Adapt one lesson for mixed readiness
Keep one common outcome: explain how equal packs produce a starting total, remove cards taken from that total, and check the remainder. This is a complete teacher lesson for learners who have met multiplication and subtraction. Readiness here is a temporary observation about this task. It is not a fixed ability label or a student revision timetable. The earlier withdrawn Q244 is not used or revived.
Start with evidence before choosing support
Give every learner this task with no method displayed: “Four packs each hold five cards. Seven cards from those packs are displayed. How many remain? Show what each number counts.” Allow five minutes as an illustrative planning choice. The answer is 4 × 5 = 20, then 20 − 7 = 13; 13 + 7 = 20. Ask what seven refers to before treating an unexpected answer as a settled misconception.
| Fictional response | Follow-up evidence | Temporary route |
|---|---|---|
| A: 4 + 5 − 7 = 2 | Asked to represent packs, A draws four groups but includes only five cards in total. | Support for the starting equal groups. |
| B: 20 + 7 = 27 | B says the seven were in the original packs, but added them anyway. | Core meaning comparison with a remaining/displayed partition. |
| C: 20 − 7 = 13, checked by 13 + 7 = 20 | C explains four equal groups and the part taken out, without a prompt. | Extension after a new independent core item. |
| D: no written response | D says the crowded print could not be read. No mathematical attempt is available. | Provide readable wording and a suitable response route, then collect evidence. Do not assign a low-readiness group from missing access. |
A completed 40-minute lesson with rejoining
| Time | Teacher and learner activity | Evidence and move |
|---|---|---|
| 0–5 m in | Common initial task above. | Keep first answers and access conditions. |
| 5–10 m in | Brief individual explanations and route choice; show that starting cards = displayed + remaining. | Route from observed method; let learners change route after a fresh check. |
| 10–22 m in | Support, core and extension tasks below. Teacher begins with support; core and extension have complete written prompts. | Support is available without a public label. Peers may discuss learning tasks; independent checks remain individual. |
| 22–28 m in | Rejoin. Compare a subtraction situation with new cards arriving; invite methods from any route. | Ask why the same two numbers can need different operations. |
| 28–35 m in | Common independent exit task below, with models concealed. | Record calculation, meaning and help separately. |
| 35–40 m in | Give answers and one next step; choose the later check. | Assisted correction is not recorded as independent success. |
Resources: paper, pencil, readable task cards and board. Paper group drawings are enough. The chosen goal is mathematical reasoning, so an oral explanation can be recorded without adding the operation. Exact grade allocation and individual access arrangements remain for the teacher.
Three complete routes toward the same outcome
Support: Use Q245’s full model M: five packs of six cards, eight displayed. Draw five labelled groups of six: 30 initially, 30 − 8 = 22 remain, checked by 22 + 8 = 30. Then give S1: three packs of four, five displayed. Supply three empty group outlines, not the total or operation. Expected 12 initially and 7 remaining; 7 + 5 = 12. If a learner still needs the teacher to fill each group, retain that assistance and revisit before an independent check.
Core: Give C1: four packs of seven, nine displayed. Q245’s completion may supply the starting 28 only if needed; record this. The learner chooses and explains 28 − 9 = 19 and checks 19 + 9 = 28. Then C2 changes the relationship: “There are 28 cards; nine new cards arrive.” The answer is 37 because the nine were not part of the starting 28. Ask for the words that change the operation.
Extension: Give E1: six packs of eight, thirteen displayed, then four of the displayed cards returned to the packs. How many are now in the packs? Work: 48 − 13 + 4 = 39. Nine remain displayed; 39 + 9 = 48. Explain why adding 13 after subtracting it would wrongly return every displayed card. For E2, write a different pack/display story whose remainder is 20 and verify it. One valid response: five packs of six with ten displayed; 30 − 10 = 20. Multiple valid cases are expected.
Evaluate responses and decide the next lesson
Common exit: Six packs contain five cards each; eight cards are moved from the packs to a display. Find the number remaining, explain both operations and check the total. Answer: 6 × 5 = 30; 30 − 8 = 22; 22 + 8 = 30. This fresh task is shared by every route, without a supplied calculation.
| Simulated exit response | Evaluation | Next action |
|---|---|---|
| A: 5+5+5+5+5+5=30; 30−8=22; each five is one pack; 22+8=30 | Independent correct response on this item after earlier support. | Later check: four packs of nine, eleven displayed; expected 25 with 25+11=36. |
| B: 30−8=24, explaining removal correctly | Operation/meaning sound; subtraction inaccurate. | Check 24+8=32, then revise to 22; fresh 36−11 task separates arithmetic from meaning. |
| C: 22 only | Correct number, but requested reasons/check absent. | Ask for those evidential parts; do not award explanation based on prior extension performance. |
Teacher adaptation task: A learner completes the support task correctly after you name the subtraction. Should they automatically enter extension?
Worked answer and review
No. Record the supplied operation. Give a short fresh core task without that hint and inspect the explanation. Route changes depend on observed responsibility for the target decisions, not time served in a group. If access to print was the barrier, repair access first and keep the mathematical outcome unchanged.
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