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

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

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.

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.