L4 · Addition and subtraction problem-solving clinic

Learning goal

“I can solve multi-step addition and subtraction problems - money, mass, and distance - by planning the steps, estimating first, computing with the standard algorithms, and finding missing numbers by undoing operations.”

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

Unknown value — a missing number in an equation, found by undoing: if the unknown + 246,815 = 700,000, then the unknown = 700,000 - 246,815.

Strategy — a chosen plan: which operations, in which order, and what estimate will check them.

Reasonable — the clinic's standing test (from L3): the final answer must sit close to the estimate made before computing.

Worked example

A school raised $12,450.75 for a playground. It spent $8,275.50 on equipment and $1,940.25 on paint and art. How much money is left? Step 1 (plan): left = raised - (equipment + paint). Two roads: combine spending first, or subtract twice. Road 1 has one addition and one subtraction - take it. Step 2 (estimate): raised is about 12,500; spending is about 8,300 + 1,900 = 10,200; left is about 2,300. Step 3 (compute): spending: 8,275.50 + 1,940.25 = 10,215.75. Left: 12,450.75 - 10,215.75 = 2,235.00. Step 4 (check): estimate said about 2,300. Inverse check: 2,235.00 + 10,215.75 = 12,450.75.

Check yourself — explain it

Combining the two expenses before subtracting works because...

Paired problem — example still visible

A library had 326,480 books, received 48,975 new books, and removed 12,308 damaged ones. How many books does it have now? -> 363,147 (326,480 + 48,975 = 375,455; 375,455 - 12,308 = 363,147)

Faded completion — last step is yours

"A tank holds 750.5 L. 128.275 L is used in the morning and 96.4 L in the afternoon. Used in total: 128.275 + 96.400 = 224.675 L. Left: 750.500 - 224.675 = ___" -> 525.825 L

Ready to practise?

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

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