# Make a plan. Check it. Make it useful.

SubjectNest by NeuroForgeIO Pty Ltd · Year4 Mathematics · Weeks13–14 / Days61–70 · written proposal1 ·13October2026.

**Written proposal awaiting a different whole review.** No generated Source, rendered art, executable tool, recorded audio, native/print/AT/classroom use, publication or annual completion accepted by this author build.

Worked material is teacher-only. Hide it before own/held attempts. Use01for routine/access/support and record all hints.

## Day61 · A pack is more than a plus sign

**Purpose:** Model equal groups and a separate extra amount, then tell someone what the answer counts.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D61

Four reading corners each need six blank bookmarks. Keep three spare bookmarks at the teacher desk.

Place four paper circles on the desk. Give each circle six marks. Point to one circle and ask what the six counts; point to all four and ask what the four counts. Keep three separate marks outside the circles. Compare 4 + 6 + 3 with 6 + 6 + 6 + 6 + 3: the first counts the labels, not all the bookmarks. Write (4 × 6) + 3. Brackets show the equal-group total is found first. Invite a second strategy, such as double six and double again. Label both 24 and 27 with bookmarks.

**Model:** 4 × 6 + 3 = 27. 27 bookmarks: 24 in the four corners and 3 spare.

**Transfer probe:** If we add a fifth corner but keep three spare, what changes? Build it before calculating: 5 × 6 + 3 = 33 bookmarks.

**Watch for:** Counting the four groups as four extra objects; absorbing the three spare into every group; writing the correct number with no unit.

### Three complete learner briefs

**A:** Make three pretend craft trays with four paper pieces each and two spare pieces.

Teacher example: 3 × 4 + 2 = 14 paper pieces.

**B:** Plan five tiny building kits with five blocks each and four loose repair blocks.

Teacher example: 5 × 5 + 4 = 29 blocks.

**C:** Seven display panels each need eight caption cards; keep six spare cards.

Teacher example: 7 × 8 + 6 = 62 caption cards.

### Own, check and next

Use W01's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C01/C02 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H01/X01 are optional new settings, not compulsory extra workload.

## Day62 · How many packs can we make?

**Purpose:** When the amount in each group is known, find the number of complete groups and label that unknown.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D62

There are 36 game cards. Each packet must hold six cards. How many packets can be made?

Make one packet of six counters, then a second, without naming the total number of packets in advance. Keep making equal packets until all 36 are used. Circle each packet once while counting the six packets. Ask what the first six in 6 × 6 describes and what the second six describes: packets and cards per packet are different roles even when their values match. Show 6 × 6 = 36 and 36 ÷ 6 = 6 as a check. Include a contrast: knowing there are six packets would be a different question.

**Model:** 36 ÷ 6 = 6. 6 complete packets, each with 6 cards.

**Transfer probe:** Use 24 cards and six cards per packet. We need 4 packets; the answer counts packets, not cards in each.

**Watch for:** Writing '6 cards' for the unknown packets; drawing six groups merely because six appears in the question; stopping after one packet.

### Three complete learner briefs

**A:** Put 24 pretend tickets into envelopes that hold four tickets each.

Teacher example: 24 ÷ 4 = 6 envelopes; label the unknown role.

**B:** Arrange 42 seed-picture cards in sets of six for an indoor paper garden.

Teacher example: 42 ÷ 6 = 7 sets; label the unknown role.

**C:** Sort 72 event labels into bundles of eight labels each.

Teacher example: 72 ÷ 8 = 9 bundles; label the unknown role.

### Own, check and next

Use W02's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C03/C04 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H02/X02 are optional new settings, not compulsory extra workload.

## Day63 · Same total, a different missing part

**Purpose:** When the number of groups is known, find how many belong in each group and distinguish this from finding how many groups.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D63

Share 40 practice cards equally among five activity stations. How many cards does each station get?

Draw five empty station boxes before placing cards. Distribute one counter to each box in turn until 40 are placed, or use 5 × 8 = 40 to propose and check eight in each. Label the five boxes 'stations', not 'cards'. Beside it, draw the contrasting question: 40 cards, five in each packet, how many packets? That answer is eight packets. The equation can look the same while the unknown and unit change. Ask the learner to point to the actual unknown in each picture.

**Model:** 40 ÷ 5 = 8. 8 cards at each of the 5 stations.

**Transfer probe:** For 42 badges shared among six desks, the answer is 7 badges per desk. For 42 badges with six badges per bag, the answer is 7 bags. Both totals must still be 42.

**Watch for:** Making groups of five instead of making five groups; losing counters during sharing; assuming one equation fixes the answer's unit.

### Three complete learner briefs

**A:** Share 18 blank music cards equally among three rehearsal tables.

Teacher example: 18 ÷ 3 = 6 cards per table; label the unknown role.

**B:** Share 56 costume-design labels equally among seven workshop desks.

Teacher example: 56 ÷ 7 = 8 labels per desk; label the unknown role.

**C:** Share 81 puzzle cards equally among nine teams in a fictional club.

Teacher example: 81 ÷ 9 = 9 cards per team; label the unknown role.

### Own, check and next

Use W03's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C05/C06 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H03/X03 are optional new settings, not compulsory extra workload.

## Day64 · Split a big group into useful parts

**Purpose:** Choose and explain an efficient multiplication strategy instead of counting every item again.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D64

Four repair kits need 16 paper labels each. How many labels are needed?

Lay out four strips, each split into a block of ten and a block of six. Match 4 × 10 to the four tens and 4 × 6 to the four sixes. Join 40 and 24 to get 64. Compare double 16 = 32, then double 32 = 64. Accept either efficient strategy if the learner can connect its parts to the context. A recall chart or calculator may check after the learner has modelled; for the selected mental-strategy opportunity, first ask for a no-calculator explanation rather than awarding calculator output as that evidence.

**Model:** 4 × 16 = (4 × 10) + (4 × 6) = 64. 64 labels, with 16 in each of 4 kits.

**Transfer probe:** For 4 × 17, the four tens stay 40 and four sevens are 28, so 68 labels. The extra one in each kit adds four labels, not one.

**Watch for:** Splitting 16 into 10 + 6 but adding four only once; finding 40 + 6; naming a strategy without explaining how it matches the groups.

### Three complete learner briefs

**A:** Three art folders each need 14 caption cards.

Teacher example: 3 × 14 = 42 caption cards; explain how an efficient tens/ones or other strategy matches.

**B:** Six display trays each need 12 blank labels.

Teacher example: 6 × 12 = 72 labels; explain how an efficient tens/ones or other strategy matches.

**C:** Seven mini-game packs each need 13 counters.

Teacher example: 7 × 13 = 91 counters; explain how an efficient tens/ones or other strategy matches.

### Own, check and next

Use W04's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C07/C08 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H04/X04 are optional new settings, not compulsory extra workload.

## Day65 · Two workable plans

**Purpose:** Compare two equal-group plans, explain the unknown in each and make a decision for a stated purpose.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D65

Seat 48 paper toy travellers. A pretend shuttle model has eight places; another has twelve places. Every traveller needs one place.

Read the purpose aloud: choose the plan that uses fewer paper models while giving each traveller one place. Model both divisions, then multiply each result by its capacity. Ask which number means travellers, places per model and models. The answer is conditional on the supplied purpose; using fewer models is not a claim about real transport safety, costs, emissions or actual vehicles. Invite a second purpose, such as fitting a narrow paper shelf, but supply the shelf facts before deciding. Use toy figures, dots or spoken reasoning; nobody must act as a passenger.

**Model:** 48 ÷ 8 = 6; 48 ÷ 12 = 4. 6 eight-place models or 4 twelve-place models. Both seat exactly 48; four models meets the stated goal of using fewer models.

**Transfer probe:** If the purpose changes to using the eight-place models already available, six may be a sensible choice. Mathematical validity and a practical preference need separate reasons.

**Watch for:** Choosing the larger capacity without calculating; comparing 8 and 12 as if they were numbers of vehicles; importing unsupplied facts about real buses.

### Three complete learner briefs

**A:** Arrange 32 paper visitor tokens in rows of eight or rows of four. Choose fewer rows.

Teacher example: 32 ÷ 8 = 4 rows; 32 ÷ 4 = 8 rows. Both supply the required total; select fewer groups for the supplied purpose.

**B:** Seat 48 toy travellers in paper models with eight places or twelve places. Choose fewer models.

Teacher example: 48 ÷ 8 = 6 models; 48 ÷ 12 = 4 models. Both supply the required total; select fewer groups for the supplied purpose.

**C:** Bundle 72 blank cards in bundles of nine or bundles of eight. Choose fewer bundles.

Teacher example: 72 ÷ 9 = 8 bundles; 72 ÷ 8 = 9 bundles. Both supply the required total; select fewer groups for the supplied purpose.

### Own, check and next

Use W05's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C09/C10 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H05/X05 are optional new settings, not compulsory extra workload.

## Day66 · A useful pretend budget

**Purpose:** Model a repeated whole-dollar cost plus a one-off cost, calculate a total and interpret the amount left from a supplied budget.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D66

A fictional activity uses six kits at $7 each, plus one $9 setup charge. The pretend budget is $60.

Place six kit labels in a row and write $7 under each. Keep the one-off $9 charge on a separate card. Ask whether seven names kits or dollars per kit. Build the repeated cost as 6 × $7 = $42, then add $9 once. Compare the total with $60 before finding the difference. Clearly label all prices 'made up for maths'. They are not local shop prices, a family budget or a recommendation to buy anything. Use plain denomination words or tokens rather than images of banknotes.

**Model:** 6 × $7 + $9 = $51; $60 − $51 = $9. The plan costs $51 and leaves $9. The $9 setup charge is paid once.

**Transfer probe:** If the setup charge were $9 for each kit, the story and equation would change to 6 × ($7 + $9) = $96. Ask the learner to identify the wording that makes that a different model.

**Watch for:** Multiplying the one-off fee by six; adding 6 + 7 + 9; reporting $9 as the cost rather than the amount left.

### Three complete learner briefs

**A:** Four pretend kits cost $6 each, with one $5 fee. A supplied budget is $40.

Teacher example: 4 × $6 + $5 = $29; $11 left.

**B:** Seven pretend sets cost $8 each, with one $6 fee. A supplied budget is $70.

Teacher example: 7 × $8 + $6 = $62; $8 left.

**C:** Nine pretend packs cost $9 each, with one $8 fee. A supplied budget is $100.

Teacher example: 9 × $9 + $8 = $89; $11 left.

### Own, check and next

Use W06's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C11/C12 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H06/X06 are optional new settings, not compulsory extra workload.

## Day67 · An estimate is a check, not a receipt

**Purpose:** Choose and explain rounding or bounds, then recognise when an exact calculation is needed near a budget limit.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D67

Six pretend kits cost $19 each, plus one $7 fee. A supplied budget is $120.

Before the exact calculation, round each $19 price up to $20 and the $7 fee up to $10. Explain why the resulting $130 is an upper estimate. It exceeds $120, but an upper estimate alone cannot prove that the actual total exceeds $120. Now use 6 × 20 − 6 = 114, then add 7 to get 121. This exact result does establish an overrun of $1. Invite the learner to describe the direction of rounding. A different sensible estimate is acceptable when its role and limitations are explained.

**Model:** 6 × $19 + $7 = $121. The exact cost is $121, so it exceeds the $120 budget by $1. Rounding to 6 × $20 + $10 = $130 is a rough upper check, not the actual price.

**Transfer probe:** Four $18 kits plus a $7 fee cost $79. The upper rounded estimate $90 exceeds an $80 budget, yet the exact price fits. This counterexample prevents treating every upper estimate as a purchase decision.

**Watch for:** Calling an estimate the actual total; inferring 'cannot afford' solely from an upper estimate over budget; rounding a one-off fee once per kit.

### Three complete learner briefs

**A:** Four pretend kits cost $18 each, plus one $7 fee. The budget is $80.

Teacher example: 4 × $18 + $7 = $79; $1 left. Provided estimate $90 is a check, not the paid cost.

**B:** Six pretend sets cost $17 each, plus one $9 fee. The budget is $110.

Teacher example: 6 × $17 + $9 = $111; $1 over. Provided estimate $130 is a check, not the paid cost.

**C:** Eight pretend packs cost $23 each, plus one $12 fee. The budget is $200. Explain why rounding down to $170 is not enough to decide.

Teacher example: 8 × $23 + $12 = $196; $4 left. Provided estimate $170 is a check, not the paid cost.

### Own, check and next

Use W07's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C13/C14 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H07/X07 are optional new settings, not compulsory extra workload.

## Day68 · Compare the same amount

**Purpose:** Compare two whole-pack offers for the same required quantity and explain a whole-dollar unit cost.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D68

Offer A is six blank pens for a pretend $18. Offer B is four blank pens for a pretend $16. Exactly 12 pens are required; whole packs only.

Do not compare the ticket prices before reading the pack sizes. Draw the required 12 places. Use two six-packs and three four-packs, then calculate total costs. Find 18 ÷ 6 = 3 dollars per pen and 16 ÷ 4 = 4 dollars per pen as a second check. Label dollars per pen separately from dollars per pack. All divisions have no remainder; do not introduce recurring decimals or real pricing claims. Whole-pack prices are invented, and this is not a recommendation about a retailer.

**Model:** 2 × $18 = $36; 3 × $16 = $48. Both plans provide exactly 12 pens. Offer A costs $36, which is $12 less. Its unit cost is $3 per pen; B is $4 per pen.

**Transfer probe:** When a cheaper ticket price buys a smaller pack, it may cost more to buy the same quantity. Ask the learner to show the quantity and money totals side by side.

**Watch for:** Choosing $16 because it is the smaller ticket price; using one pack of each rather than equal quantities; omitting 'per pen' from unit cost.

### Three complete learner briefs

**A:** Exactly 15 paper cards are required. A has three cards for $9; B has five cards for $20. Whole packs only; all prices pretend.

Teacher example: A:5packs/$45; B:3packs/$60. Both supply exactly15 items. Whole-dollar unit costs A$3/B$4 per item.

**B:** Exactly 12 labels are required. A has four for $20; B has six for $24. Whole packs only; all prices pretend.

Teacher example: A:3packs/$60; B:2packs/$48. Both supply exactly12 items. Whole-dollar unit costs A$5/B$4 per item.

**C:** Exactly 24 game cards are required. A has eight for $24; B has six for $24. Whole packs only; all prices pretend.

Teacher example: A:3packs/$72; B:4packs/$96. Both supply exactly24 items. Whole-dollar unit costs A$3/B$4 per item.

### Own, check and next

Use W08's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C15/C16 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H08/X08 are optional new settings, not compulsory extra workload.

## Day69 · Find the step that went wrong

**Purpose:** Critique a supplied model and repair its meaning, calculation and contextual statement.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D69

Seven pretend kits cost $8 each and there is one $6 fee. A fictional learner writes '7 + 8 + 6 = 21, so the total is $21'.

Read the fictional work without naming or comparing real classmates. Ask the learner to mark which numbers describe objects and which describe money. Rebuild the seven equal $8 costs using blank strips; show why the plus-only model does not match. Accept a correction that keeps 8 + 8 + 8 + 8 + 8 + 8 + 8 + 6 before introducing a shorter number sentence. Then ask for an independent check, such as 7 × 10 − 7 × 2 + 6 = 62. The repair should explain the first mistaken step, not merely replace 21 with 62.

**Model:** 7 × $8 + $6 = $62. The error is treating seven kits as seven dollars. The seven repeated $8 costs total $56; add the one $6 fee to get $62.

**Transfer probe:** A correct multiplication followed by adding the fee seven times is a different error. Ask how the picture could show that the fee occurs only once.

**Watch for:** Correcting arithmetic on the wrong model; stating only 'multiply' with no role labels; criticism that targets a person instead of the supplied work.

### Three complete learner briefs

**A:** Five pretend packs cost $9 each plus one $4 fee. A fictional note uses 5 + 9 + 4 = 18.

Teacher example: 5 × $9 + $4 = $49. The supplied18 adds labels with unlike roles rather than repeated costs.

**B:** Eight pretend sets cost $6 each plus one $7 fee. A fictional note uses 8 + 6 + 7 = 21.

Teacher example: 8 × $6 + $7 = $55. The supplied21 adds labels with unlike roles rather than repeated costs.

**C:** Nine pretend kits cost $7 each plus one $8 fee. A fictional note uses 9 + 7 + 8 = 24.

Teacher example: 9 × $7 + $8 = $71. The supplied24 adds labels with unlike roles rather than repeated costs.

### Own, check and next

Use W09's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C17/C18 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H09/X09 are optional new settings, not compulsory extra workload.

## Day70 · Send a plan someone can actually use

**Purpose:** Choose a valid whole-pack plan, model its cost and budget check, and communicate assumptions and a useful decision.

**Materials:** scrap paper,labelled groups,suitable large counters; plain fictional price/fee cards when relevant. No bought kit,device or printer required.

### Demonstration · D70

A fictional club needs exactly 30 blank activity cards. Offer A sells six cards for $12; B sells ten for $25. There is one $8 setup fee and an $80 budget. Buy whole packs and no extra cards.

Give the complete brief before showing the worked model. Ask the learner to identify required quantity, whole-pack restriction, fee paid once and budget. Allow a diagram, counters, spoken plan, signed explanation or written table. Model both options, check counts and costs, and write a note with the selected packs, total, amount left or over, and assumptions. Ask for an estimate as a reasonableness check and distinguish it from the exact decision. Teacher mediation may read the brief or scribe dictated reasoning; record that help. Use the individual exit response after partner planning as evidence.

**Model:** A: 5 × $12 + $8 = $68; B: 3 × $25 + $8 = $83. A provides exactly 30 cards and leaves $12. B provides 30 but exceeds the budget by $3. Choose A for these supplied constraints.

**Transfer probe:** Change only the fee from $8 to $20: A becomes $80 exactly; B becomes $95. The quantity stays 30 and the fee still happens once. Invite the learner to say what changed and what stayed.

**Watch for:** Finding a cheap cost that supplies too few cards; forgetting the fee; treating the budget as money that must all be spent; supplying no assumptions or usable quantity.

### Three complete learner briefs

**A:** Exactly 24 labels are needed. A packs six for $10; B packs eight for $14. One $5 fee; budget $50; whole packs and no extra labels. Both plans fit: justify a choice for lower cost.

Teacher example: A:4packs/$45; B:3packs/$47. Both supply exactly24 items. Compare both full costs against$50; give amount left/over, a decision and assumptions.

**B:** Exactly 30 cards are needed. A packs six for $12; B packs ten for $25. One $8 fee; budget $80; whole packs and no extra cards.

Teacher example: A:5packs/$68; B:3packs/$83. Both supply exactly30 items. Compare both full costs against$80; give amount left/over, a decision and assumptions.

**C:** Exactly 48 tokens are needed. A packs eight for $18; B packs six for $15. One $9 fee; budget $120; whole packs and no extra tokens.

Teacher example: A:6packs/$117; B:8packs/$129. Both supply exactly48 items. Compare both full costs against$120; give amount left/over, a decision and assumptions.

### Own, check and next

Use W10's four empty spaces and a complete selected brief. Ask for known/unknown quantities, model, sentence/strategy, check and useful message. Use C19/C20 individually and record actual support; copied work is not independent evidence. If needed choose the corresponding V01–V08target/fullN01–N32fresh mini-lesson. H10/X10 are optional new settings, not compulsory extra workload.