L9 · Add/subtract problem-solving clinic

Learning goal

“I can solve multi-step add/subtract problems in money, metric, and temperature contexts by estimating first, choosing the operations in order, computing with the standard algorithm - and checking that my answer is reasonable.”

Estimate — a quick rounded calculation done BEFORE the exact one, to predict the answer's size: 4,982 + 3,017 is about 5,000 + 3,000 = 8,000.

Reasonable — an answer is reasonable if it lands near the estimate and fits the story (change cannot exceed what you paid).

Multi-step problem — a problem needing two or more operations in a sensible order, where the answer to step 1 feeds step 2.

Worked example

A jacket costs $48.95 and boots cost $76.50. You have $130. Is that enough, and what change would you get? Step 1: ESTIMATE: 48.95 is about 49 and 76.50 is about 77; 49 + 77 = 126. Under $130 - yes, enough, with only a few dollars to spare. Step 2: EXACT total: align decimal points: 48.95 + 76.50 = $125.45. Step 3: Change is step 2: 130.00 - 125.45 = $4.55. Step 4: CHECK against the estimate: spare money is about 130 - 126 = 4, and the exact change is 4.55 - close, so reasonable. (If the exact change had come out as $45.50, the estimate would have caught the decimal slip.) Model both ways: the estimate line written ABOVE the column work, and the story number line 0 - 125.45 - 130 showing the small gap that is the change.

Check yourself — explain it

Why estimate BEFORE computing exactly?

Paired problem — example still visible

A bike costs $189.99 and a helmet $42.50. You pay with $250. Estimate, then find the exact change: estimate about 190 + 43 = 233, change about $17. Exact: total 232.49, change 250.00 - 232.49 = $17.51 - close to the estimate.

Faded completion — last step is yours

"Groceries: $23.80 + $17.45. Estimate about 24 + 17 = 41. Exact total = ___. Paid with $50, the change should be about ___ and exactly ___." -> $41.25; about $9; $8.75

Ready to practise?

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

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