L6 · Multiplication and division problem-solving clinic

Learning goal

“I can choose the right operation for a story, solve it with the standard algorithms - including two-step problems - and prove my answer with an inverse operation or an estimate.”

Two-step problem — a story that needs two operations: the answer to step 1 becomes a number in step 2.

Inverse operation — the operation that undoes another: multiplication checks division, division checks multiplication.

Known part / unknown part — in a story, decide what you KNOW (the total? the group size? the number of groups?) before choosing an operation.

Worked example

A printer prints 138 pages in one hour. How many pages in 47 hours? Step 1: Read the structure: I KNOW the group size (138 pages per hour) and the number of groups (47 hours). The UNKNOWN is the total, so multiply. Step 2: 138 x 47 with the algorithm: Row 1: 138 x 7 = 966; Row 2: 138 x 40 = 5,520. Total: 6,486 pages. Step 3: Check with an estimate: 140 x 50 = 7,000 - 6,486 is the right size. Say it plainly: multiplication builds a total from equal groups; division splits a total or finds a group size. Name what the story hands you and what it asks for BEFORE you compute anything.

Check yourself — explain it

"924 students split into classes of 6" - which operation, and why?

Paired problem — example still visible

A ferry carries 864 passengers equally over 8 trips. How many passengers per trip? -> Total known, number of groups known, group size unknown, so divide: 864 / 8 = 108 per trip.

Faded completion — last step is yours

"693 students, 7 buses, equal loads: operation is ___; 693 / 7 = ___" -> division; 99

Ready to practise?

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

Start practice →Take the unit quiz