L6 · Multiplication and Division Problem-Solving Clinic

Learning goal

“I can read a problem, choose multiplication or division, solve it with a strategy or the standard algorithm, estimate to check reasonableness, and verify a division by multiplying.”

Choose the operation — before computing, ask: am I building equal groups up (multiply) or splitting a total into equal groups (divide)?

Check — prove the answer with the inverse operation or an estimate: division is checked by multiplication (quotient x divisor + remainder = dividend).

Worked example

Problem: "A school orders 136 chairs for each of 5 halls. How many chairs in total?" Read it for structure first: we KNOW the size of one group (136) and the number of groups (5), and we want the TOTAL - building up -> multiply: 136 x 5 = 680. Problem flipped: "680 chairs are shared equally among 5 halls. How many per hall?" Now we know the total and split it -> divide: 680 / 5 = 136. Say it plainly: multiplication builds equal groups into a total; division splits a total into equal groups. Every problem in this clinic is one of those two shapes. Find the shape FIRST - the numbers are the easy part.

Check yourself — explain it

If a problem gives the total and asks how many in each group, the operation is division because...

Paired problem — example still visible

"9 buses each carry 92 students. How many students in total?" -> Building up: 92 x 9 = 828 students.

Faded completion — last step is yours

"A total of 828 students ride in 9 buses, the same number in each bus. Operation: ___. Students per bus: ___." -> Division; 828 / 9 = 92

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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