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N31 · Full next teachingYear 4 Maths · T2 W13–14 · Supplementary / N31

Previous target

V08C

Target

Communicate a plan that satisfies the whole brief

Flexible time

About 8–12 minutes, or shorter visits; unpiloted suggestion.

Prepare

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.

Complete new neutral task

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.

Specific criterion

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

Whole teaching sequence

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.

Supplied joint 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.

Equivalent offers

Make/draw using original blank group frames.

Explain/sign/point or dictate reasoning.

Type a private note or use paper; a device is optional.

Private changed task after removing model

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.

Staff changed-task possibility

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.

Observe and decide next teaching

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.

Exposure/support limit

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.

Staff literal encoding 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.

Invalid is different from missing

The stored B null is an invalid exact-quantity plan, not a zero cost and not an empty learner response. Read the complete changed task and full practice model above.