Teacher Notes & Observation Cues
Illustrative grade 7 math lesson
Say: "A correct price is a start. What does the number mean, and why does it answer this buyer's question?" Provide silent thinking time before pair discussion.
Ask: "When might the offer with the lower unit price still be the wrong purchase?" Listen for budget or quantity needed. Probe: "Which numbers support your choice?"
At minute 17, every student finds dollars per pen for 5 pens costing $4. Correct response: $0.80 per pen. Scan all responses for reversed division and unlabeled units.
If fewer than four in five students show $0.80 per pen with units, model splitting $4 into five equal groups. Recheck with 4 pens costing $3. If most are secure, ask them to compare total cost for a buyer needing only one pack.
Before submitting, students underline the unit labels and circle the sentence that explains their purchase decision. Revise one missing element.
Slide 1: Which notebook offer would you choose?
Minutes 0-5. Record initial reasoning without confirming an answer. Ask what information a fair comparison needs. The later unit rates are $2 and $1.80 per notebook.
Slide 2: The cost of one notebook
Minutes 5-11. A: 6/3 = $2 per notebook. B: 9/5 = $1.80 per notebook. Invite two methods. If students reverse division, ask which amount belongs to one notebook.
Slide 3: A claim worth revising
Minutes 11-17. The pack sizes differ. B has the lower unit price. Ask partners to test and improve explanations. Collect a revised explanation as discussion evidence.
Slide 4: Your independent check
Minutes 17-22. Answer: $0.80 per pen. If fewer than 80% are correct with units, model equal groups for three minutes in the next phase. Recheck: 4 pens for $3 gives $0.75 per pen.
Slide 5: The club needs exactly 10 notebooks
Minutes 22-33, including any reteaching. A requires 4 packs: $24 for 12. B requires 2 packs: $18 for 10. Support with a packs-to-notebooks list. Extension: explain when total cost and unit price answer different questions.
Slide 6: Your evidence of learning
Minutes 33-40. A: $1.50 per liter. B: $1.40 per liter. Accept a justified quantity or budget reason for A. Score both rates and the justification. Use the results to plan tomorrow's groups.