Make a plan. Check it. Make it useful.Year 4 Maths · T2 W13–14 · Proposal origin / 03 assessment and next · Text version

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.

Local criteria / evidence

[ "Formulate: identify what is known, what is unknown, and what the quantities count; choose a model that matches the supplied situation.", "Solve: connect a representation with a correct number sentence and use a suitable efficient strategy; distinguish selected no-calculator evidence from a digital check.", "Check: choose an estimate, inverse operation or second representation appropriate to the day; explain its limits for a close budget decision.", "Interpret: give the result with a contextual unit and a usable conclusion that respects the stated constraints and assumptions." ]

Use teacher notes, learner models, photographs of work with consent, a short spoken/signed explanation, or written/typed response. Store only what is needed under the school’s existing policy; this proposal does not create student accounts or upload evidence. Group work informs teaching, while an individual response supports a claim about that learner. Record reading/scribing prompts, calculators, changed numbers, and whether a model was provided. These four local criteria are planning prompts, not calibrated official A–E bands. A single item or this block does not establish the Year4 annual standard.

All20individual exits

[ { "answer": 17, "context": "a fictional class activity", "criterion": "Model equal groups and a separate extra amount, then tell someone what the answer counts.", "day": 61, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C01", "kind": "extra", "parameters": [ 2, 7, 3 ], "prompt": "For a fictional class activity, make 2 groups with 7 items in each and keep 3 loose extras. Label the quantities, find the total and check.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "2 × 7 + 3 = 17 items; the extras are added once." }, { "answer": 22, "context": "a fictional community display", "criterion": "Model equal groups and a separate extra amount, then tell someone what the answer counts.", "day": 61, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C02", "kind": "extra", "parameters": [ 4, 5, 2 ], "prompt": "For a fictional community display, make 4 groups with 5 items in each and keep 2 loose extras. Label the quantities, find the total and check.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "4 × 5 + 2 = 22 items; the extras are added once." }, { "answer": 4, "context": "a fictional class activity", "criterion": "When the amount in each group is known, find the number of complete groups and label that unknown.", "day": 62, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C03", "kind": "group", "parameters": [ 28, 7 ], "prompt": "For a fictional class activity, 28 items go into groups of 7. How many complete groups? Label what is unknown and check.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "28 ÷ 7 = 4 groups; 4 × 7 = 28 items." }, { "answer": 6, "context": "a fictional community display", "criterion": "When the amount in each group is known, find the number of complete groups and label that unknown.", "day": 62, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C04", "kind": "group", "parameters": [ 54, 9 ], "prompt": "For a fictional community display, 54 items go into groups of 9. How many complete groups? Label what is unknown and check.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "54 ÷ 9 = 6 groups; 6 × 9 = 54 items." }, { "answer": 7, "context": "a fictional class activity", "criterion": "When the number of groups is known, find how many belong in each group and distinguish this from finding how many groups.", "day": 63, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C05", "kind": "share", "parameters": [ 28, 4 ], "prompt": "For a fictional class activity, share 28 items equally among 4 groups. Draw the known groups, find the amount per group and check.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "28 ÷ 4 = 7 items per group; 4 × 7 = 28 items." }, { "answer": 9, "context": "a fictional community display", "criterion": "When the number of groups is known, find how many belong in each group and distinguish this from finding how many groups.", "day": 63, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C06", "kind": "share", "parameters": [ 54, 6 ], "prompt": "For a fictional community display, share 54 items equally among 6 groups. Draw the known groups, find the amount per group and check.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "54 ÷ 6 = 9 items per group; 6 × 9 = 54 items." }, { "answer": 45, "context": "a fictional class activity", "criterion": "Choose and explain an efficient multiplication strategy instead of counting every item again.", "day": 64, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C07", "kind": "strategy", "parameters": [ 3, 15 ], "prompt": "For a fictional class activity, 3 groups need 15 items each. Use and explain an efficient strategy that matches the model.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "3 × 15 = 30 + 15 = 45 items, splitting each 15 into ten and 5." }, { "answer": 76, "context": "a fictional community display", "criterion": "Choose and explain an efficient multiplication strategy instead of counting every item again.", "day": 64, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C08", "kind": "strategy", "parameters": [ 4, 19 ], "prompt": "For a fictional community display, 4 groups need 19 items each. Use and explain an efficient strategy that matches the model.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "4 × 19 = 40 + 36 = 76 items, splitting each 19 into ten and 9." }, { "answer": 4, "context": "a fictional class activity", "criterion": "Label the unknown and interpret a group plan. This exit samples quantity-role understanding, not the complete two-plan comparison.", "day": 65, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C09", "kind": "group", "parameters": [ 32, 8 ], "prompt": "For a fictional class activity, 32 items go into groups of 8. How many complete groups? Label what is unknown and check.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "32 ÷ 8 = 4 groups; 4 × 8 = 32 items." }, { "answer": 8, "context": "a fictional community display", "criterion": "Label the unknown and interpret a group plan. This exit samples quantity-role understanding, not the complete two-plan comparison.", "day": 65, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C10", "kind": "share", "parameters": [ 32, 4 ], "prompt": "For a fictional community display, share 32 items equally among 4 groups. Draw the known groups, find the amount per group and check.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "32 ÷ 4 = 8 items per group; 4 × 8 = 32 items." }, { "answer": 31, "context": "a fictional class activity", "criterion": "Model a repeated whole-dollar cost plus a one-off cost, calculate a total and interpret the amount left from a supplied budget.", "day": 66, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C11", "kind": "budget", "parameters": [ 4, 7, 3, 40 ], "prompt": "4 pretend kits for a fictional class activity cost $7 each plus one $3 fee. Budget $40. Find cost and amount left or over; all prices fictional.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "4 × $7 + $3 = $31; $9 left. Fee once." }, { "answer": 49, "context": "a fictional community display", "criterion": "Model a repeated whole-dollar cost plus a one-off cost, calculate a total and interpret the amount left from a supplied budget.", "day": 66, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C12", "kind": "budget", "parameters": [ 5, 9, 4, 60 ], "prompt": "5 pretend kits for a fictional community display cost $9 each plus one $4 fee. Budget $60. Find cost and amount left or over; all prices fictional.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "5 × $9 + $4 = $49; $11 left. Fee once." }, { "answer": 78, "context": "a fictional class activity", "criterion": "Choose and explain rounding or bounds, then recognise when an exact calculation is needed near a budget limit.", "day": 67, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C13", "kind": "estimate", "parameters": [ 4, 19, 2, 80 ], "prompt": "4 pretend kits for a fictional class activity cost $19 each plus one $2 fee; budget $80. Round both prices up to whole tens, explain the check's limits and calculate exactly.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "Upper check $90 above the budget does not alone prove an overrun. Exact $78, $2 left." }, { "answer": 83, "context": "a fictional community display", "criterion": "Choose and explain rounding or bounds, then recognise when an exact calculation is needed near a budget limit.", "day": 67, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C14", "kind": "estimate", "parameters": [ 5, 16, 3, 80 ], "prompt": "5 pretend kits for a fictional community display cost $16 each plus one $3 fee; budget $80. Round both prices up to whole tens, explain the check's limits and calculate exactly.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "Upper check $110 above the budget does not alone prove an overrun. Exact $83, $3 over." }, { "answer": [ 36, 48 ], "context": "a fictional class activity", "criterion": "Compare two whole-pack offers for the same required quantity and explain a whole-dollar unit cost.", "day": 68, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C15", "kind": "offer", "parameters": [ 12, 3, 9, 4, 16 ], "prompt": "Need exactly 12 items for a fictional class activity. Pretend A packs 3 for $9; B packs 4 for $16. Whole packs and no extras. Compare full costs for the same quantity. Work out the whole-dollar cost of one item in each offer. Explain how those unit costs help you check the full-cost comparison.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "A:4 packs/$36. B:3 packs/$48. Both supply 12 items; A costs $12 less. A costs $9 ÷ 3 = $3 per item; B costs $16 ÷ 4 = $4 per item. For 12 items, 12 × $3 = $36 and 12 × $4 = $48, matching the whole-pack totals." }, { "answer": [ 72, 96 ], "context": "a fictional community display", "criterion": "Compare two whole-pack offers for the same required quantity and explain a whole-dollar unit cost.", "day": 68, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C16", "kind": "offer", "parameters": [ 24, 6, 18, 8, 32 ], "prompt": "Need exactly 24 items for a fictional community display. Pretend A packs 6 for $18; B packs 8 for $32. Whole packs and no extras. Compare full costs for the same quantity. Work out the whole-dollar cost of one item in each offer. Explain how those unit costs help you check the full-cost comparison.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "A:4 packs/$72. B:3 packs/$96. Both supply 24 items; A costs $24 less. A costs $18 ÷ 6 = $3 per item; B costs $32 ÷ 8 = $4 per item. For 24 items, 24 × $3 = $72 and 24 × $4 = $96, matching the whole-pack totals." }, { "answer": 53, "context": "a fictional class activity", "criterion": "Model the repeated cost and one-off fee. This exit samples an accurate model; the separate day task supplies critique evidence.", "day": 69, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C17", "kind": "budget", "parameters": [ 6, 8, 5, 60 ], "prompt": "6 pretend kits for a fictional class activity cost $8 each plus one $5 fee. Budget $60. Find cost and amount left or over; all prices fictional.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "6 × $8 + $5 = $53; $7 left. Fee once." }, { "answer": 67, "context": "a fictional community display", "criterion": "Model the repeated cost and one-off fee. This exit samples an accurate model; the separate day task supplies critique evidence.", "day": 69, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C18", "kind": "budget", "parameters": [ 7, 9, 4, 80 ], "prompt": "7 pretend kits for a fictional community display cost $9 each plus one $4 fee. Budget $80. Find cost and amount left or over; all prices fictional.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "7 × $9 + $4 = $67; $13 left. Fee once." }, { "answer": [ 45, 47 ], "context": "a fictional class activity", "criterion": "Choose a valid whole-pack plan, model its cost and budget check, and communicate assumptions and a useful decision.", "day": 70, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C19", "kind": "plan", "parameters": [ 24, 6, 10, 8, 14, 5, 50 ], "prompt": "For a fictional class activity, need exactly 24 items. Pretend A packs 6 for $10; B packs 8 for $14. One $5 fee, budget $50. Whole packs/no extras. Choose lower cost among valid plans; if tied choose fewer packs. Send a useful note.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "A:4 packs/$45, $5 left. B:3 packs/$47, $3 left. Both supply 24; choose A. State quantity and fee assumptions." }, { "answer": [ 79, 79 ], "context": "a fictional community display", "criterion": "Choose a valid whole-pack plan, model its cost and budget check, and communicate assumptions and a useful decision.", "day": 70, "evidence": "An individual response in a selected mode. Read/scribe if needed and record support; hide the teacher model first. Formative partial evidence, not an annual grade.", "id": "C20", "kind": "plan", "parameters": [ 36, 6, 12, 9, 18, 7, 80 ], "prompt": "For a fictional community display, need exactly 36 items. Pretend A packs 6 for $12; B packs 9 for $18. One $7 fee, budget $80. Whole packs/no extras. Choose lower cost among valid plans; if tied choose fewer packs. Send a useful note.", "prompt_limit": "Ask one neutral 'What does that amount count?' question if necessary and record it. Teach afterwards rather than covertly supplying the model.", "teacher_model": "A:6 packs/$79, $1 left. B:4 packs/$79, $1 left. Both supply 36; choose B. State quantity and fee assumptions." } ]

Eight modules /32held full chains

The full neutral brief and own prompts are separate from these teacher possibilities. Record actual familiarity/exposure/help; no official A–E or annual-grade claim.

V01 · Distinguish groups, items per group and loose extras

Criterion: Identify the roles of all three quantities and model the equal-group total before adding the separate extra.

{ "answer": 22, "context": "display packs and spare caption cards", "criterion": "Identify the roles of all three quantities and model the equal-group total before adding the separate extra.", "example": "3 × 6 + 4 = 22 items. The groups contain 18 items; 4 extras are added once.", "followup": "If this target needs more teaching, use N01.", "id": "V01A", "kind": "extra", "own_prompt": "For display packs and spare caption cards, make 3 groups with 6 items in each and keep 4 extra items outside the groups. Find the total; label what each number counts and show a check. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 3, 6, 4 ], "practice": "Keep 3 groups of 6, but add one more loose item. Find and explain the new total.", "practice_answer": 23, "practice_model": "3 × 6 + 5 = 23 items.", "prompt": "For display packs and spare caption cards, make 3 groups with 6 items in each and keep 4 extra items outside the groups. Find the total; label what each number counts and show a check.", "target": "Distinguish groups, items per group and loose extras", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 37, "context": "repair packs and spare labels", "criterion": "Identify the roles of all three quantities and model the equal-group total before adding the separate extra.", "example": "5 × 7 + 2 = 37 items. The groups contain 35 items; 2 extras are added once.", "followup": "If this target needs more teaching, use N02.", "id": "V01B", "kind": "extra", "own_prompt": "For repair packs and spare labels, make 5 groups with 7 items in each and keep 2 extra items outside the groups. Find the total; label what each number counts and show a check. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 5, 7, 2 ], "practice": "Keep 5 groups of 7, but add one more loose item. Find and explain the new total.", "practice_answer": 38, "practice_model": "5 × 7 + 3 = 38 items.", "prompt": "For repair packs and spare labels, make 5 groups with 7 items in each and keep 2 extra items outside the groups. Find the total; label what each number counts and show a check.", "target": "Distinguish groups, items per group and loose extras", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 51, "context": "game kits and loose counters", "criterion": "Identify the roles of all three quantities and model the equal-group total before adding the separate extra.", "example": "6 × 8 + 3 = 51 items. The groups contain 48 items; 3 extras are added once.", "followup": "If this target needs more teaching, use N03.", "id": "V01C", "kind": "extra", "own_prompt": "For game kits and loose counters, make 6 groups with 8 items in each and keep 3 extra items outside the groups. Find the total; label what each number counts and show a check. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 6, 8, 3 ], "practice": "Keep 6 groups of 8, but add one more loose item. Find and explain the new total.", "practice_answer": 52, "practice_model": "6 × 8 + 4 = 52 items.", "prompt": "For game kits and loose counters, make 6 groups with 8 items in each and keep 3 extra items outside the groups. Find the total; label what each number counts and show a check.", "target": "Distinguish groups, items per group and loose extras", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 77, "context": "garden-plan folders and spare picture cards", "criterion": "Identify the roles of all three quantities and model the equal-group total before adding the separate extra.", "example": "8 × 9 + 5 = 77 items. The groups contain 72 items; 5 extras are added once.", "followup": "If this target needs more teaching, use N04.", "id": "V01D", "kind": "extra", "own_prompt": "For garden-plan folders and spare picture cards, make 8 groups with 9 items in each and keep 5 extra items outside the groups. Find the total; label what each number counts and show a check. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 8, 9, 5 ], "practice": "Keep 8 groups of 9, but add one more loose item. Find and explain the new total.", "practice_answer": 78, "practice_model": "8 × 9 + 6 = 78 items.", "prompt": "For garden-plan folders and spare picture cards, make 8 groups with 9 items in each and keep 5 extra items outside the groups. Find the total; label what each number counts and show a check.", "target": "Distinguish groups, items per group and loose extras", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

V02 · Find how many groups, rather than how many in each

Criterion: Use the known total and group size to find and label the unknown number of complete groups.

{ "answer": 4, "context": "envelopes of pretend tickets", "criterion": "Use the known total and group size to find and label the unknown number of complete groups.", "example": "24 ÷ 6 = 4 groups; 4 × 6 = 24 items checks the total.", "followup": "If this target needs more teaching, use N05.", "id": "V02A", "kind": "group", "own_prompt": "For envelopes of pretend tickets, there are 24 items in total and 6 items in each complete group. How many groups can be made? Show the grouping and label the answer. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 24, 6 ], "practice": "A further complete group of 6 items arrives. With 30 items and 6 in each group, how many groups are there?", "practice_answer": 5, "practice_model": "30 ÷ 6 = 5 groups.", "prompt": "For envelopes of pretend tickets, there are 24 items in total and 6 items in each complete group. How many groups can be made? Show the grouping and label the answer.", "target": "Find how many groups, rather than how many in each", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 6, "context": "bundles of workshop labels", "criterion": "Use the known total and group size to find and label the unknown number of complete groups.", "example": "30 ÷ 5 = 6 groups; 6 × 5 = 30 items checks the total.", "followup": "If this target needs more teaching, use N06.", "id": "V02B", "kind": "group", "own_prompt": "For bundles of workshop labels, there are 30 items in total and 5 items in each complete group. How many groups can be made? Show the grouping and label the answer. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 30, 5 ], "practice": "A further complete group of 5 items arrives. With 35 items and 5 in each group, how many groups are there?", "practice_answer": 7, "practice_model": "35 ÷ 5 = 7 groups.", "prompt": "For bundles of workshop labels, there are 30 items in total and 5 items in each complete group. How many groups can be made? Show the grouping and label the answer.", "target": "Find how many groups, rather than how many in each", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 6, "context": "packs of game cards", "criterion": "Use the known total and group size to find and label the unknown number of complete groups.", "example": "48 ÷ 8 = 6 groups; 6 × 8 = 48 items checks the total.", "followup": "If this target needs more teaching, use N07.", "id": "V02C", "kind": "group", "own_prompt": "For packs of game cards, there are 48 items in total and 8 items in each complete group. How many groups can be made? Show the grouping and label the answer. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 48, 8 ], "practice": "A further complete group of 8 items arrives. With 56 items and 8 in each group, how many groups are there?", "practice_answer": 7, "practice_model": "56 ÷ 8 = 7 groups.", "prompt": "For packs of game cards, there are 48 items in total and 8 items in each complete group. How many groups can be made? Show the grouping and label the answer.", "target": "Find how many groups, rather than how many in each", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 8, "context": "sets of display pictures", "criterion": "Use the known total and group size to find and label the unknown number of complete groups.", "example": "72 ÷ 9 = 8 groups; 8 × 9 = 72 items checks the total.", "followup": "If this target needs more teaching, use N08.", "id": "V02D", "kind": "group", "own_prompt": "For sets of display pictures, there are 72 items in total and 9 items in each complete group. How many groups can be made? Show the grouping and label the answer. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 72, 9 ], "practice": "A further complete group of 9 items arrives. With 81 items and 9 in each group, how many groups are there?", "practice_answer": 9, "practice_model": "81 ÷ 9 = 9 groups.", "prompt": "For sets of display pictures, there are 72 items in total and 9 items in each complete group. How many groups can be made? Show the grouping and label the answer.", "target": "Find how many groups, rather than how many in each", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

V03 · Find the amount in each known group

Criterion: Make the stated number of groups first, share the total equally and label the result per group.

{ "answer": 6, "context": "cards shared among activity tables", "criterion": "Make the stated number of groups first, share the total equally and label the result per group.", "example": "30 ÷ 5 = 6 items per group; 5 × 6 = 30 items.", "followup": "If this target needs more teaching, use N09.", "id": "V03A", "kind": "share", "own_prompt": "For cards shared among activity tables, share 30 items equally among 5 groups. How many items does each group get? Draw the known groups first and label the answer per group. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 30, 5 ], "practice": "Give every one of the 5 groups one extra item. The new total is 35. Find the new amount per group.", "practice_answer": 7, "practice_model": "35 ÷ 5 = 7 items per group.", "prompt": "For cards shared among activity tables, share 30 items equally among 5 groups. How many items does each group get? Draw the known groups first and label the answer per group.", "target": "Find the amount in each known group", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 9, "context": "labels shared among repair desks", "criterion": "Make the stated number of groups first, share the total equally and label the result per group.", "example": "36 ÷ 4 = 9 items per group; 4 × 9 = 36 items.", "followup": "If this target needs more teaching, use N10.", "id": "V03B", "kind": "share", "own_prompt": "For labels shared among repair desks, share 36 items equally among 4 groups. How many items does each group get? Draw the known groups first and label the answer per group. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 36, 4 ], "practice": "Give every one of the 4 groups one extra item. The new total is 40. Find the new amount per group.", "practice_answer": 10, "practice_model": "40 ÷ 4 = 10 items per group.", "prompt": "For labels shared among repair desks, share 36 items equally among 4 groups. How many items does each group get? Draw the known groups first and label the answer per group.", "target": "Find the amount in each known group", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 6, "context": "picture tokens shared among game stations", "criterion": "Make the stated number of groups first, share the total equally and label the result per group.", "example": "42 ÷ 7 = 6 items per group; 7 × 6 = 42 items.", "followup": "If this target needs more teaching, use N11.", "id": "V03C", "kind": "share", "own_prompt": "For picture tokens shared among game stations, share 42 items equally among 7 groups. How many items does each group get? Draw the known groups first and label the answer per group. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 42, 7 ], "practice": "Give every one of the 7 groups one extra item. The new total is 49. Find the new amount per group.", "practice_answer": 7, "practice_model": "49 ÷ 7 = 7 items per group.", "prompt": "For picture tokens shared among game stations, share 42 items equally among 7 groups. How many items does each group get? Draw the known groups first and label the answer per group.", "target": "Find the amount in each known group", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 8, "context": "caption cards shared among display corners", "criterion": "Make the stated number of groups first, share the total equally and label the result per group.", "example": "64 ÷ 8 = 8 items per group; 8 × 8 = 64 items.", "followup": "If this target needs more teaching, use N12.", "id": "V03D", "kind": "share", "own_prompt": "For caption cards shared among display corners, share 64 items equally among 8 groups. How many items does each group get? Draw the known groups first and label the answer per group. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 64, 8 ], "practice": "Give every one of the 8 groups one extra item. The new total is 72. Find the new amount per group.", "practice_answer": 9, "practice_model": "72 ÷ 8 = 9 items per group.", "prompt": "For caption cards shared among display corners, share 64 items equally among 8 groups. How many items does each group get? Draw the known groups first and label the answer per group.", "target": "Find the amount in each known group", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

V04 · Connect an efficient strategy to a multiplicative model

Criterion: Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.

{ "answer": 52, "context": "caption cards for art folders", "criterion": "Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.", "example": "4 × 13 = 4 × 10 + 4 × 3 = 40 + 12 = 52 items. Another valid explained strategy is acceptable.", "followup": "If this target needs more teaching, use N13.", "id": "V04A", "kind": "strategy", "own_prompt": "For caption cards for art folders, 4 groups need 13 items each. Find the total using an efficient strategy and explain how its parts appear in the model. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 4, 13 ], "practice": "Keep 4 groups, with 14 items in each. Use the earlier strategy to find the new total and explain why it changes by 4.", "practice_answer": 56, "practice_model": "4 × 14 = 40 + 16 = 56 items.", "prompt": "For caption cards for art folders, 4 groups need 13 items each. Find the total using an efficient strategy and explain how its parts appear in the model.", "target": "Connect an efficient strategy to a multiplicative model", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 54, "context": "labels for repair kits", "criterion": "Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.", "example": "3 × 18 = 3 × 10 + 3 × 8 = 30 + 24 = 54 items. Another valid explained strategy is acceptable.", "followup": "If this target needs more teaching, use N14.", "id": "V04B", "kind": "strategy", "own_prompt": "For labels for repair kits, 3 groups need 18 items each. Find the total using an efficient strategy and explain how its parts appear in the model. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 3, 18 ], "practice": "Keep 3 groups, with 19 items in each. Use the earlier strategy to find the new total and explain why it changes by 3.", "practice_answer": 57, "practice_model": "3 × 19 = 30 + 27 = 57 items.", "prompt": "For labels for repair kits, 3 groups need 18 items each. Find the total using an efficient strategy and explain how its parts appear in the model.", "target": "Connect an efficient strategy to a multiplicative model", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 84, "context": "tokens for game packs", "criterion": "Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.", "example": "6 × 14 = 6 × 10 + 6 × 4 = 60 + 24 = 84 items. Another valid explained strategy is acceptable.", "followup": "If this target needs more teaching, use N15.", "id": "V04C", "kind": "strategy", "own_prompt": "For tokens for game packs, 6 groups need 14 items each. Find the total using an efficient strategy and explain how its parts appear in the model. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 6, 14 ], "practice": "Keep 6 groups, with 15 items in each. Use the earlier strategy to find the new total and explain why it changes by 6.", "practice_answer": 90, "practice_model": "6 × 15 = 60 + 30 = 90 items.", "prompt": "For tokens for game packs, 6 groups need 14 items each. Find the total using an efficient strategy and explain how its parts appear in the model.", "target": "Connect an efficient strategy to a multiplicative model", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 95, "context": "picture cards for learning trays", "criterion": "Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.", "example": "5 × 19 = 5 × 10 + 5 × 9 = 50 + 45 = 95 items. Another valid explained strategy is acceptable.", "followup": "If this target needs more teaching, use N16.", "id": "V04D", "kind": "strategy", "own_prompt": "For picture cards for learning trays, 5 groups need 19 items each. Find the total using an efficient strategy and explain how its parts appear in the model. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 5, 19 ], "practice": "Keep 5 groups, with 20 items in each. Use the earlier strategy to find the new total and explain why it changes by 5.", "practice_answer": 100, "practice_model": "5 × 20 = 50 + 50 = 100 items.", "prompt": "For picture cards for learning trays, 5 groups need 19 items each. Find the total using an efficient strategy and explain how its parts appear in the model.", "target": "Connect an efficient strategy to a multiplicative model", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

V05 · Keep a one-off cost separate and check a budget

Criterion: Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.

{ "answer": 29, "context": "pretend craft kits", "criterion": "Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.", "example": "3 × $8 + $5 = $29; $40 − $29 = $11 left. Fee paid once.", "followup": "If this target needs more teaching, use N17.", "id": "V05A", "kind": "budget", "own_prompt": "3 pretend craft kits cost a made-up $8 each plus one $5 fee. The supplied budget is $40. Find the exact cost and amount left or over. All prices are fictional. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 3, 8, 5, 40 ], "practice": "Only the one-off fee increases by $2 to $7. Same kits and budget. What changes and what stays?", "practice_answer": 31, "practice_model": "Total $31; $9 left. Kit count and repeated cost stay the same.", "prompt": "3 pretend craft kits cost a made-up $8 each plus one $5 fee. The supplied budget is $40. Find the exact cost and amount left or over. All prices are fictional.", "target": "Keep a one-off cost separate and check a budget", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 46, "context": "pretend display packs", "criterion": "Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.", "example": "6 × $7 + $4 = $46; $50 − $46 = $4 left. Fee paid once.", "followup": "If this target needs more teaching, use N18.", "id": "V05B", "kind": "budget", "own_prompt": "6 pretend display packs cost a made-up $7 each plus one $4 fee. The supplied budget is $50. Find the exact cost and amount left or over. All prices are fictional. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 6, 7, 4, 50 ], "practice": "Only the one-off fee increases by $2 to $6. Same kits and budget. What changes and what stays?", "practice_answer": 48, "practice_model": "Total $48; $2 left. Kit count and repeated cost stay the same.", "prompt": "6 pretend display packs cost a made-up $7 each plus one $4 fee. The supplied budget is $50. Find the exact cost and amount left or over. All prices are fictional.", "target": "Keep a one-off cost separate and check a budget", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 78, "context": "pretend repair sets", "criterion": "Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.", "example": "8 × $9 + $6 = $78; $80 − $78 = $2 left. Fee paid once.", "followup": "If this target needs more teaching, use N19.", "id": "V05C", "kind": "budget", "own_prompt": "8 pretend repair sets cost a made-up $9 each plus one $6 fee. The supplied budget is $80. Find the exact cost and amount left or over. All prices are fictional. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 8, 9, 6, 80 ], "practice": "Only the one-off fee increases by $2 to $8. Same kits and budget. What changes and what stays?", "practice_answer": 80, "practice_model": "Total $80; $0 left. Kit count and repeated cost stay the same.", "prompt": "8 pretend repair sets cost a made-up $9 each plus one $6 fee. The supplied budget is $80. Find the exact cost and amount left or over. All prices are fictional.", "target": "Keep a one-off cost separate and check a budget", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": 89, "context": "pretend mini-game kits", "criterion": "Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.", "example": "7 × $12 + $5 = $89; $100 − $89 = $11 left. Fee paid once.", "followup": "If this target needs more teaching, use N20.", "id": "V05D", "kind": "budget", "own_prompt": "7 pretend mini-game kits cost a made-up $12 each plus one $5 fee. The supplied budget is $100. Find the exact cost and amount left or over. All prices are fictional. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 7, 12, 5, 100 ], "practice": "Only the one-off fee increases by $2 to $7. Same kits and budget. What changes and what stays?", "practice_answer": 91, "practice_model": "Total $91; $9 left. Kit count and repeated cost stay the same.", "prompt": "7 pretend mini-game kits cost a made-up $12 each plus one $5 fee. The supplied budget is $100. Find the exact cost and amount left or over. All prices are fictional.", "target": "Keep a one-off cost separate and check a budget", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

V06 · Use an estimate without overstating what it decides

Criterion: Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.

{ "answer": 79, "context": "pretend activity kits", "criterion": "Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.", "example": "Upper check 4 × $20 + $10 = $90. It exceeds the budget but cannot alone prove an overrun. Exact cost $79, leaving $1.", "followup": "If this target needs more teaching, use N21.", "id": "V06A", "kind": "estimate", "own_prompt": "4 pretend activity kits cost a made-up $19 each plus one $3 fee. Budget $80. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 4, 19, 3, 80 ], "practice": "The budget changes to the exact total, $79; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.", "practice_answer": 0, "practice_model": "It fits exactly with $0 left. The upper estimate stays $90; it is a check, not the paid total.", "prompt": "4 pretend activity kits cost a made-up $19 each plus one $3 fee. Budget $80. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.", "target": "Use an estimate without overstating what it decides", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer.", "upper": 90 }

{ "answer": 91, "context": "pretend workshop packs", "criterion": "Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.", "example": "Upper check 5 × $20 + $10 = $110. It exceeds the budget but cannot alone prove an overrun. Exact cost $91, over by $1.", "followup": "If this target needs more teaching, use N22.", "id": "V06B", "kind": "estimate", "own_prompt": "5 pretend workshop packs cost a made-up $17 each plus one $6 fee. Budget $90. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 5, 17, 6, 90 ], "practice": "The budget changes to the exact total, $91; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.", "practice_answer": 0, "practice_model": "It fits exactly with $0 left. The upper estimate stays $110; it is a check, not the paid total.", "prompt": "5 pretend workshop packs cost a made-up $17 each plus one $6 fee. Budget $90. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.", "target": "Use an estimate without overstating what it decides", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer.", "upper": 110 }

{ "answer": 91, "context": "pretend display sets", "criterion": "Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.", "example": "Upper check 3 × $30 + $10 = $100. It exceeds the budget but cannot alone prove an overrun. Exact cost $91, leaving $4.", "followup": "If this target needs more teaching, use N23.", "id": "V06C", "kind": "estimate", "own_prompt": "3 pretend display sets cost a made-up $28 each plus one $7 fee. Budget $95. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 3, 28, 7, 95 ], "practice": "The budget changes to the exact total, $91; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.", "practice_answer": 0, "practice_model": "It fits exactly with $0 left. The upper estimate stays $100; it is a check, not the paid total.", "prompt": "3 pretend display sets cost a made-up $28 each plus one $7 fee. Budget $95. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.", "target": "Use an estimate without overstating what it decides", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer.", "upper": 100 }

{ "answer": 105, "context": "pretend game sets", "criterion": "Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.", "example": "Upper check 6 × $20 + $10 = $130. It exceeds the budget but cannot alone prove an overrun. Exact cost $105, over by $5.", "followup": "If this target needs more teaching, use N24.", "id": "V06D", "kind": "estimate", "own_prompt": "6 pretend game sets cost a made-up $16 each plus one $9 fee. Budget $100. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 6, 16, 9, 100 ], "practice": "The budget changes to the exact total, $105; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.", "practice_answer": 0, "practice_model": "It fits exactly with $0 left. The upper estimate stays $130; it is a check, not the paid total.", "prompt": "6 pretend game sets cost a made-up $16 each plus one $9 fee. Budget $100. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.", "target": "Use an estimate without overstating what it decides", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer.", "upper": 130 }

V07 · Compare equal quantities rather than ticket prices

Criterion: Use whole packs to supply the same target quantity and compare full costs with contextual units.

{ "answer": [ 54, 72 ], "context": "blank picture cards", "criterion": "Use whole packs to supply the same target quantity and compare full costs with contextual units.", "example": "A:3 packs,18 items,$54. B:6 packs,18 items,$72. A costs $18 less.", "followup": "If this target needs more teaching, use N25.", "id": "V07A", "kind": "offer", "own_prompt": "Exactly 18 blank picture cards are required. Offer A: 6 for a made-up $18; B: 3 for $12. Whole packs only and no extras. Compare full costs and explain the cheaper plan. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 18, 6, 18, 3, 12 ], "practice": "Exactly 36 items are now required, with the same whole-pack offers. Compare again.", "practice_answer": [ 108, 144 ], "practice_model": "A:6 packs/$108; B:12 packs/$144; quantities both 36.", "prompt": "Exactly 18 blank picture cards are required. Offer A: 6 for a made-up $18; B: 3 for $12. Whole packs only and no extras. Compare full costs and explain the cheaper plan.", "target": "Compare equal quantities rather than ticket prices", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": [ 96, 72 ], "context": "repair labels", "criterion": "Use whole packs to supply the same target quantity and compare full costs with contextual units.", "example": "A:3 packs,24 items,$96. B:4 packs,24 items,$72. B costs $24 less.", "followup": "If this target needs more teaching, use N26.", "id": "V07B", "kind": "offer", "own_prompt": "Exactly 24 repair labels are required. Offer A: 8 for a made-up $32; B: 6 for $18. Whole packs only and no extras. Compare full costs and explain the cheaper plan. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 24, 8, 32, 6, 18 ], "practice": "Exactly 48 items are now required, with the same whole-pack offers. Compare again.", "practice_answer": [ 192, 144 ], "practice_model": "A:6 packs/$192; B:8 packs/$144; quantities both 48.", "prompt": "Exactly 24 repair labels are required. Offer A: 8 for a made-up $32; B: 6 for $18. Whole packs only and no extras. Compare full costs and explain the cheaper plan.", "target": "Compare equal quantities rather than ticket prices", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": [ 80, 60 ], "context": "game counters", "criterion": "Use whole packs to supply the same target quantity and compare full costs with contextual units.", "example": "A:5 packs,20 items,$80. B:4 packs,20 items,$60. B costs $20 less.", "followup": "If this target needs more teaching, use N27.", "id": "V07C", "kind": "offer", "own_prompt": "Exactly 20 game counters are required. Offer A: 4 for a made-up $16; B: 5 for $15. Whole packs only and no extras. Compare full costs and explain the cheaper plan. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 20, 4, 16, 5, 15 ], "practice": "Exactly 40 items are now required, with the same whole-pack offers. Compare again.", "practice_answer": [ 160, 120 ], "practice_model": "A:10 packs/$160; B:8 packs/$120; quantities both 40.", "prompt": "Exactly 20 game counters are required. Offer A: 4 for a made-up $16; B: 5 for $15. Whole packs only and no extras. Compare full costs and explain the cheaper plan.", "target": "Compare equal quantities rather than ticket prices", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": [ 90, 120 ], "context": "caption cards", "criterion": "Use whole packs to supply the same target quantity and compare full costs with contextual units.", "example": "A:6 packs,30 items,$90. B:5 packs,30 items,$120. A costs $30 less.", "followup": "If this target needs more teaching, use N28.", "id": "V07D", "kind": "offer", "own_prompt": "Exactly 30 caption cards are required. Offer A: 5 for a made-up $15; B: 6 for $24. Whole packs only and no extras. Compare full costs and explain the cheaper plan. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 30, 5, 15, 6, 24 ], "practice": "Exactly 60 items are now required, with the same whole-pack offers. Compare again.", "practice_answer": [ 180, 240 ], "practice_model": "A:12 packs/$180; B:10 packs/$240; quantities both 60.", "prompt": "Exactly 30 caption cards are required. Offer A: 5 for a made-up $15; B: 6 for $24. Whole packs only and no extras. Compare full costs and explain the cheaper plan.", "target": "Compare equal quantities rather than ticket prices", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

V08 · Communicate a plan that satisfies the whole brief

Criterion: Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.

{ "answer": [ 54, 66 ], "choice": "A", "context": "a fictional caption display", "criterion": "Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.", "example": "A:4 packs,24 items,$54,$6 left. B:3 packs,24 items,$66,$6 over. Choose A. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide.", "followup": "If this target needs more teaching, use N29.", "id": "V08A", "kind": "plan", "own_prompt": "For a fictional caption display, need exactly 24 items. A packs 6 for a made-up $12; B packs 8 for $20. One $6 fee for either plan; budget $60. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 24, 6, 12, 8, 20, 6, 60 ], "practice": "Only the fee rises by $2 to $8, and the budget rises by $2 to $62. Recheck quantities, costs and amounts left.", "practice_answer": [ 56, 68 ], "practice_model": "Quantity and pack counts unchanged. Both costs and budget rise by $2, so each budget difference and the original decision stay the same.", "prompt": "For a fictional caption display, need exactly 24 items. A packs 6 for a made-up $12; B packs 8 for $20. One $6 fee for either plan; budget $60. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note.", "target": "Communicate a plan that satisfies the whole brief", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": [ 65, 95 ], "choice": "A", "context": "a fictional activity club", "criterion": "Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.", "example": "A:6 packs,30 items,$65,$5 left. B:5 packs,30 items,$95,$25 over. Choose A. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide.", "followup": "If this target needs more teaching, use N30.", "id": "V08B", "kind": "plan", "own_prompt": "For a fictional activity club, need exactly 30 items. A packs 5 for a made-up $10; B packs 6 for $18. One $5 fee for either plan; budget $70. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 30, 5, 10, 6, 18, 5, 70 ], "practice": "Only the fee rises by $2 to $7, and the budget rises by $2 to $72. Recheck quantities, costs and amounts left.", "practice_answer": [ 67, 97 ], "practice_model": "Quantity and pack counts unchanged. Both costs and budget rise by $2, so each budget difference and the original decision stay the same.", "prompt": "For a fictional activity club, need exactly 30 items. A packs 5 for a made-up $10; B packs 6 for $18. One $5 fee for either plan; budget $70. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note.", "target": "Communicate a plan that satisfies the whole brief", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": [ 79, 79 ], "choice": "B", "context": "a fictional quiet game session", "criterion": "Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.", "example": "A:6 packs,36 items,$79,$1 left. B:4 packs,36 items,$79,$1 left. Choose B. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide.", "followup": "If this target needs more teaching, use N31.", "id": "V08C", "kind": "plan", "own_prompt": "For a fictional quiet game session, need exactly 36 items. A packs 6 for a made-up $12; B packs 9 for $18. One $7 fee for either plan; budget $80. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 36, 6, 12, 9, 18, 7, 80 ], "practice": "Only the fee rises by $2 to $9, and the budget rises by $2 to $82. Recheck quantities, costs and amounts left.", "practice_answer": [ 81, 81 ], "practice_model": "Quantity and pack counts unchanged. Both costs and budget rise by $2, so each budget difference and the original decision stay the same.", "prompt": "For a fictional quiet game session, need exactly 36 items. A packs 6 for a made-up $12; B packs 9 for $18. One $7 fee for either plan; budget $80. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note.", "target": "Communicate a plan that satisfies the whole brief", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

{ "answer": [ 105, 129 ], "choice": "A", "context": "a fictional repair demonstration", "criterion": "Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.", "example": "A:6 packs,48 items,$105,$5 left. B:8 packs,48 items,$129,$19 over. Choose A. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide.", "followup": "If this target needs more teaching, use N32.", "id": "V08D", "kind": "plan", "own_prompt": "For a fictional repair demonstration, need exactly 48 items. A packs 8 for a made-up $16; B packs 6 for $15. One $9 fee for either plan; budget $110. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note. Leave the four learner spaces blank: model; number sentence and strategy; check; message to the organiser.", "parameters": [ 48, 8, 16, 6, 15, 9, 110 ], "practice": "Only the fee rises by $2 to $11, and the budget rises by $2 to $112. Recheck quantities, costs and amounts left.", "practice_answer": [ 107, 131 ], "practice_model": "Quantity and pack counts unchanged. Both costs and budget rise by $2, so each budget difference and the original decision stay the same.", "prompt": "For a fictional repair demonstration, need exactly 48 items. A packs 8 for a made-up $16; B packs 6 for $15. One $9 fee for either plan; budget $110. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note.", "target": "Communicate a plan that satisfies the whole brief", "teacher": "Treat the worked model as one acceptable example, not an exhaustive answer list. Accept an equivalent accurate representation and explanation. Record actual reasoning, help and units; do not infer mastery from a copied answer." }

All32complete new-source next lessons

Teach the new example, then remove its model before the changed own attempt. Record prompts and demand changes. A different numeral is not proof of unfamiliarity.

N01 after V01A

{ "answer": 19, "context": "repair packs and spare labels", "criterion": "Identify the roles of all three quantities and model the equal-group total before adding the separate extra.", "from": "V01A", "id": "N01", "kind": "extra", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For repair packs and spare labels, make 2 groups with 8 items in each and keep 3 extra items outside the groups. Find the total; label what each number counts and show a check.", "parameters": [ 2, 8, 3 ], "practice_answer": 20, "practice_model": "2 × 8 + 4 = 20 items.", "practice_prompt": "Keep 2 groups of 8, but add one more loose item. Find and explain the new total.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Distinguish groups, items per group and loose extras", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Put one label on each group, another on the amount in each, and a separate label on the loose amount. Keep the loose amount physically outside every group. Reconstruct one group before building the rest.", "Build the supplied new example together. Teacher explanation: 2 × 8 + 3 = 19 items. The groups contain 16 items; 3 extras are added once. Ask the learner to point to the part of the model that supports each quantity. A sum of the three printed numbers counts unlike roles; adding the spare amount to every group changes the brief.", "Remove the worked example. Give this changed task privately: Keep 2 groups of 8, but add one more loose item. Find and explain the new total. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "2 × 8 + 3 = 19 items. The groups contain 16 items; 3 extras are added once.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N02 after V01B

{ "answer": 41, "context": "game kits and loose counters", "criterion": "Identify the roles of all three quantities and model the equal-group total before adding the separate extra.", "from": "V01B", "id": "N02", "kind": "extra", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For game kits and loose counters, make 4 groups with 9 items in each and keep 5 extra items outside the groups. Find the total; label what each number counts and show a check.", "parameters": [ 4, 9, 5 ], "practice_answer": 42, "practice_model": "4 × 9 + 6 = 42 items.", "practice_prompt": "Keep 4 groups of 9, but add one more loose item. Find and explain the new total.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Distinguish groups, items per group and loose extras", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Put one label on each group, another on the amount in each, and a separate label on the loose amount. Keep the loose amount physically outside every group. Reconstruct one group before building the rest.", "Build the supplied new example together. Teacher explanation: 4 × 9 + 5 = 41 items. The groups contain 36 items; 5 extras are added once. Ask the learner to point to the part of the model that supports each quantity. A sum of the three printed numbers counts unlike roles; adding the spare amount to every group changes the brief.", "Remove the worked example. Give this changed task privately: Keep 4 groups of 9, but add one more loose item. Find and explain the new total. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "4 × 9 + 5 = 41 items. The groups contain 36 items; 5 extras are added once.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N03 after V01C

{ "answer": 46, "context": "garden-plan folders and spare picture cards", "criterion": "Identify the roles of all three quantities and model the equal-group total before adding the separate extra.", "from": "V01C", "id": "N03", "kind": "extra", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For garden-plan folders and spare picture cards, make 7 groups with 6 items in each and keep 4 extra items outside the groups. Find the total; label what each number counts and show a check.", "parameters": [ 7, 6, 4 ], "practice_answer": 47, "practice_model": "7 × 6 + 5 = 47 items.", "practice_prompt": "Keep 7 groups of 6, but add one more loose item. Find and explain the new total.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Distinguish groups, items per group and loose extras", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Put one label on each group, another on the amount in each, and a separate label on the loose amount. Keep the loose amount physically outside every group. Reconstruct one group before building the rest.", "Build the supplied new example together. Teacher explanation: 7 × 6 + 4 = 46 items. The groups contain 42 items; 4 extras are added once. Ask the learner to point to the part of the model that supports each quantity. A sum of the three printed numbers counts unlike roles; adding the spare amount to every group changes the brief.", "Remove the worked example. Give this changed task privately: Keep 7 groups of 6, but add one more loose item. Find and explain the new total. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "7 × 6 + 4 = 46 items. The groups contain 42 items; 4 extras are added once.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N04 after V01D

{ "answer": 69, "context": "display packs and spare caption cards", "criterion": "Identify the roles of all three quantities and model the equal-group total before adding the separate extra.", "from": "V01D", "id": "N04", "kind": "extra", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For display packs and spare caption cards, make 9 groups with 7 items in each and keep 6 extra items outside the groups. Find the total; label what each number counts and show a check.", "parameters": [ 9, 7, 6 ], "practice_answer": 70, "practice_model": "9 × 7 + 7 = 70 items.", "practice_prompt": "Keep 9 groups of 7, but add one more loose item. Find and explain the new total.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Distinguish groups, items per group and loose extras", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Put one label on each group, another on the amount in each, and a separate label on the loose amount. Keep the loose amount physically outside every group. Reconstruct one group before building the rest.", "Build the supplied new example together. Teacher explanation: 9 × 7 + 6 = 69 items. The groups contain 63 items; 6 extras are added once. Ask the learner to point to the part of the model that supports each quantity. A sum of the three printed numbers counts unlike roles; adding the spare amount to every group changes the brief.", "Remove the worked example. Give this changed task privately: Keep 9 groups of 7, but add one more loose item. Find and explain the new total. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "9 × 7 + 6 = 69 items. The groups contain 63 items; 6 extras are added once.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N05 after V02A

{ "answer": 6, "context": "bundles of workshop labels", "criterion": "Use the known total and group size to find and label the unknown number of complete groups.", "from": "V02A", "id": "N05", "kind": "group", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For bundles of workshop labels, there are 18 items in total and 3 items in each complete group. How many groups can be made? Show the grouping and label the answer.", "parameters": [ 18, 3 ], "practice_answer": 7, "practice_model": "21 ÷ 3 = 7 groups.", "practice_prompt": "A further complete group of 3 items arrives. With 21 items and 3 in each group, how many groups are there?", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Find how many groups, rather than how many in each", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Make one complete group of the supplied size, move it away, and repeat until the total is used. Count the groups, not the individual pieces again. Label the answer as groups.", "Build the supplied new example together. Teacher explanation: 18 ÷ 3 = 6 groups; 6 × 3 = 18 items checks the total. Ask the learner to point to the part of the model that supports each quantity. Do not draw a number of groups just because the group-size number appears in the question.", "Remove the worked example. Give this changed task privately: A further complete group of 3 items arrives. With 21 items and 3 in each group, how many groups are there? Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "18 ÷ 3 = 6 groups; 6 × 3 = 18 items checks the total.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N06 after V02B

{ "answer": 8, "context": "packs of game cards", "criterion": "Use the known total and group size to find and label the unknown number of complete groups.", "from": "V02B", "id": "N06", "kind": "group", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For packs of game cards, there are 40 items in total and 5 items in each complete group. How many groups can be made? Show the grouping and label the answer.", "parameters": [ 40, 5 ], "practice_answer": 9, "practice_model": "45 ÷ 5 = 9 groups.", "practice_prompt": "A further complete group of 5 items arrives. With 45 items and 5 in each group, how many groups are there?", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Find how many groups, rather than how many in each", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Make one complete group of the supplied size, move it away, and repeat until the total is used. Count the groups, not the individual pieces again. Label the answer as groups.", "Build the supplied new example together. Teacher explanation: 40 ÷ 5 = 8 groups; 8 × 5 = 40 items checks the total. Ask the learner to point to the part of the model that supports each quantity. Do not draw a number of groups just because the group-size number appears in the question.", "Remove the worked example. Give this changed task privately: A further complete group of 5 items arrives. With 45 items and 5 in each group, how many groups are there? Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "40 ÷ 5 = 8 groups; 8 × 5 = 40 items checks the total.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N07 after V02C

{ "answer": 8, "context": "sets of display pictures", "criterion": "Use the known total and group size to find and label the unknown number of complete groups.", "from": "V02C", "id": "N07", "kind": "group", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For sets of display pictures, there are 56 items in total and 7 items in each complete group. How many groups can be made? Show the grouping and label the answer.", "parameters": [ 56, 7 ], "practice_answer": 9, "practice_model": "63 ÷ 7 = 9 groups.", "practice_prompt": "A further complete group of 7 items arrives. With 63 items and 7 in each group, how many groups are there?", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Find how many groups, rather than how many in each", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Make one complete group of the supplied size, move it away, and repeat until the total is used. Count the groups, not the individual pieces again. Label the answer as groups.", "Build the supplied new example together. Teacher explanation: 56 ÷ 7 = 8 groups; 8 × 7 = 56 items checks the total. Ask the learner to point to the part of the model that supports each quantity. Do not draw a number of groups just because the group-size number appears in the question.", "Remove the worked example. Give this changed task privately: A further complete group of 7 items arrives. With 63 items and 7 in each group, how many groups are there? Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "56 ÷ 7 = 8 groups; 8 × 7 = 56 items checks the total.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N08 after V02D

{ "answer": 7, "context": "envelopes of pretend tickets", "criterion": "Use the known total and group size to find and label the unknown number of complete groups.", "from": "V02D", "id": "N08", "kind": "group", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For envelopes of pretend tickets, there are 63 items in total and 9 items in each complete group. How many groups can be made? Show the grouping and label the answer.", "parameters": [ 63, 9 ], "practice_answer": 8, "practice_model": "72 ÷ 9 = 8 groups.", "practice_prompt": "A further complete group of 9 items arrives. With 72 items and 9 in each group, how many groups are there?", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Find how many groups, rather than how many in each", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Make one complete group of the supplied size, move it away, and repeat until the total is used. Count the groups, not the individual pieces again. Label the answer as groups.", "Build the supplied new example together. Teacher explanation: 63 ÷ 9 = 7 groups; 7 × 9 = 63 items checks the total. Ask the learner to point to the part of the model that supports each quantity. Do not draw a number of groups just because the group-size number appears in the question.", "Remove the worked example. Give this changed task privately: A further complete group of 9 items arrives. With 72 items and 9 in each group, how many groups are there? Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "63 ÷ 9 = 7 groups; 7 × 9 = 63 items checks the total.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N09 after V03A

{ "answer": 5, "context": "labels shared among repair desks", "criterion": "Make the stated number of groups first, share the total equally and label the result per group.", "from": "V03A", "id": "N09", "kind": "share", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For labels shared among repair desks, share 20 items equally among 4 groups. How many items does each group get? Draw the known groups first and label the answer per group.", "parameters": [ 20, 4 ], "practice_answer": 6, "practice_model": "24 ÷ 4 = 6 items per group.", "practice_prompt": "Give every one of the 4 groups one extra item. The new total is 24. Find the new amount per group.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Find the amount in each known group", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Draw exactly the stated number of empty group boxes before moving any marks. Share one round to every box, then use a fact or equal batches to complete the share. Check that the number of boxes did not change.", "Build the supplied new example together. Teacher explanation: 20 ÷ 4 = 5 items per group; 4 × 5 = 20 items. Ask the learner to point to the part of the model that supports each quantity. Finding the amount per group is different from finding how many groups can be made, even if both number sentences look alike.", "Remove the worked example. Give this changed task privately: Give every one of the 4 groups one extra item. The new total is 24. Find the new amount per group. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "20 ÷ 4 = 5 items per group; 4 × 5 = 20 items.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N10 after V03B

{ "answer": 9, "context": "picture tokens shared among game stations", "criterion": "Make the stated number of groups first, share the total equally and label the result per group.", "from": "V03B", "id": "N10", "kind": "share", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For picture tokens shared among game stations, share 54 items equally among 6 groups. How many items does each group get? Draw the known groups first and label the answer per group.", "parameters": [ 54, 6 ], "practice_answer": 10, "practice_model": "60 ÷ 6 = 10 items per group.", "practice_prompt": "Give every one of the 6 groups one extra item. The new total is 60. Find the new amount per group.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Find the amount in each known group", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Draw exactly the stated number of empty group boxes before moving any marks. Share one round to every box, then use a fact or equal batches to complete the share. Check that the number of boxes did not change.", "Build the supplied new example together. Teacher explanation: 54 ÷ 6 = 9 items per group; 6 × 9 = 54 items. Ask the learner to point to the part of the model that supports each quantity. Finding the amount per group is different from finding how many groups can be made, even if both number sentences look alike.", "Remove the worked example. Give this changed task privately: Give every one of the 6 groups one extra item. The new total is 60. Find the new amount per group. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "54 ÷ 6 = 9 items per group; 6 × 9 = 54 items.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N11 after V03C

{ "answer": 5, "context": "caption cards shared among display corners", "criterion": "Make the stated number of groups first, share the total equally and label the result per group.", "from": "V03C", "id": "N11", "kind": "share", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For caption cards shared among display corners, share 45 items equally among 9 groups. How many items does each group get? Draw the known groups first and label the answer per group.", "parameters": [ 45, 9 ], "practice_answer": 6, "practice_model": "54 ÷ 9 = 6 items per group.", "practice_prompt": "Give every one of the 9 groups one extra item. The new total is 54. Find the new amount per group.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Find the amount in each known group", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Draw exactly the stated number of empty group boxes before moving any marks. Share one round to every box, then use a fact or equal batches to complete the share. Check that the number of boxes did not change.", "Build the supplied new example together. Teacher explanation: 45 ÷ 9 = 5 items per group; 9 × 5 = 45 items. Ask the learner to point to the part of the model that supports each quantity. Finding the amount per group is different from finding how many groups can be made, even if both number sentences look alike.", "Remove the worked example. Give this changed task privately: Give every one of the 9 groups one extra item. The new total is 54. Find the new amount per group. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "45 ÷ 9 = 5 items per group; 9 × 5 = 45 items.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N12 after V03D

{ "answer": 9, "context": "cards shared among activity tables", "criterion": "Make the stated number of groups first, share the total equally and label the result per group.", "from": "V03D", "id": "N12", "kind": "share", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For cards shared among activity tables, share 72 items equally among 8 groups. How many items does each group get? Draw the known groups first and label the answer per group.", "parameters": [ 72, 8 ], "practice_answer": 10, "practice_model": "80 ÷ 8 = 10 items per group.", "practice_prompt": "Give every one of the 8 groups one extra item. The new total is 80. Find the new amount per group.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Find the amount in each known group", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Draw exactly the stated number of empty group boxes before moving any marks. Share one round to every box, then use a fact or equal batches to complete the share. Check that the number of boxes did not change.", "Build the supplied new example together. Teacher explanation: 72 ÷ 8 = 9 items per group; 8 × 9 = 72 items. Ask the learner to point to the part of the model that supports each quantity. Finding the amount per group is different from finding how many groups can be made, even if both number sentences look alike.", "Remove the worked example. Give this changed task privately: Give every one of the 8 groups one extra item. The new total is 80. Find the new amount per group. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "72 ÷ 8 = 9 items per group; 8 × 9 = 72 items.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N13 after V04A

{ "answer": 48, "context": "labels for repair kits", "criterion": "Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.", "from": "V04A", "id": "N13", "kind": "strategy", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For labels for repair kits, 3 groups need 16 items each. Find the total using an efficient strategy and explain how its parts appear in the model.", "parameters": [ 3, 16 ], "practice_answer": 51, "practice_model": "3 × 17 = 30 + 21 = 51 items.", "practice_prompt": "Keep 3 groups, with 17 items in each. Use the earlier strategy to find the new total and explain why it changes by 3.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Connect an efficient strategy to a multiplicative model", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Split the amount in every group into ten and the remaining ones. Point to all the tens, then all the ones. Join those two totals; alternatively build and explain a valid doubling route.", "Build the supplied new example together. Teacher explanation: 3 × 16 = 3 × 10 + 3 × 6 = 30 + 18 = 48 items. Another valid explained strategy is acceptable. Ask the learner to point to the part of the model that supports each quantity. Multiplying only the tens and adding the ones once loses the ones from the other groups.", "Remove the worked example. Give this changed task privately: Keep 3 groups, with 17 items in each. Use the earlier strategy to find the new total and explain why it changes by 3. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "3 × 16 = 3 × 10 + 3 × 6 = 30 + 18 = 48 items. Another valid explained strategy is acceptable.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N14 after V04B

{ "answer": 72, "context": "tokens for game packs", "criterion": "Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.", "from": "V04B", "id": "N14", "kind": "strategy", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For tokens for game packs, 4 groups need 18 items each. Find the total using an efficient strategy and explain how its parts appear in the model.", "parameters": [ 4, 18 ], "practice_answer": 76, "practice_model": "4 × 19 = 40 + 36 = 76 items.", "practice_prompt": "Keep 4 groups, with 19 items in each. Use the earlier strategy to find the new total and explain why it changes by 4.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Connect an efficient strategy to a multiplicative model", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Split the amount in every group into ten and the remaining ones. Point to all the tens, then all the ones. Join those two totals; alternatively build and explain a valid doubling route.", "Build the supplied new example together. Teacher explanation: 4 × 18 = 4 × 10 + 4 × 8 = 40 + 32 = 72 items. Another valid explained strategy is acceptable. Ask the learner to point to the part of the model that supports each quantity. Multiplying only the tens and adding the ones once loses the ones from the other groups.", "Remove the worked example. Give this changed task privately: Keep 4 groups, with 19 items in each. Use the earlier strategy to find the new total and explain why it changes by 4. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "4 × 18 = 4 × 10 + 4 × 8 = 40 + 32 = 72 items. Another valid explained strategy is acceptable.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N15 after V04C

{ "answer": 84, "context": "picture cards for learning trays", "criterion": "Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.", "from": "V04C", "id": "N15", "kind": "strategy", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For picture cards for learning trays, 7 groups need 12 items each. Find the total using an efficient strategy and explain how its parts appear in the model.", "parameters": [ 7, 12 ], "practice_answer": 91, "practice_model": "7 × 13 = 70 + 21 = 91 items.", "practice_prompt": "Keep 7 groups, with 13 items in each. Use the earlier strategy to find the new total and explain why it changes by 7.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Connect an efficient strategy to a multiplicative model", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Split the amount in every group into ten and the remaining ones. Point to all the tens, then all the ones. Join those two totals; alternatively build and explain a valid doubling route.", "Build the supplied new example together. Teacher explanation: 7 × 12 = 7 × 10 + 7 × 2 = 70 + 14 = 84 items. Another valid explained strategy is acceptable. Ask the learner to point to the part of the model that supports each quantity. Multiplying only the tens and adding the ones once loses the ones from the other groups.", "Remove the worked example. Give this changed task privately: Keep 7 groups, with 13 items in each. Use the earlier strategy to find the new total and explain why it changes by 7. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "7 × 12 = 7 × 10 + 7 × 2 = 70 + 14 = 84 items. Another valid explained strategy is acceptable.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N16 after V04D

{ "answer": 90, "context": "caption cards for art folders", "criterion": "Partition, double or otherwise use suitable facts and explain why each intermediate quantity belongs to the situation.", "from": "V04D", "id": "N16", "kind": "strategy", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For caption cards for art folders, 6 groups need 15 items each. Find the total using an efficient strategy and explain how its parts appear in the model.", "parameters": [ 6, 15 ], "practice_answer": 96, "practice_model": "6 × 16 = 60 + 36 = 96 items.", "practice_prompt": "Keep 6 groups, with 16 items in each. Use the earlier strategy to find the new total and explain why it changes by 6.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Connect an efficient strategy to a multiplicative model", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Split the amount in every group into ten and the remaining ones. Point to all the tens, then all the ones. Join those two totals; alternatively build and explain a valid doubling route.", "Build the supplied new example together. Teacher explanation: 6 × 15 = 6 × 10 + 6 × 5 = 60 + 30 = 90 items. Another valid explained strategy is acceptable. Ask the learner to point to the part of the model that supports each quantity. Multiplying only the tens and adding the ones once loses the ones from the other groups.", "Remove the worked example. Give this changed task privately: Keep 6 groups, with 16 items in each. Use the earlier strategy to find the new total and explain why it changes by 6. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "6 × 15 = 6 × 10 + 6 × 5 = 60 + 30 = 90 items. Another valid explained strategy is acceptable.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N17 after V05A

{ "answer": 22, "context": "pretend display packs", "criterion": "Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.", "from": "V05A", "id": "N17", "kind": "budget", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "2 pretend display packs cost a made-up $9 each plus one $4 fee. The supplied budget is $30. Find the exact cost and amount left or over. All prices are fictional.", "parameters": [ 2, 9, 4, 30 ], "practice_answer": 24, "practice_model": "Total $24; $6 left. Kit count and repeated cost stay the same.", "practice_prompt": "Only the one-off fee increases by $2 to $6. Same kits and budget. What changes and what stays?", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Keep a one-off cost separate and check a budget", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Make a card for each purchased kit and one separate fee card. Join the kit-cost total and the fee once. Put the supplied budget on a third card and compare before subtracting.", "Build the supplied new example together. Teacher explanation: 2 × $9 + $4 = $22; $30 − $22 = $8 left. Fee paid once. Ask the learner to point to the part of the model that supports each quantity. A fee charged once is not a fee on each item. The count of items is not a dollar amount.", "Remove the worked example. Give this changed task privately: Only the one-off fee increases by $2 to $6. Same kits and budget. What changes and what stays? Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "2 × $9 + $4 = $22; $30 − $22 = $8 left. Fee paid once.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N18 after V05B

{ "answer": 46, "context": "pretend repair sets", "criterion": "Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.", "from": "V05B", "id": "N18", "kind": "budget", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "5 pretend repair sets cost a made-up $8 each plus one $6 fee. The supplied budget is $60. Find the exact cost and amount left or over. All prices are fictional.", "parameters": [ 5, 8, 6, 60 ], "practice_answer": 48, "practice_model": "Total $48; $12 left. Kit count and repeated cost stay the same.", "practice_prompt": "Only the one-off fee increases by $2 to $8. Same kits and budget. What changes and what stays?", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Keep a one-off cost separate and check a budget", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Make a card for each purchased kit and one separate fee card. Join the kit-cost total and the fee once. Put the supplied budget on a third card and compare before subtracting.", "Build the supplied new example together. Teacher explanation: 5 × $8 + $6 = $46; $60 − $46 = $14 left. Fee paid once. Ask the learner to point to the part of the model that supports each quantity. A fee charged once is not a fee on each item. The count of items is not a dollar amount.", "Remove the worked example. Give this changed task privately: Only the one-off fee increases by $2 to $8. Same kits and budget. What changes and what stays? Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "5 × $8 + $6 = $46; $60 − $46 = $14 left. Fee paid once.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N19 after V05C

{ "answer": 73, "context": "pretend mini-game kits", "criterion": "Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.", "from": "V05C", "id": "N19", "kind": "budget", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "6 pretend mini-game kits cost a made-up $11 each plus one $7 fee. The supplied budget is $80. Find the exact cost and amount left or over. All prices are fictional.", "parameters": [ 6, 11, 7, 80 ], "practice_answer": 75, "practice_model": "Total $75; $5 left. Kit count and repeated cost stay the same.", "practice_prompt": "Only the one-off fee increases by $2 to $9. Same kits and budget. What changes and what stays?", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Keep a one-off cost separate and check a budget", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Make a card for each purchased kit and one separate fee card. Join the kit-cost total and the fee once. Put the supplied budget on a third card and compare before subtracting.", "Build the supplied new example together. Teacher explanation: 6 × $11 + $7 = $73; $80 − $73 = $7 left. Fee paid once. Ask the learner to point to the part of the model that supports each quantity. A fee charged once is not a fee on each item. The count of items is not a dollar amount.", "Remove the worked example. Give this changed task privately: Only the one-off fee increases by $2 to $9. Same kits and budget. What changes and what stays? Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "6 × $11 + $7 = $73; $80 − $73 = $7 left. Fee paid once.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N20 after V05D

{ "answer": 89, "context": "pretend craft kits", "criterion": "Model repeated cost plus one fixed fee, calculate the exact total and interpret the amount left or over.", "from": "V05D", "id": "N20", "kind": "budget", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "8 pretend craft kits cost a made-up $10 each plus one $9 fee. The supplied budget is $100. Find the exact cost and amount left or over. All prices are fictional.", "parameters": [ 8, 10, 9, 100 ], "practice_answer": 91, "practice_model": "Total $91; $9 left. Kit count and repeated cost stay the same.", "practice_prompt": "Only the one-off fee increases by $2 to $11. Same kits and budget. What changes and what stays?", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Keep a one-off cost separate and check a budget", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Make a card for each purchased kit and one separate fee card. Join the kit-cost total and the fee once. Put the supplied budget on a third card and compare before subtracting.", "Build the supplied new example together. Teacher explanation: 8 × $10 + $9 = $89; $100 − $89 = $11 left. Fee paid once. Ask the learner to point to the part of the model that supports each quantity. A fee charged once is not a fee on each item. The count of items is not a dollar amount.", "Remove the worked example. Give this changed task privately: Only the one-off fee increases by $2 to $11. Same kits and budget. What changes and what stays? Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "8 × $10 + $9 = $89; $100 − $89 = $11 left. Fee paid once.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N21 after V06A

{ "answer": 59, "context": "pretend workshop packs", "criterion": "Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.", "from": "V06A", "id": "N21", "kind": "estimate", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "3 pretend workshop packs cost a made-up $19 each plus one $2 fee. Budget $60. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.", "parameters": [ 3, 19, 2, 60 ], "practice_answer": 0, "practice_model": "It fits exactly with $0 left. The upper estimate stays $70; it is a check, not the paid total.", "practice_prompt": "The budget changes to the exact total, $59; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Use an estimate without overstating what it decides", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Place the exact unit price below its next whole ten-dollar amount, and the fee below its next ten-dollar amount. Name the resulting total an upper check. When that upper check is above the budget, explicitly keep the decision open and calculate the exact cost.", "Build the supplied new example together. Teacher explanation: Upper check 3 × $20 + $10 = $70. It exceeds the budget but cannot alone prove an overrun. Exact cost $59, leaving $1. Ask the learner to point to the part of the model that supports each quantity. An upper estimate above the budget does not by itself prove that the exact price is above the budget.", "Remove the worked example. Give this changed task privately: The budget changes to the exact total, $59; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "Upper check 3 × $20 + $10 = $70. It exceeds the budget but cannot alone prove an overrun. Exact cost $59, leaving $1.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N22 after V06B

{ "answer": 73, "context": "pretend display sets", "criterion": "Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.", "from": "V06B", "id": "N22", "kind": "estimate", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "4 pretend display sets cost a made-up $17 each plus one $5 fee. Budget $70. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.", "parameters": [ 4, 17, 5, 70 ], "practice_answer": 0, "practice_model": "It fits exactly with $0 left. The upper estimate stays $90; it is a check, not the paid total.", "practice_prompt": "The budget changes to the exact total, $73; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Use an estimate without overstating what it decides", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Place the exact unit price below its next whole ten-dollar amount, and the fee below its next ten-dollar amount. Name the resulting total an upper check. When that upper check is above the budget, explicitly keep the decision open and calculate the exact cost.", "Build the supplied new example together. Teacher explanation: Upper check 4 × $20 + $10 = $90. It exceeds the budget but cannot alone prove an overrun. Exact cost $73, over by $3. Ask the learner to point to the part of the model that supports each quantity. An upper estimate above the budget does not by itself prove that the exact price is above the budget.", "Remove the worked example. Give this changed task privately: The budget changes to the exact total, $73; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "Upper check 4 × $20 + $10 = $90. It exceeds the budget but cannot alone prove an overrun. Exact cost $73, over by $3.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N23 after V06C

{ "answer": 94, "context": "pretend game sets", "criterion": "Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.", "from": "V06C", "id": "N23", "kind": "estimate", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "5 pretend game sets cost a made-up $18 each plus one $4 fee. Budget $95. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.", "parameters": [ 5, 18, 4, 95 ], "practice_answer": 0, "practice_model": "It fits exactly with $0 left. The upper estimate stays $110; it is a check, not the paid total.", "practice_prompt": "The budget changes to the exact total, $94; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Use an estimate without overstating what it decides", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Place the exact unit price below its next whole ten-dollar amount, and the fee below its next ten-dollar amount. Name the resulting total an upper check. When that upper check is above the budget, explicitly keep the decision open and calculate the exact cost.", "Build the supplied new example together. Teacher explanation: Upper check 5 × $20 + $10 = $110. It exceeds the budget but cannot alone prove an overrun. Exact cost $94, leaving $1. Ask the learner to point to the part of the model that supports each quantity. An upper estimate above the budget does not by itself prove that the exact price is above the budget.", "Remove the worked example. Give this changed task privately: The budget changes to the exact total, $94; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "Upper check 5 × $20 + $10 = $110. It exceeds the budget but cannot alone prove an overrun. Exact cost $94, leaving $1.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N24 after V06D

{ "answer": 91, "context": "pretend activity kits", "criterion": "Explain the direction and purpose of rounding, then use an exact total when an estimate cannot settle a close budget question.", "from": "V06D", "id": "N24", "kind": "estimate", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "6 pretend activity kits cost a made-up $14 each plus one $7 fee. Budget $90. Round both prices up to whole tens for a check. Explain whether that check decides affordability; then calculate exactly.", "parameters": [ 6, 14, 7, 90 ], "practice_answer": 0, "practice_model": "It fits exactly with $0 left. The upper estimate stays $130; it is a check, not the paid total.", "practice_prompt": "The budget changes to the exact total, $91; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Use an estimate without overstating what it decides", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Place the exact unit price below its next whole ten-dollar amount, and the fee below its next ten-dollar amount. Name the resulting total an upper check. When that upper check is above the budget, explicitly keep the decision open and calculate the exact cost.", "Build the supplied new example together. Teacher explanation: Upper check 6 × $20 + $10 = $130. It exceeds the budget but cannot alone prove an overrun. Exact cost $91, over by $1. Ask the learner to point to the part of the model that supports each quantity. An upper estimate above the budget does not by itself prove that the exact price is above the budget.", "Remove the worked example. Give this changed task privately: The budget changes to the exact total, $91; the prices do not change. Is the plan within this new budget? Explain the role of the same upper estimate. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "Upper check 6 × $20 + $10 = $130. It exceeds the budget but cannot alone prove an overrun. Exact cost $91, over by $1.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N25 after V07A

{ "answer": [ 36, 48 ], "context": "repair labels", "criterion": "Use whole packs to supply the same target quantity and compare full costs with contextual units.", "from": "V07A", "id": "N25", "kind": "offer", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "Exactly 12 repair labels are required. Offer A: 3 for a made-up $9; B: 4 for $16. Whole packs only and no extras. Compare full costs and explain the cheaper plan.", "parameters": [ 12, 3, 9, 4, 16 ], "practice_answer": [ 72, 96 ], "practice_model": "A:8 packs/$72; B:6 packs/$96; quantities both 24.", "practice_prompt": "Exactly 24 items are now required, with the same whole-pack offers. Compare again.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Compare equal quantities rather than ticket prices", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Draw a row for the required quantity, then make each whole-pack plan against that same row. Record pack count, total items and total cost in separate columns. Compare costs only after both quantities match.", "Build the supplied new example together. Teacher explanation: A:4 packs,12 items,$36. B:3 packs,12 items,$48. A costs $12 less. Ask the learner to point to the part of the model that supports each quantity. A smaller printed pack price can cost more to supply the same quantity.", "Remove the worked example. Give this changed task privately: Exactly 24 items are now required, with the same whole-pack offers. Compare again. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "A:4 packs,12 items,$36. B:3 packs,12 items,$48. A costs $12 less.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N26 after V07B

{ "answer": [ 96, 72 ], "context": "game counters", "criterion": "Use whole packs to supply the same target quantity and compare full costs with contextual units.", "from": "V07B", "id": "N26", "kind": "offer", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "Exactly 24 game counters are required. Offer A: 6 for a made-up $24; B: 8 for $24. Whole packs only and no extras. Compare full costs and explain the cheaper plan.", "parameters": [ 24, 6, 24, 8, 24 ], "practice_answer": [ 192, 144 ], "practice_model": "A:8 packs/$192; B:6 packs/$144; quantities both 48.", "practice_prompt": "Exactly 48 items are now required, with the same whole-pack offers. Compare again.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Compare equal quantities rather than ticket prices", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Draw a row for the required quantity, then make each whole-pack plan against that same row. Record pack count, total items and total cost in separate columns. Compare costs only after both quantities match.", "Build the supplied new example together. Teacher explanation: A:4 packs,24 items,$96. B:3 packs,24 items,$72. B costs $24 less. Ask the learner to point to the part of the model that supports each quantity. A smaller printed pack price can cost more to supply the same quantity.", "Remove the worked example. Give this changed task privately: Exactly 48 items are now required, with the same whole-pack offers. Compare again. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "A:4 packs,24 items,$96. B:3 packs,24 items,$72. B costs $24 less.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N27 after V07C

{ "answer": [ 36, 54 ], "context": "caption cards", "criterion": "Use whole packs to supply the same target quantity and compare full costs with contextual units.", "from": "V07C", "id": "N27", "kind": "offer", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "Exactly 18 caption cards are required. Offer A: 3 for a made-up $6; B: 6 for $18. Whole packs only and no extras. Compare full costs and explain the cheaper plan.", "parameters": [ 18, 3, 6, 6, 18 ], "practice_answer": [ 72, 108 ], "practice_model": "A:12 packs/$72; B:6 packs/$108; quantities both 36.", "practice_prompt": "Exactly 36 items are now required, with the same whole-pack offers. Compare again.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Compare equal quantities rather than ticket prices", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Draw a row for the required quantity, then make each whole-pack plan against that same row. Record pack count, total items and total cost in separate columns. Compare costs only after both quantities match.", "Build the supplied new example together. Teacher explanation: A:6 packs,18 items,$36. B:3 packs,18 items,$54. A costs $18 less. Ask the learner to point to the part of the model that supports each quantity. A smaller printed pack price can cost more to supply the same quantity.", "Remove the worked example. Give this changed task privately: Exactly 36 items are now required, with the same whole-pack offers. Compare again. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "A:6 packs,18 items,$36. B:3 packs,18 items,$54. A costs $18 less.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N28 after V07D

{ "answer": [ 120, 96 ], "context": "blank picture cards", "criterion": "Use whole packs to supply the same target quantity and compare full costs with contextual units.", "from": "V07D", "id": "N28", "kind": "offer", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "Exactly 24 blank picture cards are required. Offer A: 4 for a made-up $20; B: 6 for $24. Whole packs only and no extras. Compare full costs and explain the cheaper plan.", "parameters": [ 24, 4, 20, 6, 24 ], "practice_answer": [ 240, 192 ], "practice_model": "A:12 packs/$240; B:8 packs/$192; quantities both 48.", "practice_prompt": "Exactly 48 items are now required, with the same whole-pack offers. Compare again.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Compare equal quantities rather than ticket prices", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Draw a row for the required quantity, then make each whole-pack plan against that same row. Record pack count, total items and total cost in separate columns. Compare costs only after both quantities match.", "Build the supplied new example together. Teacher explanation: A:6 packs,24 items,$120. B:4 packs,24 items,$96. B costs $24 less. Ask the learner to point to the part of the model that supports each quantity. A smaller printed pack price can cost more to supply the same quantity.", "Remove the worked example. Give this changed task privately: Exactly 48 items are now required, with the same whole-pack offers. Compare again. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "A:6 packs,24 items,$120. B:4 packs,24 items,$96. B costs $24 less.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N29 after V08A

{ "answer": [ 45, 65 ], "context": "a fictional activity club", "criterion": "Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.", "from": "V08A", "id": "N29", "kind": "plan", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For a fictional activity club, need exactly 20 items. A packs 5 for a made-up $10; B packs 4 for $12. One $5 fee for either plan; budget $50. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note.", "parameters": [ 20, 5, 10, 4, 12, 5, 50 ], "practice_answer": [ 47, 67 ], "practice_model": "Quantity and pack counts unchanged. Both costs and budget rise by $2, so each budget difference and the original decision stay the same.", "practice_prompt": "Only the fee rises by $2 to $7, and the budget rises by $2 to $52. Recheck quantities, costs and amounts left.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Communicate a plan that satisfies the whole brief", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Highlight each constraint in the supplied brief. Give quantity and cost their own check rows. Add the fee once to each option, compare with the budget, then write a short note that another organiser could act on.", "Build the supplied new example together. Teacher explanation: A:4 packs,20 items,$45,$5 left. B:5 packs,20 items,$65,$15 over. Choose A. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide. Ask the learner to point to the part of the model that supports each quantity. A cheap plan that supplies too few items does not solve the brief. If costs tie, the supplied tie-break purpose matters.", "Remove the worked example. Give this changed task privately: Only the fee rises by $2 to $7, and the budget rises by $2 to $52. Recheck quantities, costs and amounts left. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "A:4 packs,20 items,$45,$5 left. B:5 packs,20 items,$65,$15 over. Choose A. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N30 after V08B

{ "answer": [ 66, 60 ], "context": "a fictional quiet game session", "criterion": "Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.", "from": "V08B", "id": "N30", "kind": "plan", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For a fictional quiet game session, need exactly 24 items. A packs 6 for a made-up $15; B packs 8 for $18. One $6 fee for either plan; budget $70. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note.", "parameters": [ 24, 6, 15, 8, 18, 6, 70 ], "practice_answer": [ 68, 62 ], "practice_model": "Quantity and pack counts unchanged. Both costs and budget rise by $2, so each budget difference and the original decision stay the same.", "practice_prompt": "Only the fee rises by $2 to $8, and the budget rises by $2 to $72. Recheck quantities, costs and amounts left.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Communicate a plan that satisfies the whole brief", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Highlight each constraint in the supplied brief. Give quantity and cost their own check rows. Add the fee once to each option, compare with the budget, then write a short note that another organiser could act on.", "Build the supplied new example together. Teacher explanation: A:4 packs,24 items,$66,$4 left. B:3 packs,24 items,$60,$10 left. Choose B. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide. Ask the learner to point to the part of the model that supports each quantity. A cheap plan that supplies too few items does not solve the brief. If costs tie, the supplied tie-break purpose matters.", "Remove the worked example. Give this changed task privately: Only the fee rises by $2 to $8, and the budget rises by $2 to $72. Recheck quantities, costs and amounts left. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "A:4 packs,24 items,$66,$4 left. B:3 packs,24 items,$60,$10 left. Choose B. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N31 after V08C

{ "answer": [ 134, 113 ], "context": "a fictional animation club", "criterion": "Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.", "exposure_note": "This is a different complete mathematical source from V08C/C20, including a different private constraint decision. Record actual prior exposure and support; changed numbers or context do not verify unfamiliarity or independent mastery.", "from": "V08C", "id": "N31", "kind": "plan", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For a fictional animation club, need exactly 42 blank title cards. Pretend A packs 7 for $21; B packs 6 for $15. One $8 fee for either plan; budget $120. Whole packs, no extras. Choose the lower full cost among valid plans; if costs tie, choose fewer packs. Give the organiser a useful note with quantities, cost, amount left or shortfall, and assumptions.", "parameters": [ 42, 7, 21, 6, 15, 8, 120 ], "practice_answer": [ 176, null ], "practice_answer_meaning": "A has a valid whole cost of $176. Null for B records that no B whole-pack plan satisfies the exact quantity; it is not a zero cost or a missing learner response.", "practice_model": "A: 56 ÷ 7 = 8 packs; 8 × $21 + $8 = $176, leaving $4 from $180. B: nine packs give 54 cards, two short; ten packs give 60 cards, four extra. No whole number of B packs supplies exactly 56 cards, so B is invalid under the no-extra rule; a lower price cannot make it valid. Choose A and state the exact-quantity, whole-pack, one-off-fee and budget assumptions. Do not round a pack count or change the no-extra requirement silently.", "practice_parameters": [ 56, 7, 21, 6, 15, 8, 180 ], "practice_prompt": "A later animation display needs exactly 56 blank title cards and has a pretend $180 budget. Keep A packs of 7 for $21, B packs of 6 for $15 and the one $8 fee. Whole packs and no extra cards are still required. Check whether each option can supply exactly 56 cards before comparing costs. Write an organiser note that identifies a valid plan, or explains why a plan cannot satisfy the brief.", "practice_validity": [ true, false ], "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Communicate a plan that satisfies the whole brief", "teach": [ "Read the complete new club brief and name what each number counts: cards needed, cards per pack, dollars per pack, the one fee and the available dollars. Make separate quantity, cost and budget rows for A and B. Ask which constraints must be satisfied before choosing a plan.", "Build the new 42-card example together. A: 42 ÷ 7 = 6 packs; 6 × $21 + $8 = $134, which is $14 over $120. B: 42 ÷ 6 = 7 packs; 7 × $15 + $8 = $113, leaving $7. Both supply exactly 42 cards. Choose B: its seven packs cost less than A’s six packs and fit the budget. Fewer packs is only the tie-break when full costs tie. Assume the pretend quoted pack prices and one fee apply, whole packs must be used and no extra cards are allowed. Ask the learner to connect each multiplication/division to its labelled quantity. The plan with fewer packs is not automatically cheaper. Keep cost order and the tie-break distinct.", "Remove the worked example. Give the changed 56-card display brief privately: A later animation display needs exactly 56 blank title cards and has a pretend $180 budget. Keep A packs of 7 for $21, B packs of 6 for $15 and the one $8 fee. Whole packs and no extra cards are still required. Check whether each option can supply exactly 56 cards before comparing costs. Write an organiser note that identifies a valid plan, or explains why a plan cannot satisfy the brief. Let the learner draw or arrange groups, explain/sign/point, dictate or type the organiser note. Record any model, number, reading or scribing support; the worked 42-card example is previous exposure, not independent assessment. Teach from the actual response afterwards." ], "teacher_model": "A: 42 ÷ 7 = 6 packs; 6 × $21 + $8 = $134, which is $14 over $120. B: 42 ÷ 6 = 7 packs; 7 × $15 + $8 = $113, leaving $7. Both supply exactly 42 cards. Choose B: its seven packs cost less than A’s six packs and fit the budget. Fewer packs is only the tie-break when full costs tie. Assume the pretend quoted pack prices and one fee apply, whole packs must be used and no extra cards are allowed.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }

N32 after V08D

{ "answer": [ 108, 128 ], "context": "a fictional caption display", "criterion": "Check quantity, pack restrictions, fixed fee and budget, then give a usable decision and stated assumptions.", "from": "V08D", "id": "N32", "kind": "plan", "modes": [ "Make/draw using original blank group frames.", "Explain/sign/point or dictate reasoning.", "Type a private note or use paper; a device is optional." ], "new_prompt": "For a fictional caption display, need exactly 40 items. A packs 8 for a made-up $20; B packs 5 for $15. One $8 fee for either plan; budget $110. Whole packs, no extras. Choose lower total cost among valid plans; if tied, choose fewer packs. Give a useful organiser note.", "parameters": [ 40, 8, 20, 5, 15, 8, 110 ], "practice_answer": [ 110, 130 ], "practice_model": "Quantity and pack counts unchanged. Both costs and budget rise by $2, so each budget difference and the original decision stay the same.", "practice_prompt": "Only the fee rises by $2 to $10, and the budget rises by $2 to $112. Recheck quantities, costs and amounts left.", "reassessment": "Check the changed response against the named criterion, not against speed, spelling or a preferred-looking diagram. Record the exact support given. If the meaning is still unclear, revisit one group or one constraint with a smaller supplied number, record the change and return later to the original demand.", "setup": "Use scrap paper, group labels and appropriate large counters, or dictate a complete model to a scribe. Work at a table; no purchase, household data or public performance. Keep teacher worked material separate from blank learner spaces.", "target": "Communicate a plan that satisfies the whole brief", "teach": [ "Read the new brief and ask which quantity is missing. Name units before any calculation. Highlight each constraint in the supplied brief. Give quantity and cost their own check rows. Add the fee once to each option, compare with the budget, then write a short note that another organiser could act on.", "Build the supplied new example together. Teacher explanation: A:5 packs,40 items,$108,$2 left. B:8 packs,40 items,$128,$18 over. Choose A. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide. Ask the learner to point to the part of the model that supports each quantity. A cheap plan that supplies too few items does not solve the brief. If costs tie, the supplied tie-break purpose matters.", "Remove the worked example. Give this changed task privately: Only the fee rises by $2 to $10, and the budget rises by $2 to $112. Recheck quantities, costs and amounts left. Offer a different response mode if needed without silently changing the mathematical criterion." ], "teacher_model": "A:5 packs,40 items,$108,$2 left. B:8 packs,40 items,$128,$18 over. Choose A. State exact-quantity and one-off-fee assumptions; estimates check, exact costs decide.", "time": "About 8–12 minutes, or shorter visits; unpiloted suggestion." }