L5 · Fraction problem solving

Learning goal

“I can solve one-step and two-step problems with fractions and mixed numbers: I decide which operation the story needs, estimate first, calculate, and check the size of my answer.”

Estimate — a quick benchmark guess at the answer's size before calculating, used to check the real answer.

Two-step problem — a problem that needs two operations in a planned order, like adding what was used, then subtracting from what there was.

Sum — the result of an addition.

Difference — the result of a subtraction.

Worked example

A trail is 7/8 km long to the lookout. Sara has walked 1/2 km. How much farther does she have to walk? Step 1: Read for structure - the WHOLE distance (7/8) and ONE PART (1/2) are known; the other part is missing. Missing part means subtract. Step 2: Estimate: 7/8 is about 1 and 1/2 = 1/2, so the answer is a bit less than 1/2. Step 3: 7/8 - 1/2 = 7/8 - 4/8 = 3/8 km. Check: 3/8 is a bit less than 1/2. Both models agree: a bar in eighths with the walked 4/8 shaded and the remaining 3/8 marked as the missing part, and a 0-1 number line in eighths with the gap from 1/2 to 7/8 bracketed. Say it plainly: joining parts means add; knowing the whole and one part means subtract to find the other part.

Check yourself — explain it

This problem is a subtraction because...

Paired problem — example still visible

A jug held 3/4 L. After more water was poured in, it held 1 5/8 L. How much water was poured in? -> 1 5/8 - 3/4 = 13/8 - 6/8 = 7/8 L

Faded completion — last step is yours

"Sam ran 5/6 km on Monday and 3/4 km on Tuesday. Total distance = 5/6 + 3/4 = 10/12 + 9/12 = ___" -> 19/12 = 1 7/12 km

Ready to practise?

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

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