L6 · Decimal and percent problem-solving clinic

Learning goal

“I can solve mixed, multi-step problems that combine decimal operations and percents - choosing the right operation and direction at each step, estimating first, and verifying with the inverse operation.”

Multi-step problem — a problem needing two or more operations in sequence, where each step's answer feeds the next.

Inverse operation — the operation that undoes another: addition undoes subtraction; multiplication checks division; finding-the-part checks finding-the-whole.

Reasonableness — whether an answer fits the estimate and the story: a change amount bigger than the bill fails reasonableness on sight.

Worked example

Notebooks cost $2.75 each. Ben buys 3 and pays with a $10 bill. How much change does he get? Step 1 (plan in words): total cost first (multiplication), then change (subtraction). Write the plan BEFORE touching numbers: cost = 3 x 2.75; change = 10 - cost. Step 2 (estimate): 3 x $3 is about $9, so change is about $1. Step 3 (compute): 3 x 2.75 = 8.25. Change: 10.00 - 8.25 = 1.75. Step 4 (verify): estimate said about $1 - checks out; inverse check: 8.25 + 1.75 = 10.00. Say it plainly: in multi-step problems the operations are not the hard part - choosing them, in order, is. A written plan is the skill this lesson grades.

Check yourself — explain it

Writing the plan in words first helps because...

Paired problem — example still visible

Four juice boxes cost $1.85 each; pay with $20 -> plan: cost = 4 x 1.85; change = 20 - cost -> cost $7.40, change $12.60.

Faded completion — last step is yours

"Ribbon: 5 pieces of 1.6 m from a 10 m roll. Plan: used = 5 x 1.6 = ___ m; left = 10 - ___ = ___ m" -> 8; 8; 2

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