. Staff reference: 98+103=201, which is 1 over 200.

Ordinary source: A fictional print stand needs 485 handouts. It has 268 in one pile and 124 in another. Is there enough? Separately a pretend art plan has costs $265 and $148, within an invented AUD450 budget.

Own exit: Budget $300, fictional costs $148 and $153. Does it fit? Give an exact reason.

Partial codes

AC9M4N08 additive partial
AC9M4N07
AC9M4N06

Purpose: Formulate additive practical problems and interpret exact comparisons.

Routes

A

Complete task: An invented set needs 90 cards; there are 47 and 36. Find whether more are needed.

Entry or access: Use whole counts rather than a purchase.

Id: A

Title: Small card order

Worked staff: 83 available, 7 more.

B

Complete task: Use fictional $265+$148 and $450 budget. State total cost and money left.

Entry or access: No real cash handling or spending follows.

Id: B

Title: Art budget

Worked staff: 413 cost, 37 left; about 420 checks scale.

C

Complete task: An invented print target is 2000 sheets, with 987+1018 available. Estimate then decide exactly.

Entry or access: Compare a rough equality with exact five-extra.

Id: C

Title: Close print decision

Worked staff: 2005 available, 5 surplus; about 1000+1000=2000 is inconclusive.

Session stages

Meet the job

Instruction: Pick a made-up supply or budget job. What decision does the arithmetic need to answer? Read the source. Ask what the numbers count and the wanted quantity. Check sum/difference role and nearest-ten rounding. Show 265 rounds 270 and 148 rounds 150; nearest-ten rough cost 420 differs from exact 413. No cents, retail price or family-finance knowledge assumed.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: Handouts 268+124=392; 485−392=93 more needed. Budget 265+148=413 cost; 450−413=37 left. Nearest-ten estimate 270+150≈420 checks scale but is not the exact 413 or 37. Keep handouts and dollars separate. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: An imaginary card plan needs 600 cards; 328+195=523 available, gap 77. A separate invented budget $380 costs $197+$186=$383, $3 over. A rough $200+$190≈$390 suggests close but exact arithmetic settles it. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: Budget $300, fictional costs $148 and $153. Does it fit? Give an exact reason. Receive an available response before staff key. If an estimate is treated as exact, compare 49+52≈50+50=100 with exact 101 and target 100. Guide it is 1 over; then invite 98+103 with target 200. Staff reference: 98+103=201, which is 1 over 200.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: A correct additive model, exact 301 and interpretation of $1 over agree; approximate 300 is not affordability proof.

Staff key: 301 cost, $1 over. A nearest-ten estimate 150+150≈300 cannot settle the tight decision.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: An estimate helps. An exact check decides.

Make a useful note of your own

Adult model: 675+148=823; 823−236=587 labels left. Check 587+236=823 and 823−148=675. A plan to use 236 is a model condition; only an actual authorised observation could establish real use.

Child direction: Choose a small planning problem you care about: a game, a collection, a pretend budget or a number puzzle. Make one note useful to someone else. Pick one route. Show what the numbers mean, try a way, then check one result. You can stop after a useful part.

Common tangle: the plan lacks given counts; check the roles and equivalent quantities, rather than memorising a printed answer.

Day: 60

Different guided practice: Guide a different fictional game: 508 cards, 176 arrive, 245 used; 684−245=439 left. Ask the learner to select addition then subtraction from roles, not follow a hiddenpreset. Receive one useful step if the whole chain is too much.

Entry check and teach: Review actual work. If partitioning, unknown roles or comparison remain unclear, choose that teaching instead of an open project. For a new problem teach identifying given counts/unit/wanted quantity with small 12+8=20 first.

Hook: Choose a small planning problem you care about: a game, a collection, a pretend budget or a number puzzle. Make one note useful to someone else.

Next teaching: If the plan lacks given counts, offer empty start/change/question headings and neutral scribing. Teach one missing relationship using fictional 35 plus 18 then 12 used=41. Invite a new own small problem later.

Ordinary source: Adult example: a fictional making station has 675 labels, receives 148 more and uses 236. How many remain? No real making or stock count is claimed.

Own exit: Choose one result from your own problem. What does it count and what check supports it?

Partial codes

AC9M4N08 additive partial
AC9M4N06
AC9M4A01 optional

Purpose: Formulate a complete additive situation, solve and check it for a reader.

Routes

A

Complete task: Choose imaginary starting cards 20–60, an arrival 10–30 and use 0–20. State all values and find cards left.

Entry or access: Values are choices, not pupil possessions.

Id: A

Title: Small game note

Worked staff: Adult possibility 35+18−12=41. Other valid selected values accepted.

B

Complete task: Use 675+148−236. Prepare a short source/strategy/check note for another maker.

Entry or access: A handover note is not proof real use.

Id: B

Title: Maker handover

Worked staff: 587 labels left; inverse checks above.

C

Complete task: Choose whole a, b, c from 100–2000 with a+b≥c; write a+□=b+c and find the unknown only if b+c≥a. Or choose a nonnegative starting/use story.

Entry or access: Teach the role and eligibility before selecting this open equality.

Id: C

Title: Own puzzle card

Worked staff: Adult possibility 480+□=600+125→245; both sides 725.

Session stages

Meet the job

Instruction: Choose a small planning problem you care about: a game, a collection, a pretend budget or a number puzzle. Make one note useful to someone else. Read the source. Ask what the numbers count and the wanted quantity. Review actual work. If partitioning, unknown roles or comparison remain unclear, choose that teaching instead of an open project. For a new problem teach identifying given counts/unit/wanted quantity with small 12+8=20 first.

Minutes suggestion: 5

Stage: Meet the job

Teach one relationship

Instruction: 675+148=823; 823−236=587 labels left. Check 587+236=823 and 823−148=675. A plan to use 236 is a model condition; only an actual authorised observation could establish real use. Show on separate adult paper. Pause after one transformation; invite explanation before showing the next.

Minutes suggestion: 10

Stage: Teach one relationship

Guide then choose

Instruction: Guide a different fictional game: 508 cards, 176 arrive, 245 used; 684−245=439 left. Ask the learner to select addition then subtraction from roles, not follow a hiddenpreset. Receive one useful step if the whole chain is too much. Offer one complete route below, not all three as a quota. Let the learner select a representation and pause or switch.

Minutes suggestion: 15

Stage: Guide then choose

Receive and choose tomorrow

Instruction: Choose one result from your own problem. What does it count and what check supports it? Receive an available response before staff key. If the plan lacks given counts, offer empty start/change/question headings and neutral scribing. Teach one missing relationship using fictional 35 plus 18 then 12 used=41. Invite a new own small problem later.

Minutes suggestion: 5

Stage: Receive and choose tomorrow

Specific criterion: Available own formulation, strategy, result, units and check agree; unsupported or unfinished steps remain visible.

Staff key: No prescribed own numbers. Fixed routes below have separate staff possibilities. Check against the learner actual stated conditions; do not fill missing choices from adult work.

Status: Proposed 35-minute shape, unpiloted and freely reorderable; resource day not school calendar requirement.

Title: Make a useful note of your own

Original SubjectNest by NeuroForgeIO Pty Ltd2026, CC BY4.0. Curriculum and other outside material retains the separate notices in SOURCE-NOTICE.md. Written proposal, pending different whole review; no source/interface/art/audio or classroom acceptance.

Useful ordinary practice and family offers

All supplied counts, prices and events below are original fiction. They are complete stand-alone taught offers, not unseen assessment. The separate adult possibility is for teaching after an available attempt. Changing a number requires restating units and conditions and computing a new result. The real denomination fact in CURRICULUM-RIGHTS is a separate sourced fact; it does not make the fictional budgets current prices.

Contexts

C01

A: 312

B: 124

Id: C01

Job: join

Reason: Name both parts and the whole.

Source: A fictional repair desk receives 312 paper slips and 124 more of the same kind.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Repair slips

Worked staff: 436 slips: 300+100+10+20+2+4=436.

C02

A: 523

B: 245

Id: C02

Job: join

Reason: Distinct card types can join as a total card count; no story quality claim.

Source: An invented story archive joins 523 scene cards and 245 character cards; all are counted as cards.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Story cards

Worked staff: 768 cards: 500+200+20+40+3+5.

C03

A: 186

B: 257

Id: C03

Job: join

Reason: Rename 13 ones and 14 tens without losing value.

Source: A fictional badge set has 186 blue and 257 plain badges.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Game badges

Worked staff: 443 badges: 300+130+13.

C04

A: 438

B: 185

Id: C04

Job: join

Reason: Represent one hundred crossing.

Source: An imagined sound game has 438 prompt cards and 185 new prompt cards. No volume or hearing task is required.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Sound prompt cards

Worked staff: 623 cards: 438+100+80+5.

C05

A: 399

B: 146

Id: C05

Job: join

Reason: Show the extra one and its removal.

Source: A fictional sticker plan joins 399 and 146 stickers.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Sticker strips

Worked staff: 545: 400+146−1.

C06

A: 698

B: 257

Id: C06

Job: join

Reason: Contrast about 700+300=1000 with exact 955.

Source: An invented costume plan joins 698 and 257 labels.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Costume labels

Worked staff: 955: 700+257−2.

C07

A: 705

B: 268

Id: C07

Job: remove

Reason: No real map or journey claim.

Source: A fictional tabletop map has 705 tiles, removes 268 from the design.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Map tiles

Worked staff: 437 left; 705=6 hundreds 9 tens 15 ones; 268+437=705.

C08

A: 902

B: 457

Id: C08

Job: remove

Reason: Keep count-up as connected check.

Source: An imagined puzzle store has 902 pieces and uses 457 once.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Puzzle pieces

Worked staff: 445 left; 457→500(+43)→900(+400)→902(+2).

C09

A: 1301

B: 987

Id: C09

Job: compare

Reason: Difference counts slips, not reading ability.

Source: Two made-up reading stations list 1301 and 987 slips. Both collections remain.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Reading slips

Worked staff: 314 difference: 13+300+1.

C10

A: 2002

B: 1786

Id: C10

Job: compare

Reason: No environmental impact claim.

Source: Two invented recycling-game trays show 2002 and 1786 point cards; no waste-weight observation.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Recycling game

Worked staff: 216 difference: 14+200+2.

C11

A: 287

B: 630

Id: C11

Job: missing_addend

Reason: Box is the missing part, not 630.

Source: A fictional print target is 630 cards, 287 available: 287+□=630.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Print target

Worked staff: 343 needed; 287+343=630.

C12

A: 576

B: 900

Id: C12

Job: missing_addend

Reason: Nothing about real animals or habitat.

Source: An invented creature card target is 900, 576 already counted.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Creature game

Worked staff: 324 needed; 576+324=900.

C13

A: 840

B: 518

Id: C13

Job: missing_used

Reason: Unknown is used amount.

Source: A fictional archive starts 840 cards, ends 518: 840−□=518.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Archive retirement

Worked staff: 322 removed; 840−322=518.

C14

A: 237

B: 486

Id: C14

Job: missing_start

Reason: Not actual ticket sales.

Source: A fictional theatre uses 237 paper tickets and has 486 left:□−237=486.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Paper theatre

Worked staff: 723 start; 723−237=486.

C15

A: 176

B: 430

Id: C15

Job: equality

Reason: Compute known side before missing part.

Source: An invented equation is 176+□=400+30.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Two-box puzzle

Worked staff: 254; 176+254=430.

C16

A: 328

B: 650

Id: C16

Job: equality

Reason: Do not copy 650 into the box.

Source: An imaginary equation is 900−250=□+328.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Shelf puzzle

Worked staff: 322; 650=322+328.

C17

A: 197

B: 186

Id: C17

Job: join

Reason: No real fee, cents or financial advice.

Source: Pretend AUD costs $197 and $186 are compared with $380 budget.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Poster budget

Worked staff: 383 cost, $3 over; about $200+$190≈$390 is rough.

C18

A: 278

B: 195

Id: C18

Job: join

Reason: An estimate can check scale, not exact gap.

Source: A made-up puzzle needs 500 clue slips; 278+195 are available.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Clue supply

Worked staff: 473 available; 27 more needed.

C19

A: 685

B: 147

Id: C19

Job: join

Reason: Plant words are fiction, no growing instructions.

Source: An invented paper-garden game starts 685 markers, receives 147, then uses 238.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Paper garden game

Worked staff: 832 before use; 594 left; 594+238=832.

C20

A: 1207

B: 286

Id: C20

Job: remove

Reason: Order and units are stated, not guessed.

Source: A fictional robot card tray starts 1207, uses 286, then receives 149.

Status: Original fictional ordinary practice; teach source/help before any own application.

Title: Robot-card relay

Worked staff: 921 after use; 1070 after arrival; 1070−149=921.

Home

H01

Day: 51

Id: H01

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Try small 12+5 if tens/ones are unavailable.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Draw/describe tens and ones; join 30+20 and 2+4; write 56 labels; check 56−24=32.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Make a tiny note someone could use.

Routes

A small beginning

Instruction: Try small 12+5 if tens/ones are unavailable.

Name: A small beginning

Make the useful note

Instruction: Make a tiny note someone could use. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: Pretend 32 labels join 24 more.

Title: A drawer note

H02

Day: 52

Id: H02

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Use 28+7 first if regrouping is new.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Rename 8+7=15 ones as 1 ten 5; 40+10+15=65; check 65−17=48.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Show a ten moving as a group.

Routes

A small beginning

Instruction: Use 28+7 first if regrouping is new.

Name: A small beginning

Make the useful note

Instruction: Show a ten moving as a group. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: A fictional kit has 48 cards and receives 17.

Title: A game-kit top-up

H03

Day: 53

Id: H03

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Use 19+6 before 99+36.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Work 100+36−1=135; mark extra one; contrast about 100+40=140 with exact 135.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Tell someone why you put one back.

Routes

A small beginning

Instruction: Use 19+6 before 99+36.

Name: A small beginning

Make the useful note

Instruction: Tell someone why you put one back. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: An invented card set joins 99 and 36.

Title: A friendly-number trick

H04

Day: 54

Id: H04

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Use 30−8 first if regrouping needs teaching.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Rename 102 as 9 tens 12 ones; subtract 3 tens 8 ones=64; check 64+38=102.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Keep a left-count note.

Routes

A small beginning

Instruction: Use 30−8 first if regrouping needs teaching.

Name: A small beginning

Make the useful note

Instruction: Keep a left-count note. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: A pretend tray has 102 labels and uses 38.

Title: A tray after use

H05

Day: 55

Id: H05

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Compare 7 and 4 first; neither collection is removed.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Count 68→70(+2)→80(+10)→81(+1)=13; check 68+13=81.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Say more without calling one player better.

Routes

A small beginning

Instruction: Compare 7 and 4 first; neither collection is removed.

Name: A small beginning

Make the useful note

Instruction: Say more without calling one player better. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: Fictional game counts 81 and 68.

Title: Two imaginary scores

H06

Day: 56

Id: H06

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Use 18+□=31 first if box role is new.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Count 57→60(+3)→95(+35)=38; substitute 57+38=95.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Make a refill request for the further labels needed.

Routes

A small beginning

Instruction: Use 18+□=31 first if box role is new.

Name: A small beginning

Make the useful note

Instruction: Make a refill request for the further labels needed. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: A made-up kit needs 95 labels, has 57: 57+□=95.

Title: What is missing?

H07

Day: 57

Id: H07

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Contrast□−4=9 and 13−□=9 first.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Join 26 used and 47 left to get 73 start; check 73−26=47; label start/used/left.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Help a new maker read the missing role.

Routes

A small beginning

Instruction: Contrast□−4=9 and 13−□=9 first.

Name: A small beginning

Make the useful note

Instruction: Help a new maker read the missing role. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: An invented label box starts with an unknown count of labels. It uses26 labels and has47 left: □−26=47. Find the start and check it.

Title: Start or used?

H08

Day: 58

Id: H08

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Use small 12+3=10+5 if=needs teaching.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Known side 32; unknown 14; check 18+14=32 and 25+7=32; keep both sides visible.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Write a two-side puzzle.

Routes

A small beginning

Instruction: Use small 12+3=10+5 if=needs teaching.

Name: A small beginning

Make the useful note

Instruction: Write a two-side puzzle. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: Fictional 18+□=25+7.

Title: A puzzle for a friend

H09

Day: 59

Id: H09

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Use card counts with target 100 if dollars are unfamiliar.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Rough 50+50≈100; exact 101 is $1 over; offer keep/check/change without actual purchase.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Catch a very close decision.

Routes

A small beginning

Instruction: Use card counts with target 100 if dollars are unfamiliar.

Name: A small beginning

Make the useful note

Instruction: Catch a very close decision. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: Invented AUD budget $100, costs $49 and $52.

Title: A pretend budget

H10

Day: 60

Id: H10

Notice: Ordinary optional home practice, not unseen assessment or proof a child actually handled stock. Suggested 5–12 minutes, unpiloted; stop after a useful part.

Numbered moves

Read the stated source and choose paper, description or usual communication. Adult supply only a separate 35+18−12=41 model if needed; own choices stay blank.
Try one own way before the grown-up model. Keep your values and unit labels.
Grown-up separate practice possibility: Name your values, add arrival, subtract use; check left+used=after arrival; keep before/after labels.
Receive one available explanation or check. Ask whether to keep, change, pause or finish; another example is optional.

Purpose: Create one useful game or collection note.

Routes

A small beginning

Instruction: Adult supply only a separate 35+18−12=41 model if needed; own choices stay blank.

Name: A small beginning

Make the useful note

Instruction: Create one useful game or collection note. Use complete provided source and label the answer unit.

Name: Make the useful note

Change one condition

Instruction: Choose a different whole count within 0–200 that keeps the result nonnegative. Restate all conditions and check the new result; the original worked answer cannot fill it.

Name: Change one condition

Source: Choose invented start 20–60, arrival 10–30, use 0–20.

Title: A note of your own

Projects

X01

Day: 51

Id: X01

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 378 slips.
Build the intended tangible note/puzzle/gallery or exact description. Design a source/count/strategy/check note, then choose a new pair between 100 and 500; explain what may join as like units.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Design a source/count/strategy/check note, then choose a new pair between 100 and 500; explain what may join as like units.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Design a source/count/strategy/check note, then choose a new pair between 100 and 500; explain what may join as like units.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: An imagined desk joins 246 and 132 repair slips.

Title: Repair-desk organiser

Worked staff: 378 slips.

X02

Day: 52

Id: X02

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 434; 400+30+4.
Build the intended tangible note/puzzle/gallery or exact description. Make a labelled regrouping display using bundles/descriptions; compare chunk addition with the same quantity partition.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Make a labelled regrouping display using bundles/descriptions; compare chunk addition with the same quantity partition.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Make a labelled regrouping display using bundles/descriptions; compare chunk addition with the same quantity partition.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: A fictional display joins 278 and 156 badges.

Title: Badge-bundle display

Worked staff: 434; 400+30+4.

X03

Day: 53

Id: X03

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 455 and 545.
Build the intended tangible note/puzzle/gallery or exact description. Create a pair of puzzles showing extra 2/extra 1 and their removal; include exact answers on separate adult key.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Create a pair of puzzles showing extra 2/extra 1 and their removal; include exact answers on separate adult key.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Create a pair of puzzles showing extra 2/extra 1 and their removal; include exact answers on separate adult key.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: Invented totals are 198+257 and 399+146.

Title: Friendly-number puzzle set

Worked staff: 455 and 545.

X04

Day: 54

Id: X04

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 636; 368+636=1004.
Build the intended tangible note/puzzle/gallery or exact description. Create a left-count note with a regrouping or count-up check; show the zero-tens bridge explicitly.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Create a left-count note with a regrouping or count-up check; show the zero-tens bridge explicitly.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Create a left-count note with a regrouping or count-up check; show the zero-tens bridge explicitly.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: A pretend archive starts 1004 cards, uses 368.

Title: Archive-left note

Worked staff: 636; 368+636=1004.

X05

Day: 55

Id: X05

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 216 difference.
Build the intended tangible note/puzzle/gallery or exact description. Create a comparison card for a maker: retained both whole counts, gap label, no preference from size alone.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Create a comparison card for a maker: retained both whole counts, gap label, no preference from size alone.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Create a comparison card for a maker: retained both whole counts, gap label, no preference from size alone.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: Imaginary game boards need 1503 and 1287 tiles.

Title: Game-board comparison

Worked staff: 216 difference.

X06

Day: 56

Id: X06

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 625 needed; 875+625=1500.
Build the intended tangible note/puzzle/gallery or exact description. Make a refill request with a part-whole diagram and original-equation check; choose a smaller needed quantity if entry requires.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Make a refill request with a part-whole diagram and original-equation check; choose a smaller needed quantity if entry requires.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Make a refill request with a part-whole diagram and original-equation check; choose a smaller needed quantity if entry requires.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: An invented set needs 1500 sheets, has 875.

Title: Print-refill request

Worked staff: 625 needed; 875+625=1500.

X07

Day: 57

Id: X07

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 322 used and 723 start.
Build the intended tangible note/puzzle/gallery or exact description. Write two clearly different stories whose unknown roles match; keep numbers and units complete, then check each.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Write two clearly different stories whose unknown roles match; keep numbers and units complete, then check each.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Write two clearly different stories whose unknown roles match; keep numbers and units complete, then check each.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: Fictional equations 840−□=518 and□−237=486.

Title: Missing-role story pair

Worked staff: 322 used and 723 start.

X08

Day: 58

Id: X08

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 254 and 322.
Build the intended tangible note/puzzle/gallery or exact description. Make a gallery of one or two puzzles with separate solution key; both sides must retain source conditions.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Make a gallery of one or two puzzles with separate solution key; both sides must retain source conditions.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Make a gallery of one or two puzzles with separate solution key; both sides must retain source conditions.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: Imaginary equations 176+□=400+30 and 900−250=□+328.

Title: Equal-value puzzle gallery

Worked staff: 254 and 322.

X09

Day: 59

Id: X09

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 1005 available, 5 surplus.
Build the intended tangible note/puzzle/gallery or exact description. Compare nearest-ten estimate 500+510≈1010 with exact 1005; create a precise decision without calling estimate proof.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Compare a nearest-ten estimate with your exact calculation; create a precise decision without calling the estimate proof.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Compare a nearest-ten estimate with your exact calculation; create a precise decision without calling the estimate proof.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: An invented maker needs 1000 cards; 498+507 are available.

Title: Close supply decision

Worked staff: 1005 available, 5 surplus.

X10

Day: 60

Id: X10

Notice: Ordinary larger optional project, 20–40 minutes or several sittings unpiloted; not proof practical making, independence or whole code attainment.

Numbered moves

Read the complete fictional source; name wanted quantity and units. Select a representation after checking the day entry.
Make a source/problem/strategy note. Work the stated problem on own paper or usual communication.
Compare with a separate adult possibility only after available own work: 594 left; 685+147=832; 832−238=594.
Build the intended tangible note/puzzle/gallery or exact description. Make a complete handover note: source, given unit, question, strategy, result, check, one wanted future change. Another person can read; real use is not required.
Try a different stated condition if wanted. Label the first and changed version separately; keep/check/change/pause/finish are choices.

Purpose: Make a complete handover note: source, given unit, question, strategy, result, check, one wanted future change. Another person can read; real use is not required.

Routes

One useful component

Instruction: State quantities and try one operation with smaller whole counts. Keep actual mathematical help visible.

Name: One useful component

A note another maker can read

Instruction: Make a complete handover note: source, given unit, question, strategy, result, check, one wanted future change. Another person can read; real use is not required.

Name: A note another maker can read

A second version

Instruction: Select one count to change by 10–50 while keeping nonnegative values. State all new conditions, compute and check; an uncomputed change is a plan.

Name: A second version

Source: Pretend 685 markers, 147 arrive, 238 used.

Title: Maker handover

Worked staff: 594 left; 685+147=832; 832−238=594.

Scripts

A total worth checking

Day: 51

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: A total worth checking

Written script: Let’s make something useful. Can we make a stock note that someone else can trust? Today: Join like whole counts using place-value partitioning. Here is our made-up source. Fictional badge studio: 612 blank badges arrive in one parcel and 243 in another. Every badge is counted once. How many badges are available? What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. An invented drawing archive has 421 cards plus 136 new cards. Invite the partition before the total: 400 + 100, 20 + 30, 1 + 6, then 557 cards. Ask why units can be joined. Your turn can be one useful part: For 304 + 152, give a total and one way to check its parts. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

Ten ones can travel together

Day: 52

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: Ten ones can travel together

Written script: Let’s make something useful. Make a plan for a collection that crosses a ten or a hundred. Today: Regroup an addition without changing its value. Here is our made-up source. An invented costume cupboard has 364 tags, then receives 278 tags of the same kind. Find the new count. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. A fictional picture station joins 527 cards and 186 cards: 527 + 100 = 627, +80 = 707, +6 = 713. Ask the learner to show where a hundred boundary was crossed. Your turn can be one useful part: Try 258 + 167. Show the regroup or describe it exactly. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

Borrow a friendly number, then put it back

Day: 53

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: Borrow a friendly number, then put it back

Written script: Let’s make something useful. Would moving to a nearby round number make this job easier? Today: Use exact compensation and distinguish it from estimation. Here is our made-up source. An invented sticker design has 398 blue stickers and 267 plain stickers. Find the exact total. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. For fictional prompt cards, 497 + 186 = 500 + 186 − 3 = 683. Contrast the wrong 686: it counts the three extra cards. Invite a different check: 497 + 180 + 6. Your turn can be one useful part: Work 299 + 146 exactly using a friendly number, and name the adjustment. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

Take away without losing the place values

Day: 54

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: Take away without losing the place values

Written script: Let’s make something useful. Can a repair drawer show what is left clearly? Today: Subtract through regrouping or a connected count-up check. Here is our made-up source. A fictional repair drawer starts with 806 labels. It uses 247 labels once. Find labels left. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. A made-up card store has 704 cards, uses 168. Guide 6 hundreds 9 tens 14 ones minus 1 hundred 6 tens 8 ones = 536. Or subtract 100, 60, 8 in chunks. Your turn can be one useful part: For 603 − 157, show what remains and a connected check. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

How much more?

Day: 55

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: How much more?

Written script: Let’s make something useful. Help two made-up teams compare their counts without calling one better. Today: Find a difference by counting up; distinguish comparison from a removal event. Here is our made-up source. Two fictional poster designs require 1203 labels and 987 labels. What is the difference in their requirements? No labels have been removed. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. Two invented folders contain 1501 and 1297 cards. Guide +3 to 1300,+200 to 1500,+1 to 1501 =204. Ask whether taking 1297 away from 1501 gives the same difference. Your turn can be one useful part: A fictional score sheet lists 1002 and 875 points. Find the difference and explain its meaning. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

Find the missing part

Day: 56

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: Find the missing part

Written script: Let’s make something useful. What needs to join a collection to reach the target? Today: Use addition/subtraction relationships for an unknown addend. Here is our made-up source. An invented card kit needs 725 cards in total. It already has 468. How many more are needed? 468 + □ = 725. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. A fictional badge target is 630 with 275 available. Guide 275+□=630; 275→300(+25)→630(+330)=355. Check 275+355. Your turn can be one useful part: Solve 386 + □ = 540, and show the check in the original equation. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

Which part is missing?

Day: 57

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: Which part is missing?

Written script: Let’s make something useful. A missing count can sit at the start or in the amount used. Can your note make that clear? Today: Distinguish unknown starting quantity from unknown subtraction amount. Here is our made-up source. A fictional store starts with 930 tags and finishes with 586. How many were used?930−□=586. Separately, a fictional box uses 175 cards and has 428 left. How many did it start with?□−175=428. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. A fictional game starts with 702 tokens and ends with 459: used 243. A different game uses 126 and ends with 387: start 513. Guide both original-equation checks, one case at a time. Your turn can be one useful part: Solve □ − 148 =367 and explain what the box counts. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

Both sides mean the same amount

Day: 58

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: Both sides mean the same amount

Written script: Let’s make something useful. Make a puzzle another person can check without guessing what the equals sign means. Today: Find an unknown when each side contains a calculation. Here is our made-up source. An invented display equation is 245+□=390+75. Find the box value and check both sides. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. For a fictional drawer 620−185=□+240: left 435, unknown 195, check 195+240=435. Invite the learner to compute the known side before undoing the other part. Your turn can be one useful part: Solve 128+□=200+47 and check the two sides. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

An estimate helps. An exact check decides.

Day: 59

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: An estimate helps. An exact check decides.

Written script: Let’s make something useful. Pick a made-up supply or budget job. What decision does the arithmetic need to answer? Today: Formulate additive practical problems and interpret exact comparisons. Here is our made-up source. A fictional print stand needs 485 handouts. It has 268 in one pile and 124 in another. Is there enough? Separately a pretend art plan has costs $265 and $148, within an invented AUD450 budget. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. An imaginary card plan needs 600 cards; 328+195=523 available, gap 77. A separate invented budget $380 costs $197+$186=$383, $3 over. A rough $200+$190≈$390 suggests close but exact arithmetic settles it. Your turn can be one useful part: Budget $300, fictional costs $148 and $153. Does it fit? Give an exact reason. Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

Make a useful note of your own

Day: 60

Status: Original written read-together script only; no generated/voice-reviewed audio or pronunciation/translation claim. Adult mathematical example is practice and cannot stand for own work.

Title: Make a useful note of your own

Written script: Let’s make something useful. Choose a small planning problem you care about: a game, a collection, a pretend budget or a number puzzle. Make one note useful to someone else. Today: Formulate a complete additive situation, solve and check it for a reader. Here is our made-up source. Adult example: a fictional making station has 675 labels, receives 148 more and uses 236. How many remain? No real making or stock count is claimed. What do the numbers count? You can show, draw, type, sign or tell an agreeing helper. We will try one way together, then you choose a task. Guide a different fictional game: 508 cards, 176 arrive, 245 used; 684−245=439 left. Ask the learner to select addition then subtraction from roles, not follow a hiddenpreset. Receive one useful step if the whole chain is too much. Your turn can be one useful part: Choose one result from your own problem. What does it count and what check supports it? Keep, change, pause or finish. You do not have to read aloud, handle objects or hurry.

Worksheets

W01

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 51

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W01

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: Fictional badge studio: 612 blank badges arrive in one parcel and 243 in another. Every badge is counted once. How many badges are available?

Title: A total worth checking · my work

W02

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 52

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W02

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: An invented costume cupboard has 364 tags, then receives 278 tags of the same kind. Find the new count.

Title: Ten ones can travel together · my work

W03

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 53

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W03

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: An invented sticker design has 398 blue stickers and 267 plain stickers. Find the exact total.

Title: Borrow a friendly number, then put it back · my work

W04

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 54

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W04

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: A fictional repair drawer starts with 806 labels. It uses 247 labels once. Find labels left.

Title: Take away without losing the place values · my work

W05

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 55

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W05

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: Two fictional poster designs require 1203 labels and 987 labels. What is the difference in their requirements? No labels have been removed.

Title: How much more? · my work

W06

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 56

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W06

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: An invented card kit needs 725 cards in total. It already has 468. How many more are needed? 468 + □ = 725.

Title: Find the missing part · my work

W07

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 57

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W07

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: A fictional store starts with 930 tags and finishes with 586. How many were used?930−□=586. Separately, a fictional box uses 175 cards and has 428 left. How many did it start with?□−175=428.

Title: Which part is missing? · my work

W08

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 58

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W08

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: An invented display equation is 245+□=390+75. Find the box value and check both sides.

Title: Both sides mean the same amount · my work

W09

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 59

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W09

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: A fictional print stand needs 485 handouts. It has 268 in one pile and 124 in another. Is there enough? Separately a pretend art plan has costs $265 and $148, within an invented AUD450 budget.

Title: An estimate helps. An exact check decides. · my work

W10

Blank areas

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My numbers, units and question

Paper: Empty broad rectangle, not lined unless requested.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Paper: Empty broad rectangle with no dots, values, arrows or preset diagram.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Paper: Empty broad rectangle.

Day None

Initial content: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or next wanted move

Paper: Empty broad rectangle.

Day: 60

Eligibility: Ordinary taught practice only. Held first sources and their four genuine blank prompts are separate.

Id: W10

Instruction: Choose one ordinary route or your own complete stated problem. Use any of these four empty areas. A label does not require a filled box. Adult models/answers stay on staff work.

Source: Adult example: a fictional making station has 675 labels, receives 148 more and uses 236. How many remain? No real making or stock count is claimed.

Title: Make a useful note of your own · my work

Eight formative sources · own prompts and separate staff teaching

These public original sources are informal formative opportunities. The four own responses start as literal empty strings. Native same-page ordinary disclosure must preserve current words; staff criteria, worked answers and next lessons must remain on separate staff pages. First/later are opportunity names, not compulsory order, equal-difficulty forms or causal learning measures. Receive one genuine component when useful. Count and handwriting/speech/device performance are distinct; missing access or time is not wrong mathematics. No automatic score, official band conversion or daily full form.

Cases

A-first

Access and help: Read or sign the exact source and prompts neutrally, enlarge them, or scribe the learner’s chosen words. A figure, operation, regrouping, equation role or check supplied by an adult is mathematical help and is recorded as such. Show, draw, type, sign or use usual communication. One component can be enough; pause/pass/finish are choices. Four own spaces are genuinely empty. Models, criteria and next lessons stay on separate staff pages.

Components

A-first-Q1

Criterion: 364 and 278 are like badge counts joined by addition; a suitable model is 364+278.

Id: A-first-Q1

Next teaching

Access: Read or sign the exact source and prompts neutrally, enlarge them, or scribe the learner’s chosen words. A figure, operation, regrouping, equation role or check supplied by an adult is mathematical help and is recorded as such. Show, draw, type, sign or use usual communication. One component can be enough; pause/pass/finish are choices. Four own spaces are genuinely empty. Models, criteria and next lessons stay on separate staff pages.

Complete different guided source: An imaginary music game joins 321 prompt cards and 142 more.

Complete new source: An invented tabletop train game has 213 station cards and 124 new station cards.

Complete own invitation: A fictional creature game joins 231 cards and 156.

Entry and teach: Check like units with 12 cards+5 cards.

Guided instruction: 321+142=463; 300+100, 20+40, 1+2. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT01

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Observe and follow up: Receive one available own relationship before staff possibility. If it matches criterion, offer another small new context later; this is not automatic mastery. If not, return to the entry relationship and fade one hint. Record the actual mathematical help. If access/time is not available, change access or sitting rather than marking wrong.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Check like units with 12 cards+5 cards.
Model on separate adult paper. 213+124=337; 200+100+10+20+3+4. Label starting/new/combined cards.
Guide a different complete source. An imaginary music game joins 321 prompt cards and 142 more. 321+142=463; 300+100, 20+40, 1+2.
Receive one own attempt. A fictional creature game joins 231 cards and 156. Staff reference only: 387; 200+100+30+50+1+6.
Compare available work with: A joining model keeps two like-count parts and the whole distinct. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: A joining model keeps two like-count parts and the whole distinct.

Staff own possibility: 387; 200+100+30+50+1+6.

Teacher model: 213+124=337; 200+100+10+20+3+4. Label starting/new/combined cards.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Train-card total

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: What does each count represent? Write a number sentence for the new total.

Worked staff: 364 starting badges plus 278 arriving badges; 364+278. No multiplication of the two counts is intended.

A-first-Q2

Criterion: A valid strategy keeps all parts and gives 642 badges.

Id: A-first-Q2

Next teaching

Complete different guided source: A pretend theatre joins 376 tickets and 158.

Complete new source: A fictional tabletop map kit joins 258 and 167 tiles.

Complete own invitation: An imagined map box joins 247 and 185 tiles.

Entry and teach: Teach 8+7=15 and 10 ones=1 ten if needed.

Guided instruction: 534; 400+120+14. Ask where a hundred boundary occurs. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT02

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach 8+7=15 and 10 ones=1 ten if needed.
Model on separate adult paper. 258+167=300+110+15=425; rename to 4 hundreds 2 tens 5 ones.
Guide a different complete source. A pretend theatre joins 376 tickets and 158. 534; 400+120+14. Ask where a hundred boundary occurs.
Receive one own attempt. An imagined map box joins 247 and 185 tiles. Staff reference only: 432; 300+120+12.
Compare available work with: An equivalent regroup and exact total retain every unit. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: An equivalent regroup and exact total retain every unit.

Staff own possibility: 432; 300+120+12.

Teacher model: 258+167=300+110+15=425; rename to 4 hundreds 2 tens 5 ones.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Map-piece bridge

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Find the total using a way you can explain or show.

Worked staff: 364+200=564;+70=634;+8=642. Or 500+130+12=642 with renaming.

A-first-Q3

Criterion: An explained exchange or boundary crossing preserves equivalent quantities in this calculation; do not demand a column method.

Id: A-first-Q3

Next teaching

Complete different guided source: A pretend robot game joins 57 and 18 cards.

Complete new source: A fictional costume game joins 48 and 26 clue cards.

Complete own invitation: An invented puppet game joins 68 and 17 cards.

Entry and teach: Show ten ones can be one ten without changing count.

Guided instruction: 75; 60+15. Describe rather than demand handling. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT03

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Show ten ones can be one ten without changing count.
Model on separate adult paper. 48+26=60+14=74; 14 ones=1 ten 4 ones. Point to every retained part.
Guide a different complete source. A pretend robot game joins 57 and 18 cards. 75; 60+15. Describe rather than demand handling.
Receive one own attempt. An invented puppet game joins 68 and 17 cards. Staff reference only: 85; 70+15.
Compare available work with: Renaming ten ones as a ten preserves the amount. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Renaming ten ones as a ten preserves the amount.

Staff own possibility: 85; 70+15.

Teacher model: 48+26=60+14=74; 14 ones=1 ten 4 ones. Point to every retained part.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: A ten travels

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Show why any regrouping in your way keeps the amount unchanged. If your way uses no written regrouping, describe crossing a ten or hundred.

Worked staff: 12 ones =1 ten 2 ones; the resulting 14 tens =1 hundred 4 tens. Chunks cross 634→642 while retaining all 8.

A-first-Q4

Criterion: A valid inverse or independently recombined calculation supports 642, interpreted as badges in the model.

Id: A-first-Q4

Next teaching

Complete different guided source: An invented stamp-game joins 427 and 132 entry cards.

Complete new source: A fictional puzzle catalogue joins 315 and 146 entries.

Complete own invitation: An imaginary comic archive joins 236 and 152 cards.

Entry and teach: Check why a total minus one part recovers the other on 20+7=27.

Guided instruction: 559; 559−132=427. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT04

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Check why a total minus one part recovers the other on 20+7=27.
Model on separate adult paper. 315+146=461; 461−146=315 verifies the original relationship.
Guide a different complete source. An invented stamp-game joins 427 and 132 entry cards. 559; 559−132=427.
Receive one own attempt. An imaginary comic archive joins 236 and 152 cards. Staff reference only: 388; 388−152=236.
Compare available work with: A connected inverse and unit meaning support the total. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: A connected inverse and unit meaning support the total.

Staff own possibility: 388; 388−152=236.

Teacher model: 315+146=461; 461−146=315 verifies the original relationship.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Check a joined collection

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Give a connected check and state what your total counts.

Worked staff: 642−278=364. Alternatively 364+278=500+130+12=642. A claimed real delivery is unsupported.

Eligibility: After joining like counts and regrouping have actually been taught with ordinary sources, e.g. Days 51–52. If not, teach first or treat as supported exploration, not an unseen first check.

First later limit: First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen.

Id: A-first

Neutral whole source: A fictional badge cupboard has 364 badges. Another parcel supplies 278 badges of the same kind. Count each badge once. The task is to find the new total; no actual stock or delivery is claimed.

Own page: Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled.

Source disclosure: Full neutral whole source is initially closed native same-page details on own response page; reading it never navigates away or loses typed work. No worked/criterion/next source inside its child disclosure. Staff index is separate.

Title: A pretend badge cupboard

A-later

Components

A-later-Q1

Criterion: 704 is starting cards, 168 used cards; 704−168 models the left count.

Id: A-later-Q1

Next teaching

Complete different guided source: A fictional reading game starts 375 cards, uses 142.

Complete new source: A pretend board game starts 286 tokens and uses 123.

Complete own invitation: A pretend sound game starts 487 cards, uses 156.

Entry and teach: Label start/use/left with 16−5=11 before bigger counts.

Guided instruction: 233; 375−100−40−2. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT05

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Label start/use/left with 16−5=11 before bigger counts.
Model on separate adult paper. 286−123=163; subtract 100, 20, 3. Start and used are like units with different roles.
Guide a different complete source. A fictional reading game starts 375 cards, uses 142. 233; 375−100−40−2.
Receive one own attempt. A pretend sound game starts 487 cards, uses 156. Staff reference only: 331; 487−100−50−6.
Compare available work with: A subtraction model matches start/use/remaining roles. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: A subtraction model matches start/use/remaining roles.

Staff own possibility: 331; 487−100−50−6.

Teacher model: 286−123=163; subtract 100, 20, 3. Start and used are like units with different roles.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: What remains in a game?

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: What does each count mean, and what number sentence finds cards left?

Worked staff: 704 starting, 168 used, 704−168.

A-later-Q2

Criterion: A valid exact strategy gives 536 cards left.

Id: A-later-Q2

Next teaching

Complete different guided source: A fictional robot kit starts 602 cards, uses 247.

Complete new source: An imagined print game starts 503 slips and uses 178.

Complete own invitation: A pretend mask drawer starts 801 labels, uses 356.

Entry and teach: Teach 102−38=64 by trading a hundred then a ten.

Guided instruction: 355; 5 hundreds 9 tens 12 ones−2 hundreds 4 tens 7 ones. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT06

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach 102−38=64 by trading a hundred then a ten.
Model on separate adult paper. 503=4 hundreds 9 tens 13 ones; minus 1 hundred 7 tens 8 ones=325.
Guide a different complete source. A fictional robot kit starts 602 cards, uses 247. 355; 5 hundreds 9 tens 12 ones−2 hundreds 4 tens 7 ones.
Receive one own attempt. A pretend mask drawer starts 801 labels, uses 356. Staff reference only: 445; 7 hundreds 9 tens 11 ones minus 3 hundreds 5 tens 6 ones.
Compare available work with: Regrouping across zero retains all starting units and produces a valid difference. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Regrouping across zero retains all starting units and produces a valid difference.

Staff own possibility: 445; 7 hundreds 9 tens 11 ones minus 3 hundreds 5 tens 6 ones.

Teacher model: 503=4 hundreds 9 tens 13 ones; minus 1 hundred 7 tens 8 ones=325.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: A zero bridge

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Find cards left using a strategy you can show.

Worked staff: 704−100=604;−60=544;−8=536. Or 6 hundreds 9 tens 14 ones minus 1 hundred 6 tens 8 ones.

A-later-Q3

Criterion: Rejects the direction-changing digit procedure and identifies the need to preserve the original quantities, with a valid repair.

Id: A-later-Q3

Next teaching

Complete different guided source: An imaginary game uses 37 of 82 tokens.

Complete new source: A fictional theatre has 63 tickets and uses 28. A wrong note gives 45 from 6−2 and 8−3.

Complete own invitation: A pretend craft store uses 46 of 91 labels.

Entry and teach: Use a place-value representation, not digit-size swapping.

Guided instruction: 45 left; 7 tens 12 ones−3 tens 7 ones. Compare original 82−37 with wrong digit-swapping 55. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT07

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Use a place-value representation, not digit-size swapping.
Model on separate adult paper. 63=5 tens 13 ones; subtract 2 tens 8 ones=35. Reversing only the ones changes the operation.
Guide a different complete source. An imaginary game uses 37 of 82 tokens. 45 left; 7 tens 12 ones−3 tens 7 ones. Compare original 82−37 with wrong digit-swapping 55.
Receive one own attempt. A pretend craft store uses 46 of 91 labels. Staff reference only: 45 left; 4 tens 5 ones after regroup.
Compare available work with: Repair rejects direction-changing digit subtraction and supplies a quantity-preserving method. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Repair rejects direction-changing digit subtraction and supplies a quantity-preserving method.

Staff own possibility: 45 left; 4 tens 5 ones after regroup.

Teacher model: 63=5 tens 13 ones; subtract 2 tens 8 ones=35. Reversing only the ones changes the operation.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Digits are quantities

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: A made-up note says “subtract each smaller digit from each bigger digit, so 704−168=664”. Keep or repair this method with a reason.

Worked staff: The note wrongly treats ones as 8−4 and tens as 6−0. Regroup 704 as 600+90+14: 600−100=500, 90−60=30, 14−8=6, total 536.

A-later-Q4

Criterion: A connected check supports 536 left cards; real use is not inferred.

Id: A-later-Q4

Next teaching

Complete different guided source: A pretend game has 724 cards, uses 185.

Complete new source: A fictional archive has 615 cards, uses 238.

Complete own invitation: An invented puzzle kit has 832 cards, uses 267.

Entry and teach: Teach left+used=start on 17−8=9.

Guided instruction: 539; 539+185=724. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT08

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach left+used=start on 17−8=9.
Model on separate adult paper. 377 left; 377+238=615. Name card units and preserve the original source.
Guide a different complete source. A pretend game has 724 cards, uses 185. 539; 539+185=724.
Receive one own attempt. An invented puzzle kit has 832 cards, uses 267. Staff reference only: 565; 565+267=832.
Compare available work with: An inverse supports remaining count, not a claim of real handling. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: An inverse supports remaining count, not a claim of real handling.

Staff own possibility: 565; 565+267=832.

Teacher model: 377 left; 377+238=615. Name card units and preserve the original source.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Check a remaining amount

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Check your result and explain what it counts.

Worked staff: 536+168=704; the model count remaining is 536 cards.

Eligibility: After subtraction with regrouping and inverse checks have actually been taught, e.g. Day 54. Teaching this source makes its later use exposed; receive supported work honestly.

First later limit: First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen.

Id: A-later

Neutral whole source: An imagined paper store starts with 704 cards and uses 168 cards once. Find the cards left. This is a different opportunity after teaching, not an equal-difficulty test form or a progress measure.

Own page: Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled.

Title: A fictional paper store

B-first

Components

B-first-Q1

Criterion: Box is missing labels needed, 468 the available part and 725 the target whole.

Id: B-first-Q1

Next teaching

Complete different guided source: An imaginary gallery needs 92 tiles, has 58.

Complete new source: A fictional poster plan needs 74 tiles, has 39.

Complete own invitation: A pretend maze needs 85 tiles, has 47.

Entry and teach: Use an empty known part/unknown part/whole bar; 35 joins 39 to 74.

Guided instruction: 34 needed; 58+34=92. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT09

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Use an empty known part/unknown part/whole bar; 35 joins 39 to 74.
Model on separate adult paper. 39+□=74; box counts needed tiles, not whole 74. Count up 35.
Guide a different complete source. An imaginary gallery needs 92 tiles, has 58. 34 needed; 58+34=92.
Receive one own attempt. A pretend maze needs 85 tiles, has 47. Staff reference only: 38 needed; 47+38=85.
Compare available work with: Labels distinguish known part, target whole and missing part. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Labels distinguish known part, target whole and missing part.

Staff own possibility: 38 needed; 47+38=85.

Teacher model: 39+□=74; box counts needed tiles, not whole 74. Count up 35.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: A part and a whole

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: What does the box count? Describe the known part and the whole.

Worked staff: Missing refill, not the target 725 or existing 468.

B-first-Q2

Criterion: A valid difference/count-up method gives 257.

Id: B-first-Q2

Next teaching

Complete different guided source: An imaginary game target is 920, 456 available.

Complete new source: A fictional print target is 810 cards, 347 available.

Complete own invitation: A fictional clue target is 730, 286 available.

Entry and teach: Teach 47→50(+3)→80(+30)→81(+1)first.

Guided instruction: 464: 44 to 500+420. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT10

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach 47→50(+3)→80(+30)→81(+1)first.
Model on separate adult paper. 347→350(+3)→800(+450)→810(+10); 463 needed.
Guide a different complete source. An imaginary game target is 920, 456 available. 464: 44 to 500+420.
Receive one own attempt. A fictional clue target is 730, 286 available. Staff reference only: 444: 14 to 300+430.
Compare available work with: Count-up increments total the exact unknown addend. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Count-up increments total the exact unknown addend.

Staff own possibility: 444: 14 to 300+430.

Teacher model: 347→350(+3)→800(+450)→810(+10); 463 needed.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Stepping to a target

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Find a value for the box with a useful strategy.

Worked staff: 468→500(+32)→725(+225); 32+225=257.

B-first-Q3

Criterion: Substitution retains 468+□=725 and yields 468+257=725.

Id: B-first-Q3

Next teaching

Complete different guided source: An invented reading plan has 378+□=650 cards.

Complete new source: A pretend puppet plan has 246+□=580 labels.

Complete own invitation: A fictional toy-map target is 720 with 459 available.

Entry and teach: Teach substitution with 9+□=14→5.

Guided instruction: 272; 378+272=650. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT11

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach substitution with 9+□=14→5.
Model on separate adult paper. □=334; 246+334=580. Keep original known part and whole.
Guide a different complete source. An invented reading plan has 378+□=650 cards. 272; 378+272=650.
Receive one own attempt. A fictional toy-map target is 720 with 459 available. Staff reference only: 261; 459+261=720.
Compare available work with: The substitute makes the original equation true. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: The substitute makes the original equation true.

Staff own possibility: 261; 459+261=720.

Teacher model: □=334; 246+334=580. Keep original known part and whole.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Put the number back

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Put your value into the original equation and check it.

Worked staff: 468+257=725; both sides 725. A different equation alone is not this requested substitution.

B-first-Q4

Criterion: Explains equality of the two sides and the unknown’s part role; rejects 725 as this missing part.

Id: B-first-Q4

Next teaching

Complete different guided source: An imaginary story puzzle says 38+□=72.

Complete new source: A fictional code puzzle says 27+□=64.

Complete own invitation: A pretend rocket puzzle says 46+□=83.

Entry and teach: Show two equal amounts for 12+3=10+5.

Guided instruction: 34; 38+34=72. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT12

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Show two equal amounts for 12+3=10+5.
Model on separate adult paper. □=37 because 27+37=64; using 64 gives 91, not 64.
Guide a different complete source. An imaginary story puzzle says 38+□=72. 34; 38+34=72.
Receive one own attempt. A pretend rocket puzzle says 46+□=83. Staff reference only: 37; 46+37=83.
Compare available work with: The missing part is distinguished from the whole-side value and equality is interpreted relationally. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: The missing part is distinguished from the whole-side value and equality is interpreted relationally.

Staff own possibility: 37; 46+37=83.

Teacher model: □=37 because 27+37=64; using 64 gives 91, not 64.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Equal does not mean next

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: A fictional note says “the box is 725 because that is the answer after the equals sign”. Keep or repair it with a reason.

Worked staff: 468+725=1193, not 725. The missing part is 257; = relates two equal amounts, not a direction to copy the total.

Eligibility: After unknown addend, part/whole and substitution have been taught, e.g. Day 56. No assumed mastery from resource-week labels.

First later limit: First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen.

Id: B-first

Neutral whole source: A fictional kit needs 725 labels in total. It has 468 labels available. Find the further labels needed: 468+□=725. The box stands for a whole-number value. No real refill is supplied.

Own page: Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled.

Title: The missing refill

B-later

Components

B-later-Q1

Criterion: Box is the starting count 603, formed by joining 175 used and 428 left.

Id: B-later-Q1

Next teaching

Complete different guided source: A pretend theatre uses 248 tickets, has 356 left.

Complete new source: A fictional puzzle box uses 126 cards and has 387 left.

Complete own invitation: An invented mask box uses 175 labels, has 468 left.

Entry and teach: Teach□−4=9: used 4 joins left 9 to get 13.

Guided instruction: 604 start; 604−248=356. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT13

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach□−4=9: used 4 joins left 9 to get 13.
Model on separate adult paper. Starting 513=126+387; 513−126=387.
Guide a different complete source. A pretend theatre uses 248 tickets, has 356 left. 604 start; 604−248=356.
Receive one own attempt. An invented mask box uses 175 labels, has 468 left. Staff reference only: 643 start; 643−175=468.
Compare available work with: Unknown start is rebuilt from used and left, with roles explained. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Unknown start is rebuilt from used and left, with roles explained.

Staff own possibility: 643 start; 643−175=468.

Teacher model: Starting 513=126+387; 513−126=387.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Rebuild the beginning

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: For Record 1, say what the box counts and find it.

Worked staff: 428+175=603 starting cards. Selecting subtraction solely from the word remain would be wrong here.

B-later-Q2

Criterion: 603−175=428 supports the unknown start.

Id: B-later-Q2

Next teaching

Complete different guided source: An imaginary map record is□−247=386.

Complete new source: A fictional game record is□−138=275.

Complete own invitation: A pretend music record is□−156=428.

Entry and teach: Check a smaller□−7=12→19 in original form.

Guided instruction: 633; 633−247=386. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT14

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Check a smaller□−7=12→19 in original form.
Model on separate adult paper. Starting 413=138+275; 413−138=275.
Guide a different complete source. An imaginary map record is□−247=386. 633; 633−247=386.
Receive one own attempt. A pretend music record is□−156=428. Staff reference only: 584; 584−156=428.
Compare available work with: A substitution check retains unknown start and original subtraction. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: A substitution check retains unknown start and original subtraction.

Staff own possibility: 584; 584−156=428.

Teacher model: Starting 413=138+275; 413−138=275.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Starting equation check

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Substitute your Record 1 value into its original equation and check.

Worked staff: 603−175=428. The value 603 is not the used amount.

B-later-Q3

Criterion: Known side 435; missing part 195 so 195+240=435.

Id: B-later-Q3

Next teaching

Complete different guided source: A fictional card puzzle is 186+□=420+35.

Complete new source: An invented mural-count puzzle is 215+□=340+68.

Complete own invitation: A pretend tile puzzle is 237+□=500+46.

Entry and teach: Use 18+□=25+7 and name known side 32.

Guided instruction: Known 455, box 269. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT15

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Use 18+□=25+7 and name known side 32.
Model on separate adult paper. Known side 408; box 193; 215+193=408.
Guide a different complete source. A fictional card puzzle is 186+□=420+35. Known 455, box 269.
Receive one own attempt. A pretend tile puzzle is 237+□=500+46. Staff reference only: Known 546, box 309.
Compare available work with: Known side value and box value are distinguished through inverse reasoning. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Known side value and box value are distinguished through inverse reasoning.

Staff own possibility: Known 546, box 309.

Teacher model: Known side 408; box 193; 215+193=408.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Two complete sides

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: For Record 2, find the box value. Show what the complete known side is first.

Worked staff: 620−185=435;□=435−240=195. Do not put 435 directly in the box.

B-later-Q4

Criterion: Original left and right sides both give 435 after inserting 195.

Id: B-later-Q4

Next teaching

Complete different guided source: An imaginary display equation is 850−376=□+218.

Complete new source: A fictional archive equation is 700−268=□+195.

Complete own invitation: A pretend theatre-equation is 920−485=□+167.

Entry and teach: Teach 35−8=□+12: known 27, box 15.

Guided instruction: Left 474, box 256; both sides 474. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT16

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach 35−8=□+12: known 27, box 15.
Model on separate adult paper. Left 432; box 237; 237+195=432.
Guide a different complete source. An imaginary display equation is 850−376=□+218. Left 474, box 256; both sides 474.
Receive one own attempt. A pretend theatre-equation is 920−485=□+167. Staff reference only: Left 435, box 268; both sides 435.
Compare available work with: Both complete original sides are computed and agree after substitution. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Both complete original sides are computed and agree after substitution.

Staff own possibility: Left 435, box 268; both sides 435.

Teacher model: Left 432; box 237; 237+195=432.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Both sides after substitution

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Check both full sides of Record 2 after substitution.

Worked staff: 620−185=435 and 195+240=435. The box 195 differs from each whole side 435.

Eligibility: After unknown start and two-sided equality have both been taught, e.g. Days 57–58. One record or one prompt may be enough; do not require all four for a useful observation.

First later limit: First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen.

Id: B-later

Neutral whole source: Two separate fictional records use cards. Record 1:□−175=428, where 175 cards are used and 428 remain. Record 2: 620−185=□+240. Keep the records separate. There is no supplied history of a learner’s earlier work.

Own page: Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled.

Title: Two missing roles

C-first

Components

C-first-Q1

Criterion: A model totals 268+124 handouts and compares that with 485 needed; an appropriate gap equation is 485−(268+124).

Id: C-first-Q1

Next teaching

Complete different guided source: A pretend paper stage needs 420 slips; 178+196 available.

Complete new source: A fictional game needs 360 slips; 146 and 185 are available.

Complete own invitation: An invented map kit needs 500 tiles; 237+218 available.

Entry and teach: Check joining two piles before comparing with a separate target.

Guided instruction: 374 available, 46 needed. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT17

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Check joining two piles before comparing with a separate target.
Model on separate adult paper. 146+185=331 available; 360−331=29 needed. State both operations and units.
Guide a different complete source. A pretend paper stage needs 420 slips; 178+196 available. 374 available, 46 needed.
Receive one own attempt. An invented map kit needs 500 tiles; 237+218 available. Staff reference only: 455 available, 45 needed.
Compare available work with: A total-and-comparison model matches like units and target. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: A total-and-comparison model matches like units and target.

Staff own possibility: 455 available, 45 needed.

Teacher model: 146+185=331 available; 360−331=29 needed. State both operations and units.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Enough clue slips?

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: What question would settle whether the supply is enough? Write a model with units.

Worked staff: Available count 268+124, compared with need 485. Do not multiply the two piles.

C-first-Q2

Criterion: 392 available, 93 short, calculated validly.

Id: C-first-Q2

Next teaching

Complete different guided source: A fictional poster plan needs 700 labels; 348+175 available.

Complete new source: An imaginary badge plan needs 650 badges; 287 and 196 available.

Complete own invitation: A pretend game needs 800 cards; 456+187 available.

Entry and teach: Use count up to a target or exact subtraction, not subtract each pile from target separately then add gaps.

Guided instruction: 523 available, 177 needed. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT18

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Use count up to a target or exact subtraction, not subtract each pile from target separately then add gaps.
Model on separate adult paper. 483 available; 650−483=167 needed.
Guide a different complete source. A fictional poster plan needs 700 labels; 348+175 available. 523 available, 177 needed.
Receive one own attempt. A pretend game needs 800 cards; 456+187 available. Staff reference only: 643 available, 157 needed.
Compare available work with: Exact available count and one properly interpreted gap are valid. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Exact available count and one properly interpreted gap are valid.

Staff own possibility: 643 available, 157 needed.

Teacher model: 483 available; 650−483=167 needed.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Calculate the gap

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Find the exact available count and the amount missing or extra.

Worked staff: 268+124=392; 485−392=93.

C-first-Q3

Criterion: Supply is not enough for the stated need; 93 further handouts would be required.

Id: C-first-Q3

Next teaching

Complete different guided source: An invented art plan needs 450 labels; 236+198 available.

Complete new source: A fictional theatre plan needs 300 tickets; 148+167 available.

Complete own invitation: A pretend library game needs 600 cards; 287+328 available.

Entry and teach: Name availability versus need; surplus is not shortfall.

Guided instruction: 434 available, 16 short; need 16 more. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT19

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Name availability versus need; surplus is not shortfall.
Model on separate adult paper. 315 available, 15 extra; the stated need is met.
Guide a different complete source. An invented art plan needs 450 labels; 236+198 available. 434 available, 16 short; need 16 more.
Receive one own attempt. A pretend library game needs 600 cards; 287+328 available. Staff reference only: 615 available, 15 extra; need is met.
Compare available work with: Decision direction and gap unit agree with the original model. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Decision direction and gap unit agree with the original model.

Staff own possibility: 615 available, 15 extra; need is met.

Teacher model: 315 available, 15 extra; the stated need is met.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: A decision with units

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Make the decision in terms of the source.

Worked staff: The plan is short 93 handouts. This is a mathematical requirement, not proof another parcel will arrive.

C-first-Q4

Criterion: Distinguishes rough 390 from exact 392 and repairs the exact shortfall to 93.

Id: C-first-Q4

Next teaching

Complete different guided source: An invented print plan needs 500 sheets; 248+247 available.

Complete new source: A fictional game needs 400 cards; 197+186 available.

Complete own invitation: A pretend maker needs 600 tags; 298+307 available.

Entry and teach: Teach nearest-ten rounding and ≈ separately from exact=.

Guided instruction: About 250+250≈500; exact 495, 5 short. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT20

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach nearest-ten rounding and ≈ separately from exact=.
Model on separate adult paper. About 200+190≈390; exact 383, 17 short; rough 10 short is not exact 17.
Guide a different complete source. An invented print plan needs 500 sheets; 248+247 available. About 250+250≈500; exact 495, 5 short.
Receive one own attempt. A pretend maker needs 600 tags; 298+307 available. Staff reference only: About 300+310≈610; exact 605, 5 extra.
Compare available work with: Approximation purpose and exact decision remain separate. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Approximation purpose and exact decision remain separate.

Staff own possibility: About 300+310≈610; exact 605, 5 extra.

Teacher model: About 200+190≈390; exact 383, 17 short; rough 10 short is not exact 17.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: An estimate is a guide

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: A made-up note says “about 270+120 is 390, so we know the exact shortfall is 95”. Keep or repair it.

Worked staff: Estimate 390 is close but not the exact total.485−392=93; 485−390=95 belongs to the approximate model.

Eligibility: After joining counts, differences and interpreting a target comparison have been taught, e.g. Days 51–55 and 59. Formulation is taught before use as a check.

First later limit: First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen.

Id: C-first

Neutral whole source: An invented display needs 485 handouts. It has 268 handouts in one pile and 124 in another, counted once. Decide whether the supply meets the need. No real print stock or event is observed.

Own page: Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled.

Title: A handout supply decision

C-later

Components

C-later-Q1

Criterion: 148+153 dollars is total cost compared with 300 dollars; roles and units agree.

Id: C-later-Q1

Next teaching

Complete different guided source: A pretend AUD budget $300 has costs $147 and $128.

Complete new source: A fictional AUD budget $250 has invented costs $126 and $98.

Complete own invitation: An invented AUD budget $400 has costs $186 and $195.

Entry and teach: Teach dollars as a single unit; no cents or real spending needed.

Guided instruction: 275 cost, 25 left. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT21

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach dollars as a single unit; no cents or real spending needed.
Model on separate adult paper. Cost 126+98=224 dollars; compare 224≤250.
Guide a different complete source. A pretend AUD budget $300 has costs $147 and $128. 275 cost, 25 left.
Receive one own attempt. An invented AUD budget $400 has costs $186 and $195. Staff reference only: 381 cost, 19 left.
Compare available work with: Additive cost model and budget constraint have consistent dollar roles. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Additive cost model and budget constraint have consistent dollar roles.

Staff own possibility: 381 cost, 19 left.

Teacher model: Cost 126+98=224 dollars; compare 224≤250.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Whole-dollar model

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Write a model for the combined cost and its comparison with the budget.

Worked staff: Cost $148+$153; compare with $300. No pack multiplication or cents are supplied.

C-later-Q2

Criterion: About $150+$150≈$300 is a scale check, not the exact cost or an affordability proof.

Id: C-later-Q2

Next teaching

Complete different guided source: A pretend AUD plan costs $247 and $138, budget $390.

Complete new source: A fictional AUD plan has costs $176 and $158, budget $340.

Complete own invitation: An invented AUD plan costs $298 and $207, budget $500.

Entry and teach: Place 176 between 170/180 and 158 between 150/160; round nearest ten.

Guided instruction: About 250+140≈390; exact 385, 5 left. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT22

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Place 176 between 170/180 and 158 between 150/160; round nearest ten.
Model on separate adult paper. About 180+160≈340 checks scale; exact 334 must settle a fit.
Guide a different complete source. A pretend AUD plan costs $247 and $138, budget $390. About 250+140≈390; exact 385, 5 left.
Receive one own attempt. An invented AUD plan costs $298 and $207, budget $500. Staff reference only: About 300+210≈510; exact 505, 5 over.
Compare available work with: Nearest-ten values and approximation limitation are stated, not called exact cost. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Nearest-ten values and approximation limitation are stated, not called exact cost.

Staff own possibility: About 300+210≈510; exact 505, 5 over.

Teacher model: About 180+160≈340 checks scale; exact 334 must settle a fit.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: A purpose for rounding

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Give a nearest-ten estimate and state its purpose.

Worked staff: Using nearest-ten rounding gives about $300. This estimate cannot settle a tight decision against $300.

C-later-Q3

Criterion: Exact $301 exceeds $300 by $1, so this stated plan does not fit.

Id: C-later-Q3

Next teaching

Complete different guided source: A pretend AUD budget $350 costs $176 and $175.

Complete new source: A fictional AUD budget $200 costs $97 and $104.

Complete own invitation: An invented AUD budget $500 costs $248 and $251.

Entry and teach: Check why exact comparison is necessary near threshold.

Guided instruction: 351 cost, 1 over. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT23

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Check why exact comparison is necessary near threshold.
Model on separate adult paper. 201 cost, 1 over; an estimate 100+100≈200 cannot prove the plan fits.
Guide a different complete source. A pretend AUD budget $350 costs $176 and $175. 351 cost, 1 over.
Receive one own attempt. An invented AUD budget $500 costs $248 and $251. Staff reference only: 499 cost, 1 left.
Compare available work with: Exact cost and money-left/excess direction support affordability in the model. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Exact cost and money-left/excess direction support affordability in the model.

Staff own possibility: 499 cost, 1 left.

Teacher model: 201 cost, 1 over; an estimate 100+100≈200 cannot prove the plan fits.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: One over matters

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Calculate exactly and decide whether it fits. State the money left or excess.

Worked staff: 148+153=301; $301−$300=$1 over. Money left is not positive $1.

C-later-Q4

Criterion: A valid check supports 301; approximate 300 missed the 1-dollar excess.

Id: C-later-Q4

Next teaching

Complete different guided source: A pretend AUD plan costs $148 and $247, budget $400.

Complete new source: A fictional AUD plan costs $237 and $186, budget $430.

Complete own invitation: An invented AUD plan costs $267 and $236, budget $500.

Entry and teach: Teach sum minus one part recovers other on $18+$7=$25.

Guided instruction: 395 cost, 5 left; 395−148=247. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT24

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach sum minus one part recovers other on $18+$7=$25.
Model on separate adult paper. 423 cost, 7 left; 423−186=237 checks. About 240+190≈430 is inconclusive.
Guide a different complete source. A pretend AUD plan costs $148 and $247, budget $400. 395 cost, 5 left; 395−148=247.
Receive one own attempt. An invented AUD plan costs $267 and $236, budget $500. Staff reference only: 503 cost, 3 over; 503−267=236.
Compare available work with: An exact connected check supports the decision; rough rounding alone does not. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: An exact connected check supports the decision; rough rounding alone does not.

Staff own possibility: 503 cost, 3 over; 503−267=236.

Teacher model: 423 cost, 7 left; 423−186=237 checks. About 240+190≈430 is inconclusive.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Check a budget result

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Give an exact check and explain why the rough estimate alone was insufficient here.

Worked staff: 301−148=153. The estimate equalled budget but exact cost is 1 more; a revised plan would need its own conditions/check.

Eligibility: After additive financial modelling, estimate limits and exact comparisons have been taught, e.g. Day 59. Whole-dollar interpretation is checked; if unfamiliar, teach equivalent card-count target separately.

First later limit: First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen.

Id: C-later

Neutral whole source: A fictional Australian-dollar budget is $300. Two invented whole-dollar costs are $148 and $153. There are no other costs in this model. These are not current prices, personal finances or a purchase invitation.

Own page: Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled.

Title: A close pretend budget

D-first

Components

D-first-Q1

Criterion: Complete chosen conditions meet stated ranges, share a unit and make the wanted quantity explicit; target is given if needed.

Id: D-first-Q1

Next teaching

Complete different guided source: A fictional maze plan has 246 tiles plus 128, target 400.

Complete new source: An ordinary imaginary sculpture-card plan has 132 cards plus 175 new cards, target 320.

Complete own invitation: Choose imaginary start 100–500, added 10–200, same unit; optional target 200–800.

Entry and teach: Teach source/unit/question on 12+8, target 25 before own formulation.

Guided instruction: 374, 26 short; learner may formulate total only first. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT25

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach source/unit/question on 12+8, target 25 before own formulation.
Model on separate adult paper. Ask whether there are enough: 132+175=307, 13 short. Label all givens.
Guide a different complete source. A fictional maze plan has 246 tiles plus 128, target 400. 374, 26 short; learner may formulate total only first.
Receive one own attempt. Choose imaginary start 100–500, added 10–200, same unit; optional target 200–800. Staff reference only: No single answer; check actually chosen conditions. Staff new possibility 213+146=359, target 400→41 short.
Compare available work with: Own conditions and wanted quantity are complete without adult values fill. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Own conditions and wanted quantity are complete without adult values fill.

Staff own possibility: No single answer; check actually chosen conditions. Staff new possibility 213+146=359, target 400→41 short.

Teacher model: Ask whether there are enough: 132+175=307, 13 short. Label all givens.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Choose a collection problem

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: State your chosen conditions, units and the question you want to answer.

Worked staff: Staff possibility only: fictional 236 game cards plus 148 cards, target 400; want to know whether target is met. Own work must not be filled with this example.

D-first-Q2

Criterion: A suitable additive total and optional target comparison match the actually chosen conditions.

Id: D-first-Q2

Next teaching

Complete different guided source: A fictional theatre has 237 tickets and adds 186.

Complete new source: An ordinary invented rocket game has 176 tokens and adds 148; the question asks for total tokens.

Complete own invitation: Choose an imaginary like-unit start 100–500 and addition 10–200; write a matching model.

Entry and teach: Distinguish joining from multiplying different counts.

Guided instruction: 423 tickets; choose chunks or partition. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT26

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Distinguish joining from multiplying different counts.
Model on separate adult paper. 176+148 models 324 tokens; 176×148 would not count two piles.
Guide a different complete source. A fictional theatre has 237 tickets and adds 186. 423 tickets; choose chunks or partition.
Receive one own attempt. Choose an imaginary like-unit start 100–500 and addition 10–200; write a matching model. Staff reference only: Staff possibility 248+137=385; other valid own conditions accepted.
Compare available work with: Formulated operation/unit roles match own wanted quantity. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Formulated operation/unit roles match own wanted quantity.

Staff own possibility: Staff possibility 248+137=385; other valid own conditions accepted.

Teacher model: 176+148 models 324 tokens; 176×148 would not count two piles.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: A model from a question

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Make a number sentence or model for your question, keeping the roles clear.

Worked staff: For staff possibility 236+148 compared with 400. Other valid own choices accepted.

D-first-Q3

Criterion: Correct exact result and interpretation agree with the learner’s chosen conditions, not a prescribed example.

Id: D-first-Q3

Next teaching

Complete different guided source: A fictional puzzle plan has 318 cards plus 156, target 460.

Complete new source: An ordinary imaginary art plan has 286 labels plus 147, target 450.

Complete own invitation: Choose a like-unit start 100–500, addition 10–200, target 200–800; solve and interpret.

Entry and teach: Teach total and gap as different answer roles.

Guided instruction: 474 available, 14 extra; need is met. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT27

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach total and gap as different answer roles.
Model on separate adult paper. 433 available, 17 short; 433 alone answers total, not whether enough.
Guide a different complete source. A fictional puzzle plan has 318 cards plus 156, target 460. 474 available, 14 extra; need is met.
Receive one own attempt. Choose a like-unit start 100–500, addition 10–200, target 200–800; solve and interpret. Staff reference only: No prescribed own answer; staff possibility 275+138=413, target 400→13 extra.
Compare available work with: Own result and target meaning agree; missing interpretation remains missing. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Own result and target meaning agree; missing interpretation remains missing.

Staff own possibility: No prescribed own answer; staff possibility 275+138=413, target 400→13 extra.

Teacher model: 433 available, 17 short; 433 alone answers total, not whether enough.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Interpret an own answer

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Solve exactly and explain what the result means.

Worked staff: Staff possibility 384 cards, 16 short of 400. A total alone can supply calculation evidence while interpretation remains not yet seen.

D-first-Q4

Criterion: A valid check supports the own result; wanted next action can be stated without requiring a new computation or made artifact.

Id: D-first-Q4

Next teaching

Complete different guided source: A fictional map plan has 328 tiles plus 145, target 480.

Complete new source: An ordinary pretend game has 247 cards plus 156, target 420.

Complete own invitation: Choose a complete own like-unit plan and give one connected mathematical check against its current conditions. A wanted next action is optional; label any unworked change as a plan.

Entry and teach: Teach one connected check against the current chosen conditions; a wanted next action is optional and an unworked change is a plan.

Guided instruction: 473, 7 short; check 473−145=328 against the given 328+145 and target 480. After checking, an optional proposed target 470 is a plan. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT28

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Teach one connected check against the current chosen conditions; a wanted next action is optional and an unworked change is a plan.
Model on separate adult paper. 403, 17 short; check 403−156=247 against the given 247+156 and target 420. After the check, an optional proposed added 180 is a plan, not yet computed.
Guide a different complete source. A fictional map plan has 328 tiles plus 145, target 480. 473, 7 short; check 473−145=328 against the given 328+145 and target 480. After checking, an optional proposed target 470 is a plan.
Receive one own attempt. Choose a complete own like-unit plan and give one connected mathematical check against its current conditions. A wanted next action is optional; label any unworked change as a plan. Staff reference only: Check against own conditions; an unworked change is a plan. Staff possibility 196+158=354; 354−158=196.
Compare available work with: One valid connected check supports the own result under its actual stated conditions. A wanted next action is optional; do not require a newly computed change or a made artifact. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: One valid connected check supports the own result under its actual stated conditions. A wanted next action is optional; do not require a newly computed change or a made artifact.

Staff own possibility: Check against own conditions; an unworked change is a plan. Staff possibility 196+158=354; 354−158=196.

Teacher model: 403, 17 short; check 403−156=247 against the given 247+156 and target 420. After the check, an optional proposed added 180 is a plan, not yet computed.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: A wanted next move

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Choose a connected check. What would you keep, change or try next?

Worked staff: Staff possibility 384−148=236; keep note or propose 150 added instead. Proposed changed total is not claimed computed until worked.

Eligibility: After ordinary additive formulation, exact strategies and interpretation have been taught. If number ranges block access, teach a smaller ordinary version; do not silently change the stated held source and claim equivalent difficulty.

First later limit: First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen.

Id: D-first

Neutral whole source: Choose an imaginary collection or whole-dollar plan. Choose a start count from 100 to 900 and an added count from 10 to 300, both in the same unit. Ask for the combined amount or ask whether it meets a separately chosen target from 200 to 1200. State all chosen conditions. No real possession, purchase or completed activity is required.

Own page: Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled.

Title: A note of your own

D-later

Components

D-later-Q1

Criterion: Complete current conditions and change statements are supported by available work; no invented previous history.

Id: D-later-Q1

Next teaching

Complete different guided source: A fictional music plan has 347 cards plus 128, target 500.

Complete new source: An ordinary imaginary puppet plan has 258 labels plus 137, target 420.

Complete own invitation: Make a new own like-unit start 100–500, added 10–200, target optional 200–800, or state one change of an available plan.

Entry and teach: Provide a new complete plan when earlier work is absent; no memory test.

Guided instruction: 475, 25 short; compare only with actually available earlier conditions. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT29

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Provide a new complete plan when earlier work is absent; no memory test.
Model on separate adult paper. 395, 25 short; call new plan new. If earlier available 258+127, only new addition 137 is changed.
Guide a different complete source. A fictional music plan has 347 cards plus 128, target 500. 475, 25 short; compare only with actually available earlier conditions.
Receive one own attempt. Make a new own like-unit start 100–500, added 10–200, target optional 200–800, or state one change of an available plan. Staff reference only: No one answer; check current conditions. Staff possibility 279+156=435.
Compare available work with: Complete current conditions and change attribution are document-supported. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Complete current conditions and change attribution are document-supported.

Staff own possibility: No one answer; check current conditions. Staff possibility 279+156=435.

Teacher model: 395, 25 short; call new plan new. If earlier available 258+127, only new addition 137 is changed.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: New or actually changed

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: State all current conditions and identify any new or unchanged part.

Worked staff: Staff new possibility: 417 fictional labels plus 186, target 600. If this is a new plan, say new, not improved.

D-later-Q2

Criterion: Current additive model and exact result agree with selected quantities.

Id: D-later-Q2

Next teaching

Complete different guided source: A pretend story book plan changes start from 327 to 347 and keeps 156 added.

Complete new source: An ordinary fictional costume plan changes its added count from 148 to 168 while current start is 286.

Complete own invitation: Choose an own complete additive plan, change one count by 10–30 and recompute.

Entry and teach: Do not retain old answer after changing an input.

Guided instruction: Current 503; old 483 is earlier version. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT30

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Do not retain old answer after changing an input.
Model on separate adult paper. Current 286+168=454; old 434 belongs to 286+148. Label both versions.
Guide a different complete source. A pretend story book plan changes start from 327 to 347 and keeps 156 added. Current 503; old 483 is earlier version.
Receive one own attempt. Choose an own complete additive plan, change one count by 10–30 and recompute. Staff reference only: Check the actual new sum; staff possibility 248+135=383 then 268+135=403.
Compare available work with: Current calculation uses current values; earlier result is not silently reused. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Current calculation uses current values; earlier result is not silently reused.

Staff own possibility: Check the actual new sum; staff possibility 248+135=383 then 268+135=403.

Teacher model: Current 286+168=454; old 434 belongs to 286+148. Label both versions.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Compute current conditions

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Formulate and calculate the current wanted quantity with a useful strategy.

Worked staff: 417+186=603 labels by+100,+80,+6. A new target comparison uses current 603.

D-later-Q3

Criterion: Meaning and optional comparison agree with the selected plan and correct result.

Id: D-later-Q3

Next teaching

Complete different guided source: A fictional card plan has 428 plus 157, target 600.

Complete new source: An ordinary imagined map plan has 387 tiles plus 146, target 520.

Complete own invitation: Choose current like-unit conditions and target; compute and interpret for reader.

Entry and teach: Distinguish an excess from shortage; units and target stay fixed.

Guided instruction: 585, 15 short; need 15 more. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT31

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Distinguish an excess from shortage; units and target stay fixed.
Model on separate adult paper. 533 available, 13 extra; the stated need is met.
Guide a different complete source. A fictional card plan has 428 plus 157, target 600. 585, 15 short; need 15 more.
Receive one own attempt. Choose current like-unit conditions and target; compute and interpret for reader. Staff reference only: Staff possibility 376+148=524, target 500→24 extra; own numbers differ.
Compare available work with: Exact current result and direction match selected source conditions. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Exact current result and direction match selected source conditions.

Staff own possibility: Staff possibility 376+148=524, target 500→24 extra; own numbers differ.

Teacher model: 533 available, 13 extra; the stated need is met.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Current result in context

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Interpret the current result in its situation. If a target is chosen, say whether it is met.

Worked staff: Staff possibility 603 meets 600 with 3 extra. No actual labelling is claimed.

D-later-Q4

Criterion: Offered check is valid if supplied; offered future change is clearly a plan, with no requirement for both a check and a change.

Id: D-later-Q4

Next teaching

Complete different guided source: A fictional badge plan has 247 plus 178, target 450.

Complete new source: An ordinary invented archive plan has 314 cards plus 186, target 520.

Complete own invitation: Give one valid check or one wanted change for your own complete plan; state what is worked and what is proposed.

Entry and teach: Model a wanted change without implying it was recalculated or happened.

Guided instruction: 425, 25 short; propose added 203 or check 425−178=247. Invite each relationship before the answer; teach missing facts and name help.

Id: NEXT32

Materials: Broad paper/empty bar or line/place-value headings as useful; usual communication; no actual stock/handling/purchase.

Relationship to check: Teach the observed missing relationship in a new ordinary domain; not an answer repetition or further held item.

Session sequence

Read the new source and name units/wanted quantity. Model a wanted change without implying it was recalculated or happened.
Model on separate adult paper. Current 500, 20 short; check 500−186=314. Proposed added 206 is unworked until 314+206=520 is actually computed.
Guide a different complete source. A fictional badge plan has 247 plus 178, target 450. 425, 25 short; propose added 203 or check 425−178=247.
Receive one own attempt. Give one valid check or one wanted change for your own complete plan; state what is worked and what is proposed. Staff reference only: No prescribed own choice; valid check or clearly unworked future change accepted.
Compare available work with: Evidence of calculation and future intention remain distinct without demanding both. Choose one follow-up offer; never infer independence from a copied model.

Specific criterion: Evidence of calculation and future intention remain distinct without demanding both.

Staff own possibility: No prescribed own choice; valid check or clearly unworked future change accepted.

Teacher model: Current 500, 20 short; check 500−186=314. Proposed added 206 is unworked until 314+206=520 is actually computed.

Timing: An adjustable 10–20 minute ordinary lesson, unpiloted; split/stop after one useful part.

Title: Worked or planned?

Own initial value: Genuinely empty: zero characters; no model or hidden exemplar.

Prompt: Give a connected check or one wanted next change. Say what has been worked out and what is still proposed.

Worked staff: Staff possibility 603−186=417 checks. Or propose target 620 and say not yet worked. Either matches the one-of invitation; do not demand both.

Eligibility: After the actual required mathematics has been taught. Receive current work as new/supported/exposed according to actual source history; do not infer prior choices or improvement.

First later limit: First/later are opportunity labels, not fixed order, matches, calibrated difficulty or learning gain. If source/answer exposed, record that rather than claim unseen.

Id: D-later

Neutral whole source: Make a new fictional additive plan with start 100–900, added 10–300, same unit; optional target 200–1200. Or change one stated condition of an actually available earlier plan, keeping all current conditions complete and in range. Earlier work may be visible; if absent, start anew. No matched difficulty or learning gain is supplied.

Own page: Four labelled true empty text areas with literal blank initial values; kept draft not required for judgement; staff information behind separate link, not autofilled.

Title: One useful changed plan

Status: Written proposal only; original neutral data, four genuine blank prompts each, full 32 separate ordinary next lessons.

Working-Notes Bench · complete future interaction and paper specification

A proposed temporary place for the learner's literal chosen words. Nothing is implemented here. Paper and usual communication retain the full mathematical task. No automatic computation, held-answer generation, assessment judgement or network assistant.

Actions: Initial HTML hides and disables view selector, field selector, Preview, Keep1, Keep2, Compare, Restore1, Restore2 and Clear; confirmation controls are also unavailable. Only after all listeners and state initialize successfully can script show or enable them and apply view hiding. Forced initialization failure leaves every affected action unavailable, all seven ordinary blank fields visible, native source details usable and honest paper guidance present. A no-JS page cannot promise these automatic actions.

Cancellation: Only one replacement or Clear choice can be pending. Block affected state changes while it is pending, preserving source reading and all words. Explicit Keep current note and Escape both cancel that pending choice through the same cancel routine, retaining seven drafts, current view/selection, preview and both kept identities; focus returns to the initiating button. Escape outside a pending choice has no effect. Confirm Clear empties all seven drafts, preview and both kept slots, resets Source view/source selection and focuses the source field. It does not erase ordinary sources or another page’s work.

Claims: Finite callback observations will not certify native Browser keyboard/layout/assistive technology, classroom outcomes, audio or translations. This proposal is unpiloted; full-year coverage and A–E decisions remain open.

Field contract: All seven genuinely empty textareas appear in plain no-script flow. Initialization preserves literal strings without trim, normalisation, arithmetic parsing or HTML interpretation. Input is capped at1200 Array.from codepoints; textarea maxlength2400 UTF16 allows all 1200 supplementary characters. The interface explains the1200character limit. Stable field IDs preserve drafts across views. No personal data is required.

Fields

source

Id: source

Initial literal value: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My source or situation

Textarea maxlength utf16: 2400

Unicode limit codepoints: 1200

quantity_1

Id: quantity_1

Initial literal value: Genuinely empty: zero characters; no model or hidden exemplar.

Label: First count and unit

Textarea maxlength utf16: 2400

Unicode limit codepoints: 1200

quantity_2

Id: quantity_2

Initial literal value: Genuinely empty: zero characters; no model or hidden exemplar.

Label: Second count and unit

Textarea maxlength utf16: 2400

Unicode limit codepoints: 1200

question

Id: question

Initial literal value: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My wanted quantity or equation

Textarea maxlength utf16: 2400

Unicode limit codepoints: 1200

strategy

Id: strategy

Initial literal value: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My strategy or representation

Textarea maxlength utf16: 2400

Unicode limit codepoints: 1200

result

Id: result

Initial literal value: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My result and what it means

Textarea maxlength utf16: 2400

Unicode limit codepoints: 1200

check

Id: check

Initial literal value: Genuinely empty: zero characters; no model or hidden exemplar.

Label: My check or wanted next move

Textarea maxlength utf16: 2400

Unicode limit codepoints: 1200

Finite required tests

Exact seven blank fields/labels/limits, four views and visible selection rules.
Initial hidden+disabled script actions, honest no-JS wording, forced initializer failure retaining plain flow and source disclosures.
All20ordinary sources × every visible field/view selection: seven multiline Unicode drafts/view/selection/preview/both kept identities and words preserved; help Close returns current visible selected field focus.
Supplementary Unicode limit:1200 Array.from codepoints and2400 UTF16 maxlength, literal strings and blanks preserved.
Explicit Keep1/2, occupied-slot Replace/cancel/Escape/confirm, chosen-version identity retention and no automatic saving.
Compare chosen kept versions only; Restore1/2 copies every literal field; empty slot never changes work.
Clear cancel/Escape preserves state; Confirm clears/resets/focuses source; Escape outside pending choice does nothing.
Eight same-page own source disclosures × four multiline drafts retain values; exact paper/own prompt parity.
Actual native keyboard/Tab/zoom/mobile/print/Reader/whole-art Browser tests follow construction as a separate gate.

Initial selected field: source

Initial view: source

Manual model activity: Choose a part/whole, start/use/left or two equal sides relationship. Arrange your own paper labels, draw it, describe it or direct a helper. The optional digital note can hold literal labels and the learner’s exact description; it must not silently calculate or assess them. Calculation, reasoning, an actual manipulation and a proposed manipulation remain distinct evidence. A grown-up can check mathematics on separate work.

Name: Additive Work Bench

Own assessment contract: Each of eight own pages has four genuinely empty textareas with exact CASE prompts and initially closed native same-page disclosure of its full neutral source. Disclosure never navigates away or resets words. Staff keys link separately with each criterion, worked possibility and full next lesson. No model or answer autofill, criterion in a child source, automatic marking or claimed unseen eligibility. Any optional four-field draft retention is memory only.

Paper equivalence: Provide the same seven labelled genuinely empty areas, all twenty complete neutral sources and usual communication options. Keep a first and second note manually with complete conditions/words including blank areas. Name the two versions chosen for a comparison. An update requires a complete new version or an explicit changed area. Paper guidance must not imply automatic Preview, Keep, Compare, Restore or Clear without script. Adult checking remains separate from the learner’s own response.

Preview: Explicit Preview copies all seven literal strings into a labelled plain-text reader, including blanks, without solving or grading. Return to my words retains values and focuses the currently selected visible field. A preview is a supplied rendering of words, not evidence that an explanation is mathematically correct or independently made.

Purpose: Make a useful additive note, choose how to represent a relationship and compare two explicitly kept drafts. This is a workspace for the learner’s own words, not a solver or automatic judgement.

Selection and focus: Field selector offers only fields visible in the selected view. If a new editable view excludes the last selected field, choose its first visible field. Reader permits all seven. Compare focuses its heading and retains the last editable selection for Return. Closing enhanced source help focuses the actual currently selected visible field. Typing does not force cursor jumps. Use native buttons and selectors, Enter/Space activation and logical Tab order with no keyboard trap.

Source help: Twenty initially closed native details contain C01–C20 exact complete neutral fictional sources, titles and ordinary purposes only. No worked result, held source, criterion or next answer appears inside them. They open in place without a fetch or autofill. Enhanced help returns focus to the currently selected visible field on Close; if selection changes while open, use that current selection. Help preserves all seven drafts, view, selected field, preview and both kept identities and words. Native disclosures remain available without script.

Status: Written implementation contract only; different whole proposal acceptance is required before source construction. No interface or callback has been made or tested.

Temporary lifecycle: Keep state only in this page’s memory. No account, upload, network, cookies, localStorage, sessionStorage, AI or automatic recording. Prominent notice says reload or tab closure loses both unexported draft and kept words. Optional Copy my note requires a user gesture and produces labelled plain text containing every field including blanks; manual select/copy remains available when clipboard access fails. No hidden transmission or promised persistent saving.

Versions: Keep1 or Keep2 copies all seven strings, including blank ones, into a fixed slot with version ID1 or2 and a new monotonic local sequence identity. Keeping an empty slot needs no replacement choice; keeping into an occupied slot needs an explicit named Replace/Keep current note choice. Cancel preserves the original slot and all draft state. Confirm Replace copies the then-confirmed full draft into only the chosen slot. Reading sources, switching fields and editing do not automatically keep a version. Compare shows only the two explicitly chosen kept identities and all their literal words; unsaved draft words cannot replace them. Restore1/2 explicitly copies every value from an occupied chosen slot, while an empty slot reports unavailable without changing work. Version differences do not prove progress.

Views

source

Id: source

Name: Read my problem

Visible fields

source
quantity_1
quantity_2
question

work

Id: work

Name: Work it out

Visible fields

strategy
result
check

reader

Id: reader

Name: My complete note

Visible fields

source
quantity_1
quantity_2
question
strategy
result
check

compare

Id: compare

Name: Two kept notes

Visible fields

Twenty original future visual and blank-aid specifications

Written specifications only; no actual geometry, rendering or visual acceptance is claimed. V01–V08 are adult ordinary mathematical models, V09–V16 are exact neutral held sources with32 genuinely empty response interiors, V17–V20 are four own aids with16 genuinely empty interiors. Every full alternative is written below. A future constructor must render and personally inspect every whole plane and keep staff models separate from own work.

Visuals

V01

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Format: Future original SVG; no raster or SVG has been made in this proposal. Use semantic title/desc plus full linked text alternative; body font at least 24 px except long held sources 22 px, labels 28 px, stroke 3 px, white background/black text. Keep at least 24 px clearance. Wrapping must be explicit tspans, not clipped foreignObject. Test whole plane, mobile zoom, mono print and text alternative after construction. Colour can assist but never carry sole meaning.

Full alternative: A labelled adult place-value model for fictional badges. The first parcel 612 is 600+10+2; the second 243 is 200+40+3. Joining same-unit parts gives 800+50+5=855 badges. A second path adds 200, 40 and 3 to 612, reaching 812, 852 and 855. Neither display is a learner response or real stock count.

Geometry: viewBox 0 0 1200 850. Heading(44, 54). Place-value table outer rect(44, 140, 1112, 360), 3 equal columns 370.6667 for hundreds/tens/ones. Rows y 140, 230, 320, 410, 500, labels 28 px. Row 1 values 600/10/2, row 2 values 200/40/3, row 3 combined 800/50/5; plus label outside each row and equation 855 under at(44, 570). No blocks counted individually. Separate chunk-path text at(44, 650): 612→812(+200)→852(+40)→855(+3). Label both as adult models, not own work.

Id: V01

Rights: Original planned geometry and prose ©NeuroForgeIO Pty Ltd 2026, CC BY 4.0; curriculum/source text stays under its own notices. No banknote designs, logos, cultural motif or pupil-image copying.

Role: Adult ordinary model; exposed solution separate from genuine blank own work

Source: Day 51 ordinary badge source, 612+243=855.

Title: One total, every part

V02

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Full alternative: An adult model of 364+278 tags. Partitioning gives 500+130+12. Twelve ones rename as one ten and two ones, so 500+140+2. Fourteen tens rename as one hundred and four tens, yielding 600+40+2=642. The tag quantity remains the same through each renaming. A separate chunk check also yields 642.

Geometry: viewBox 0 0 1200 850. Three panel rectangles(44, 130, 350, 260),(424, 130, 350, 260),(804, 130, 350, 260). Panel 1 labels 500 from hundreds, 130 from tens, 12 ones. Panel 2 labels 500+140+2 after 12 ones→1 ten 2 ones. Panel 3 labels 600+40+2 after 14 tens→1 hundred 4 tens. Arrows x 402 y 260 and 782 y 260; their labels sit above, not across numbers. Equation at 44, 470. Bottom(44, 580) textchunk check 364+200+70+8=642. Every arrow explicitly names equivalent renaming, not removal.

Id: V02

Role: Adult ordinary model; exposed solution separate from genuine blank own work

Source: Day 52 ordinary costume tag source, 364+278=642.

Title: The amount stays the same

V03

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Full alternative: An adult exact-compensation model. Fictional 398 and 267 stickers total 665. Replacing 398 with 400 adds two extra, gives 667, then removing those extra two yields 665. A separate estimate 400+300≈700 checks scale; it is not the exact total.

Geometry: viewBox 0 0 1200 850. Upper three-box row y 160 h 160, x 44 w 310, x 414 w 310, x 784 w 370. Box 1 text 398+267; Box 2 text 400+267=667 and extra 2 label; Box 3 text 667−2=665. Arrow labels add 2 and remove 2 at mid clearance. At 44, 420 separate exact equation. At 44, 550 dashed-border panel w 1112 h 180: estimate 400+300≈700, not exact. Dash is border style only; word ESTIMATE visible. No double-adjustment or rounded 667 total mis label.

Id: V03

Role: Adult ordinary model; exposed solution separate from genuine blank own work

Source: Day 53 ordinary 398+267 sticker source.

Title: Add an extra, then remove it

V04

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Full alternative: An adult model for 806 labels with 247 used. It first renames 806 as 7 hundreds, 9 tens and 16 ones. Subtracting 2 hundreds, 4 tens and 7 ones leaves 5 hundreds, 5 tens and 9 ones, or 559 labels. Check 247+559=806. A count-up path from 247 to 250 to 800 to 806 adds 3+550+6=559. This is modelled remaining stock, not an observed action.

Geometry: viewBox 0 0 1200 850. Table(44, 150, 1112, 300), columns label hundreds/tens/ones. Top row 7 hundreds/9 tens/16 ones=806; subtraction row 2 hundreds/4 tens/7 ones; result row 5 hundreds/5 tens/9 ones=559. Supply text 806=700+90+16 above table, not crossing headers. Inverse check 247+559=806 at 44, 560. Bottom count-up 987 must not appear: exact path 247→250(+3)→800(+550)→806(+6), total 559 at 44, 650.

Id: V04

Role: Adult ordinary model; exposed solution separate from genuine blank own work

Source: Day 54 ordinary 806−247 labels source.

Title: A zero can be regrouped

V05

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Full alternative: A precisely scaled adult number line compares fictional poster requirements 987 and 1203 labels. Counting from 987 to 1000 adds 13, from 1000 to 1200 adds 200, and from 1200 to 1203 adds 3. The gap is 216 labels, checked by 987+216=1203. Both design requirements remain; the greater number is not a judgement about design quality.

Geometry: viewBox 0 0 1200 850. Exact number line from 980 to 1220 at x 100 to 1060, y 360, scale 4 px per label. Major labelled ticks 980, 1000, 1100, 1200, 1220; endpoint 987 at x 128, 1203 at x 992. Three bracket arcs 987→1000(x 128→180), 1000→1200(x 180→980), 1200→1203(x 980→992), labels+13,+200,+3 with leaders placed at y 200/250/300 to avoid endpoint crowding. Difference 216 text at 44, 520. Text at 44, 650 says both whole counts remain, no actual removal or better design judgement.

Id: V05

Role: Adult ordinary model; exposed solution separate from genuine blank own work

Source: Day 55 ordinary poster requirement 1203 versus 987 labels.

Title: A gap with a meaning

V06

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Full alternative: An adult part-whole model uses 725 fictional cards as the whole. The known part is 468; the further part is initially shown with a box. The separate adult key gives 257, with 468+257=725. The two bar widths are proportional to 468 and 257. This labelled adult model must not be used as a genuinely empty own aid or an unseen held source.

Geometry: viewBox 0 0 1200 850. Exact bar x 80 width 1015, y 240 h 140 representing 725 units at 1.4 px per unit. Known part width 655.2 for 468; unknown part width 359.8 for 257. Vertical divider x 735.2. Whole 725 bracket above. Unknown bar initially label□in adult prompt panel, solution 257 only in separate lower adult key panel at 44, 560; other panel shows 468+257=725. Own sheet is V18, not this model. Distinguish unknown part label from whole 725.

Id: V06

Role: Adult ordinary model; exposed solution separate from genuine blank own work

Source: Day 56 ordinary 468+□=725 cards target.

Title: Known part, missing part, whole

V07

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Full alternative: Two separate adult unknown-role models. In a fictional tag record 930 start and 586 left give 344 used; 930−344=586. In a different fictional card record 175 used and 428 left give 603 start; 603−175=428. The unknown counts a used amount in the first equation and a starting amount in the second. Card and tag quantities are not combined.

Geometry: viewBox 0 0 1200 850. Two independent panels rect(44, 130, 1112, 270)and(44, 440, 1112, 270). First line 930−□=586, the starting 930 tags and left 586 tags are given; separate key used 344. Second line□−175=428, the used 175 cards and left 428 cards are given; key 603 starting cards. Panel roles start/use/left are labelled at y 200/y 510, sources never joined. Footer explicitly says separate invented records. All numbers with units.

Id: V07

Role: Adult ordinary model; exposed solution separate from genuine blank own work

Source: Day 57 ordinary 930−□=586 tags and□−175=428 cards.

Title: Which number is missing?

V08

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Full alternative: An adult equality model for 245+□=390+75. The known right side is 465. The missing left part is 220 because 465−245=220. Substitution gives 245+220=465 and 390+75=465. Schematic bars stand for equal whole amounts and are explicitly not to scale; the box value 220 is not the whole-side value 465.

Geometry: viewBox 0 0 1200 850. Heading(44, 54). Original equation 245+□=390+75 at 44, 150. Two equal-length schematic bars x 44/x 634, width 520, y 250 h 130; explicit SCHEMATIC NOT SCALE label, both wholes label 465. Left parts 245/220, right 390/75, labels with leaders outside bar if small. Original substitution 245+220=465 and 390+75=465 at 44, 500. Box value 220 distinct from whole 465 in text at 44, 650. No physical balance weight inference.

Id: V08

Role: Adult ordinary model; exposed solution separate from genuine blank own work

Source: Day 58 ordinary 245+□=390+75.

Title: Each full side is equal

V09

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: Complete neutral fictional source: A fictional badge cupboard has 364 badges. Another parcel supplies 278 badges of the same kind. Count each badge once. The task is to find the new total; no actual stock or delivery is claimed. Four exact own prompts, in order: 1. What does each count represent? Write a number sentence for the new total. 2. Find the total using a way you can explain or show. 3. Show why any regrouping in your way keeps the amount unchanged. If your way uses no written regrouping, describe crossing a ten or hundred. 4. Give a connected check and state what your total counts. Each response area is genuinely empty; no sample answer, equation, strategy, faint model or watermark appears inside it. Staff criteria and next lessons are separate.

Geometry: viewBox 0 0 1200 1800. Heading at(44, 54). Whole neutral source at(44, 100), max 1112 width and 240 height, 22 px font/32 leading; hard-wrap preserving exact complete text. Four prompt/body groups begin y 390, 710, 1030, 1350. Each exact prompt uses 22 px/30 leading within 100 height. Each genuinely empty response rectangle at(x 44, ygroup+115, w 1112, h 185), 3 px stroke. No interior text, model, equation, dotted guide, answer, shadow marks or instructions; labels outside. Footer y 1760 says usual communication/pause/pass/finish. Non interactive SVG does not store words; actual own HTML/paper correspondence separately required. The four prompts are exactly CASE-DATA components, not staff criteria.

Id: V09

Prompt ids

A-first-Q1
A-first-Q2
A-first-Q3
A-first-Q4

Role: Neutral held source plus four genuine empty areas; 32 total empty interiors, source exposure tracked

Source: A fictional badge cupboard has 364 badges. Another parcel supplies 278 badges of the same kind. Count each badge once. The task is to find the new total; no actual stock or delivery is claimed.

Title: A pretend badge cupboard · neutral source and my turn

V10

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: Complete neutral fictional source: An imagined paper store starts with 704 cards and uses 168 cards once. Find the cards left. This is a different opportunity after teaching, not an equal-difficulty test form or a progress measure. Four exact own prompts, in order: 1. What does each count mean, and what number sentence finds cards left? 2. Find cards left using a strategy you can show. 3. A made-up note says “subtract each smaller digit from each bigger digit, so 704−168=664”. Keep or repair this method with a reason. 4. Check your result and explain what it counts. Each response area is genuinely empty; no sample answer, equation, strategy, faint model or watermark appears inside it. Staff criteria and next lessons are separate.

Id: V10

Prompt ids

A-later-Q1
A-later-Q2
A-later-Q3
A-later-Q4

Role: Neutral held source plus four genuine empty areas; 32 total empty interiors, source exposure tracked

Source: An imagined paper store starts with 704 cards and uses 168 cards once. Find the cards left. This is a different opportunity after teaching, not an equal-difficulty test form or a progress measure.

Title: A fictional paper store · neutral source and my turn

V11

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: Complete neutral fictional source: A fictional kit needs 725 labels in total. It has 468 labels available. Find the further labels needed: 468+□=725. The box stands for a whole-number value. No real refill is supplied. Four exact own prompts, in order: 1. What does the box count? Describe the known part and the whole. 2. Find a value for the box with a useful strategy. 3. Put your value into the original equation and check it. 4. A fictional note says “the box is 725 because that is the answer after the equals sign”. Keep or repair it with a reason. Each response area is genuinely empty; no sample answer, equation, strategy, faint model or watermark appears inside it. Staff criteria and next lessons are separate.

Id: V11

Prompt ids

B-first-Q1
B-first-Q2
B-first-Q3
B-first-Q4

Role: Neutral held source plus four genuine empty areas; 32 total empty interiors, source exposure tracked

Source: A fictional kit needs 725 labels in total. It has 468 labels available. Find the further labels needed: 468+□=725. The box stands for a whole-number value. No real refill is supplied.

Title: The missing refill · neutral source and my turn

V12

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: Complete neutral fictional source: Two separate fictional records use cards. Record 1:□−175=428, where 175 cards are used and 428 remain. Record 2: 620−185=□+240. Keep the records separate. There is no supplied history of a learner’s earlier work. Four exact own prompts, in order: 1. For Record 1, say what the box counts and find it. 2. Substitute your Record 1 value into its original equation and check. 3. For Record 2, find the box value. Show what the complete known side is first. 4. Check both full sides of Record 2 after substitution. Each response area is genuinely empty; no sample answer, equation, strategy, faint model or watermark appears inside it. Staff criteria and next lessons are separate.

Id: V12

Prompt ids

B-later-Q1
B-later-Q2
B-later-Q3
B-later-Q4

Role: Neutral held source plus four genuine empty areas; 32 total empty interiors, source exposure tracked

Source: Two separate fictional records use cards. Record 1:□−175=428, where 175 cards are used and 428 remain. Record 2: 620−185=□+240. Keep the records separate. There is no supplied history of a learner’s earlier work.

Title: Two missing roles · neutral source and my turn

V13

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: Complete neutral fictional source: An invented display needs 485 handouts. It has 268 handouts in one pile and 124 in another, counted once. Decide whether the supply meets the need. No real print stock or event is observed. Four exact own prompts, in order: 1. What question would settle whether the supply is enough? Write a model with units. 2. Find the exact available count and the amount missing or extra. 3. Make the decision in terms of the source. 4. A made-up note says “about 270+120 is 390, so we know the exact shortfall is 95”. Keep or repair it. Each response area is genuinely empty; no sample answer, equation, strategy, faint model or watermark appears inside it. Staff criteria and next lessons are separate.

Id: V13

Prompt ids

C-first-Q1
C-first-Q2
C-first-Q3
C-first-Q4

Role: Neutral held source plus four genuine empty areas; 32 total empty interiors, source exposure tracked

Source: An invented display needs 485 handouts. It has 268 handouts in one pile and 124 in another, counted once. Decide whether the supply meets the need. No real print stock or event is observed.

Title: A handout supply decision · neutral source and my turn

V14

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: Complete neutral fictional source: A fictional Australian-dollar budget is $300. Two invented whole-dollar costs are $148 and $153. There are no other costs in this model. These are not current prices, personal finances or a purchase invitation. Four exact own prompts, in order: 1. Write a model for the combined cost and its comparison with the budget. 2. Give a nearest-ten estimate and state its purpose. 3. Calculate exactly and decide whether it fits. State the money left or excess. 4. Give an exact check and explain why the rough estimate alone was insufficient here. Each response area is genuinely empty; no sample answer, equation, strategy, faint model or watermark appears inside it. Staff criteria and next lessons are separate.

Id: V14

Prompt ids

C-later-Q1
C-later-Q2
C-later-Q3
C-later-Q4

Role: Neutral held source plus four genuine empty areas; 32 total empty interiors, source exposure tracked

Source: A fictional Australian-dollar budget is $300. Two invented whole-dollar costs are $148 and $153. There are no other costs in this model. These are not current prices, personal finances or a purchase invitation.

Title: A close pretend budget · neutral source and my turn

V15

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: Complete neutral fictional source: Choose an imaginary collection or whole-dollar plan. Choose a start count from 100 to 900 and an added count from 10 to 300, both in the same unit. Ask for the combined amount or ask whether it meets a separately chosen target from 200 to 1200. State all chosen conditions. No real possession, purchase or completed activity is required. Four exact own prompts, in order: 1. State your chosen conditions, units and the question you want to answer. 2. Make a number sentence or model for your question, keeping the roles clear. 3. Solve exactly and explain what the result means. 4. Choose a connected check. What would you keep, change or try next? Each response area is genuinely empty; no sample answer, equation, strategy, faint model or watermark appears inside it. Staff criteria and next lessons are separate.

Id: V15

Prompt ids

D-first-Q1
D-first-Q2
D-first-Q3
D-first-Q4

Role: Neutral held source plus four genuine empty areas; 32 total empty interiors, source exposure tracked

Source: Choose an imaginary collection or whole-dollar plan. Choose a start count from 100 to 900 and an added count from 10 to 300, both in the same unit. Ask for the combined amount or ask whether it meets a separately chosen target from 200 to 1200. State all chosen conditions. No real possession, purchase or completed activity is required.

Title: A note of your own · neutral source and my turn

V16

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: Complete neutral fictional source: Make a new fictional additive plan with start 100–900, added 10–300, same unit; optional target 200–1200. Or change one stated condition of an actually available earlier plan, keeping all current conditions complete and in range. Earlier work may be visible; if absent, start anew. No matched difficulty or learning gain is supplied. Four exact own prompts, in order: 1. State all current conditions and identify any new or unchanged part. 2. Formulate and calculate the current wanted quantity with a useful strategy. 3. Interpret the current result in its situation. If a target is chosen, say whether it is met. 4. Give a connected check or one wanted next change. Say what has been worked out and what is still proposed. Each response area is genuinely empty; no sample answer, equation, strategy, faint model or watermark appears inside it. Staff criteria and next lessons are separate.

Id: V16

Prompt ids

D-later-Q1
D-later-Q2
D-later-Q3
D-later-Q4

Role: Neutral held source plus four genuine empty areas; 32 total empty interiors, source exposure tracked

Source: Make a new fictional additive plan with start 100–900, added 10–300, same unit; optional target 200–1200. Or change one stated condition of an actually available earlier plan, keeping all current conditions complete and in range. Earlier work may be visible; if absent, start anew. No matched difficulty or learning gain is supplied.

Title: One useful changed plan · neutral source and my turn

V17

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: My place-value or strategy space. Four labelled, completely empty areas: My quantities and unit; My representation or strategy; My result and meaning; My check or next move. Use for ordinary addition/subtraction, not a printed adult model. No values, answers, diagrams or claims of completed work are supplied. Write, draw, type in an accompanying page or use your usual communication; filling every area is optional.

Geometry: viewBox 0 0 1200 1450. Heading(44, 54). Four external 28 px label blocks at y 120, 430, 740, 1050(max 2 lines). Four empty rectangles x 44, y label+80, w 1112, h 210. Absolutely empty interiors: no text/marks/numbers/arrows/micro dots. Footer at 44, 1410 usual communication/private/pause/pass. Labels outside are exact: ["My quantities and unit", "My representation or strategy", "My result and meaning", "My check or next move"] Use for ordinary addition/subtraction, not a printed adult model.

Id: V17

Role: Genuine empty own aid

Source: Original blank own aid; no supplied numerical source or answer.

Title: My place-value or strategy space

V18

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: My part and whole. Four labelled, completely empty areas: My complete source and question; My known part and wanted part; My calculation or description; My original-equation check. No scale, predetermined parts, values or answer. Child chooses a useful representation. No values, answers, diagrams or claims of completed work are supplied. Write, draw, type in an accompanying page or use your usual communication; filling every area is optional.

Geometry: viewBox 0 0 1200 1450. Heading(44, 54). Four external 28 px label blocks at y 120, 430, 740, 1050(max 2 lines). Four empty rectangles x 44, y label+80, w 1112, h 210. Absolutely empty interiors: no text/marks/numbers/arrows/micro dots. Footer at 44, 1410 usual communication/private/pause/pass. Labels outside are exact: ["My complete source and question", "My known part and wanted part", "My calculation or description", "My original-equation check"] No scale, predetermined parts, values or answer. Child chooses a useful representation.

Id: V18

Role: Genuine empty own aid

Source: Original blank own aid; no supplied numerical source or answer.

Title: My part and whole

V19

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: My two versions. Four labelled, completely empty areas: First complete conditions and work; First check or interpretation; Second complete conditions and work; Second check or wanted next move. A second version is optional; blank first/second spaces do not supply history. No values, answers, diagrams or claims of completed work are supplied. Write, draw, type in an accompanying page or use your usual communication; filling every area is optional.

Geometry: viewBox 0 0 1200 1450. Heading(44, 54). Four external 28 px label blocks at y 120, 430, 740, 1050(max 2 lines). Four empty rectangles x 44, y label+80, w 1112, h 210. Absolutely empty interiors: no text/marks/numbers/arrows/micro dots. Footer at 44, 1410 usual communication/private/pause/pass. Labels outside are exact: ["First complete conditions and work", "First check or interpretation", "Second complete conditions and work", "Second check or wanted next move"] A second version is optional; blank first/second spaces do not supply history.

Id: V19

Role: Genuine empty own aid

Source: Original blank own aid; no supplied numerical source or answer.

Title: My two versions

V20

Actual status: Written full brief only; no rendering, Browser, human access trial or visual acceptance claimed.

Empty interiors: 4

Full alternative: A current local example. Four labelled, completely empty areas: Source, publisher, place, date, checked date and unit; Actual fact or authorised observation; Clearly fictional or future assumption and wanted question; My model, result, check and limits. An adult reviews the full primary source/permissions before use. No real local fact, stock, price or child data is prefilled. No values, answers, diagrams or claims of completed work are supplied. Write, draw, type in an accompanying page or use your usual communication; filling every area is optional.

Geometry: viewBox 0 0 1200 1450. Heading(44, 54). Four external 28 px label blocks at y 120, 430, 740, 1050(max 2 lines). Four empty rectangles x 44, y label+80, w 1112, h 210. Absolutely empty interiors: no text/marks/numbers/arrows/micro dots. Footer at 44, 1410 usual communication/private/pause/pass. Labels outside are exact: ["Source, publisher, place, date, checked date and unit", "Actual fact or authorised observation", "Clearly fictional or future assumption and wanted question", "My model, result, check and limits"] An adult reviews the full primary source/permissions before use. No real local fact, stock, price or child data is prefilled.

Id: V20

Role: Genuine empty own aid

Source: Original blank own aid; no supplied numerical source or answer.

Title: A current local example

National meanings, Queensland judgement and factual doors

Exact complete national selection

NATIONAL.json retains every138 canonical selected record, full HTML attributes/plain meaning, canonical pin and inherited acquisition metadata unchanged. NATIONAL-MEANINGS.md is a full reader, not a code-only list. RAW.json keeps every actual1650 cell slot with absent/present-empty/present-value distinctions, native cell attributes/styles/types/shared-string indices and full decoded values. NATIVE-XML.json keeps all138 complete native row-XML byte substrings with hashes and complete worksheet/shared-string identities. The current official workbook was actually acquired20013October2026, same exact inherited bytes/SHA db446882d2c00cf7c085a03e250e2442fda6c44011fc114680c46c1dc7a822c3 . Attribute-level equality verifies the selected records. Selection is not a full workbook curriculum-meaning review.

New partial teaching map

Day None

Code: AC9M4N01

Complete official meaning: recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4N02

Complete official meaning: explain and use the properties of odd and even numbers

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4N03

Complete official meaning: find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4N04

Complete official meaning: count by fractions including mixed numerals; locate and represent these fractions as numbers on number lines

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4N05

Complete official meaning: solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4N06

Complete official meaning: develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder

New scope: Partial additive scope: Days51–55 strategy choice/regrouping/difference,59–60 synthesis. No new multiplication/division coverage; optional Bench holds literal notes, not automatic calculation.

Day None

Code: AC9M4N07

Complete official meaning: choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions

New scope: Partial: Day53 scale estimates and Day59 tight budget/exact decision, C17/C18, C cases. Chosen rounding must explain reasonableness; estimate alone does not prove exact fit.

Day None

Code: AC9M4N08

Complete official meaning: use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation

New scope: Partial additive and whole-dollar modelling: Day59 supply/budget and Day60 own plans; C/D sources formulate, choose strategy, interpret and communicate. No new multiplicative modelling.

Day None

Code: AC9M4N09

Complete official meaning: follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4A01

Complete official meaning: find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations

New scope: Partial unknown addend/subtrahend/start/two-sided equality: Days56–58; B cases plus ordinary C11–C16. Known sides/unknown roles/substitution taught. No claim every equation form is mastered.

Day None

Code: AC9M4A02

Complete official meaning: recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4M01

Complete official meaning: interpret unmarked and partial units when measuring and comparing attributes of length, mass, capacity, duration and temperature, using scaled and digital instruments and appropriate units

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4M02

Complete official meaning: recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4M03

Complete official meaning: solve problems involving the duration of time including situations involving “am” and “pm” and conversions between units of time

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4M04

Complete official meaning: estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4SP01

Complete official meaning: represent and approximate composite shapes and objects in the environment, using combinations of familiar shapes and objects

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4SP02

Complete official meaning: create and interpret grid reference systems using grid references and directions to locate and describe positions and pathways

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4SP03

Complete official meaning: recognise line and rotational symmetry of shapes and create symmetrical patterns and pictures, using dynamic geometric software where appropriate

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4ST01

Complete official meaning: acquire data for categorical and discrete numerical variables to address a question of interest or purpose, using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4ST02

Complete official meaning: analyse the effectiveness of different displays or visualisations in illustrating and comparing data distributions, then discuss the shape of distributions and the variation in the data

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4ST03

Complete official meaning: conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4P01

Complete official meaning: describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Day None

Code: AC9M4P02

Complete official meaning: conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results

New scope: Not newly taught or assessed by this block. Full meaning retained for year planning; previous resource opportunities do not certify completion.

Full year achievement-standard boundary

By the end of Year 4, students use their understanding of place value to represent tenths and hundredths in decimal form and to multiply natural numbers by multiples of 10. They use mathematical modelling to solve financial and other practical problems , formulating the problem using number sentences, solving the problem choosing efficient strategies and interpreting the results in terms of the situation. Students use their proficiency with addition and multiplication facts to add and subtract, multiply and divide numbers efficiently. They choose rounding and estimation strategies to determine whether results of calculations are reasonable. Students use the properties of odd and even numbers. They recognise equivalent fractions and make connections between fraction and decimal notations. Students count and represent fractions on a number line. They find unknown values in numerical equations involving addition and subtraction. Students follow and create algorithms that generate sets of numbers and identify emerging patterns. They use scaled instruments and appropriate units to measure length, mass, capacity and temperature. Students measure and approximate perimeters and areas. They convert between units of time when solving problems involving duration. Students compare angles relative to a right angle using angle names. They represent and approximate shapes and objects in the environment. Students create and interpret grid references. They identify line and rotational symmetry in plane shapes and create symmetrical patterns. Students create many-to-one data displays, assess the suitability of displays for representing data and discuss the shape of distributions and variation in data. They use surveys and digital tools to generate categorical or discrete numerical data in statistical investigations and communicate their findings in context. Students order events or the outcomes of chance experiments in terms of likelihood and identify whether events are independent or dependent. They conduct repeated chance experiments and describe the variation in results.

The block offers actual future evidence only for the taught additive strategy/modelling, estimate and unknown-equation relationships. It does not complete the Year4 achievement standard. Fraction/decimal/place-multiplication/parity/algorithm opportunities earlier in the fixed tree remain partial. Measurement, space, statistics, chance and the other retained descriptions require their own instruction and actual evidence.

Queensland · using the guidance fairly

The April2025 official11-page standards-elaborations PDF was read as complete operative parsed text; all871 numbered lines are saved with actual web provenance. The two403DOCX responses remain unsuccessful acquisitions. No matrix-diagram inspection is inferred. The two-page March2023 alignment and three-page October2023 techniques/conditions were read in full operative parsed form; direct download403 is kept distinct from web success.

The standards elaborations support teacher on-balance judgement about qualities in a folio across the year/band, using opportunities actually taught and observed. Achievement-standard expectations relate to the C standard. Understanding, fluency, reasoning and problem-solving interact; correct calculator/Bench output, copied wording or an adult representation does not supply an unobserved learner proficiency. The32 original criteria are formative task-specific statements, not official calibrated A–E bands, grade conversions or causal progress measures.

Simple familiar tasks have few obvious elements and identifiable procedures with no needed interpretation/analysis. Complex familiar work has several elements and some interpretation/analysis within identifiable procedures or prior related experience. Complex unfamiliar work has unclear procedures and limited prior related experience, needing interpretation, clarification and analysis. Number size or route letter alone does not assign a complexity/band: actual prior experience, scaffolding, steps, representations and cross-strand links matter. Do not make route A/B/C permanent learner categories.

Schools choose range/balance and appropriate local contexts. The guidance lists project modes as written/spoken-signed/practical/multimodal and supervised modes as written/spoken-signed/practical. Teacher observation can contribute documented evidence against relevant achievement aspects. These everyday proposals are not official supervised assessments by default. Its suggested project up-to200 words/one-minute spoken-signed and supervised up-to40 minutes+5perusal/planning/instruction/up-to200total/50per short item are suggestions, not daily quotas or requirements to fill all boxes. Tasks may be staged and exact instructions read; longer responses do not necessarily offer better evidence. Practical work needs schools' current safety arrangements. Here paper descriptions, usual communication and agreed helper direction are fully available; no purchase, actual stock handling, recording or public display is required.

A real Australian fact with an original small application

The RBA's current education page gives Australian banknote denominations $5,$10,$20,$50,$100. Source: Reserve Bank of Australia2026, https://www.rba.gov.au/education/topics/banknotes/ , direct200 and narrow sentence verified13October2026. Optional ordinary application: use original plain number cards labelled20,50,10 dollars. The invented total is80dollars; to reach a hypothetical100-dollar target would need20more. Child can choose just one sum/check, use a card-count analogue or skip money. No actual banknote possession, design copying, current price, transaction, cash-handling skill or personal finance is claimed. Staff model20+50+10=80; inverse100−80=20. RBA images/designs are excluded; use plain original text/shapes only.

Local information that a teacher can review

Choose a narrow nonpersonal quantity from an actual current official publisher, or count an authorised shared fictional/ordinary collection.
Save the publisher/place/URL, date checked, complete quantity/unit and any uncertainty. If a source is undated or inaccessible, keep it held.
Check rights/permission before copying; a link or plain original paraphrase can suffice. Avoid pupil identities/location histories, FirstNations translations or cultural knowledge without authority.
Distinguish the real stated fact from original invented numbers and the child's actual observation. Verify arithmetic and compare a second primary source when conflict matters.
Restate the complete new situation and answer conditions. Test the prompt/criterion/art together; changes are not silently equivalent-difficulty forms. Record what remains unverified. This is a paper/edit workflow, not a live-data service. Council403/undated brochure are not current availability evidence.

Reuse, edits and review limits

Source notices and original reuse

SubjectNest by NeuroForgeIO Pty Ltd · Work it out. Make a useful note. · Year4 Mathematics resource11–12 / Days51–60 · written proposal edition1 ·13October2026. Source project https://neuroforge.io/subjectnest/ is not proof this proposal is published. Retain title/version, source, notices/licences and modification history.

Original education and code

©NeuroForgeIO Pty Ltd2026. Original AI-assisted teaching, original fictional situations, criteria, full next-teaching lessons, written read-aloud scripts and planned art/prose are CC BY4.0 https://creativecommons.org/licenses/by/4.0/ . Attribution: SubjectNest by NeuroForgeIO Pty Ltd. Copy/share/adapt/use commercially under the licence; retain copyright, attribution, source, licence and disclaimer notices, indicate changes, and do not imply endorsement. Full unchanged EDUCATION-LICENSE.txt applies, including as-is/as-available/liability limits as permitted by law. This covers company-held expression, not learner work, private data, outside copyright, logos, designs or communal cultural rights.

Original proposal literal constructor and checks are Apache2.0, ©NeuroForgeIO Pty Ltd2026. CODE-LICENSE.txt is the full unchanged legal code. Retain copyright/NOTICE/licence and identify modifications. No runtime library, font binary, outside media or RBA infrastructure/code is bundled. CC legal code retains its own legal-source CC0 dedication; legal texts are not company education.

ACARA attribution · full core/platform statements

© Australian Curriculum, Assessment and Reporting Authority (ACARA)2010 to present, unless otherwise indicated. This material was downloaded from the Australian Curriculum website https://www.australiancurriculum.edu.au/ (accessed13October2026; original retained workbook acquisition29September2026 remains unchanged in NATIONAL.json) and was modified: the selected138 complete records and actual1650 raw cell slots were extracted unchanged; plain-text readers remove HTML formatting; original mapping and resources were added. The material is licensed under CC BY4.0 Attribution4.0 International https://creativecommons.org/licenses/by/4.0/ . Version updates are tracked in the Curriculum version history section on the About the Australian Curriculum page of the Australian Curriculum website.

ACARA does not endorse any product that uses the Australian Curriculum or make any representations as to the quality of such products. Any product that uses material published on this website should not be taken to be affiliated with ACARA or have the sponsorship or approval of ACARA. It is up to each person to make their own assessment of the product, taking into account matters including, but not limited to, the version number and the degree to which the materials align with the content descriptions and achievement standards (where relevant). Where there is a claim of alignment, it is important to check that the materials align with the content descriptions and achievement standards (endorsed by all education Ministers), not the elaborations (examples provided by ACARA).

It is important to check the frequency with which the platform or app is updated and, if the platform or app allows users to download the Australian Curriculum to their portable device, how often and in what circumstances the user's device synchronises with the platform.

This is a dated snapshot with no automatic refresh or device synchronisation. Complete current terms https://www.australiancurriculum.edu.au/copyright-and-terms-of-use apply. National witnesses/meanings are ACARA material with an original reader scaffold, not company-authored meanings. Exact inherited metadata and dates stay in NATIONAL.json, with the new actual200 workbook receipt and direct native XML selection recorded separately in AUTHORITY-READS.json/RAW.json/NATIVE-XML.json.

Core CC does not include logos, trademarks or site design; third-party rights require their permission. National Literacy Learning Progressions may be BY-NC. Photos/videos/teacher-support resources are separately restricted, including unaltered personal/organisational non-commercial education conditions, no adaptation/sublicensing and outside-platform terms. None is bundled. ICIP is communally held: seek free prior informed consent, negotiate benefit/payment, attribute owners and consult about cultural integrity and the relevant published protocols. A public URL or CC label does not authorise cultural invention, translation or copying.

Queensland · verified equivalent official PDF

Modified from Year4 Mathematics achievement-standard alignment, March2023 https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/curriculum/ac9_maths_yr4_as_cd_alignment.pdf and Years3–4 Mathematics techniques/conditions, October2023 https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/assessment/ac9_maths_technique_cond_yr3-4.pdf , ©State of Queensland (QCAA)2023, https://www.qcaa.qld.edu.au/copyright , CC BY4.0. Modified from Year4 Mathematics standards elaborations, April2025 https://www.qcaa.qld.edu.au/downloads/aciqv9/mathematics/assessment/ac9_maths_se_yr4.pdf , ©State of Queensland (QCAA)2025, https://www.qcaa.qld.edu.au/copyright , CC BY4.0. Complete11-page operative parsed body read and preserved, all871 numbered lines; no matrix-diagram or native-PDF visual-plane inspection claim. Both refused403DOCX acquisitions are retained, not read DOCX bodies. Official PDF is the accepted equivalent operative primary source.

Current copyright operative meaning read13October2026; direct403 and web success are separate. Exceptions retain coats of arms/QCAA-QSA marks, third-party/alternative notices, stand-alone student images, student works and glossary definitions; student audio/video may be BY-ND4.0. None is bundled. Remove protected logos from adaptations and do not imply QCAA association/approval. Underlying ACARA content retains its own notice.

Real denomination fact and outside rights

Source: Reserve Bank of Australia2026, https://www.rba.gov.au/education/topics/banknotes/ ; current direct200 primary HTML acquired13October2026 and the narrow denomination sentence read. Australia has five banknote denominations: $5,$10,$20,$50,$100. This is an original paraphrase/link; the optional20+50+10=80 and100−80=20 model is invented and has no actual-money/purchase claim. RBA current copyright https://www.rba.gov.au/copyright/ permits most nonexcluded material under CC BY4.0 with RBA attribution/no endorsement, but banknote images/designs, logos, third-party material, multimedia/site infrastructure and special financial/model data retain separate conditions. No images, designs, media, scripts, logos or financial data are bundled. The earlier wrong404copyright URL and later web education timeouts remain failures, not successful reads. Correct200 primary receipts and successful rights web reading are separately preserved.

Council direct403 and an undated brochure remain held historical local candidates, not current opening/availability/observation facts. All routine child sources are fiction. An adult can review an authorised nonpersonal local quantity/date with publisher/place/URL/date-checked/unit, rights and a second source where disputed, then distinguish fact from invented calculation. No live local feed, automatic rights clearance, pupil-data collection or community translation is supplied.

Evidence and adaptation

Written source proposal only; no implemented interface, source art, raster/PDF bank, recorded narration, classroom/translation/AT/print/Browser acceptance, funder endorsement or learning-gain claim. Record actual learner choices, communication/support, helper work and exposed models honestly. Review timing/access/cultural/local/school suitability. Share proposed edits with resource ID/version/exact paragraph, changed wording, source/rights/date and reason, excluding children's personal work. Submission/review workflow is proposed, not an implemented sending action.