Multi-Step Problem Solving (age 8+)
Make sense of multi-step problems involving four operations, fractions, and area/volume by identifying sub-steps, choosing a strategy, and monitoring progress
What a learner can do afterwards
- Break a two-step word problem into parts and explain a plan before calculating
- Choose between drawing a diagram or writing equations for a perimeter problem
- Check a fraction-of-quantity answer by estimating: 3/5 of 20 must be more than half of 20
1 · Read
You already know how to break a problem into two steps. Now some problems get trickier: they might mix adding, subtracting, multiplying, dividing, fractions, and area all in one problem. The plan stays the same. Read the problem, figure out what it is really asking, then decide which step comes first.
Before you touch a calculator, make a quick plan. Decide what you need to find first, and what you will do with that answer next. Saying your plan out loud, like 'first I'll find the area, then I'll work out a fraction of it,' helps you stay on track.
Sam has a rectangular patch 5 metres by 2 metres, and he wants flowers on 3/5 of it. First he finds the area: 5 x 2 = 10 square metres. He estimates before he goes on: 3/5 is more than half, so the answer should beat 5. Then 3/5 of 10 is 6, which does beat 5.
For a perimeter problem you get a choice. You can sketch the shape and label every side, or write an equation that adds the side lengths. Both do the same job, so pick the one that makes the steps easier to see. Then check your answer against your estimate.
Break a problem into steps, plan your order, estimate before you calculate, and check your answer makes sense.
More to read
Solve multi-step word problems and interpret remainders
Two step problems hide two questions inside one story. First find the hidden total, then use it to answer the real question. Two boxes of 24 apples hide 48 apples; half of that is 24 packed. Plan both steps before touching numbers. Write step 1 and step 2 as short phrases. Remainders need interpreting too: 25 apples in bags of 6 fill 4 bags with 1 left over. The leftover is not a fifth bag, it is just 1 apple. Plans plus leftover sense solve most stories.
Solve two-step word problems by using addition and subtraction
Addition then subtraction stories reward order. Add up what you have, then take away what leaves. Missing either step breaks the answer: stopping after the add leaves the takeaway uncounted. Draw the story as two jumps on a number line. First jump up by the gain, second jump back by the loss. Landing spot is the answer. Check by retelling: does your answer fit every sentence of the story. If one sentence disagrees, a step went missing.
Solve multi-step word problems involving multiplication and division
Multiply then divide stories need the same discipline. Three shelves of 8 tins make 24 tins; boxes of 6 swallow them 4 boxes full. Do the multiply first to build the stock, then divide to pack it. Writing the hidden total in a circle helps. Circle 24, then feed it into the divide step. Skipping the circle tempts the brain to divide 8 by 6 instead. Neat staging beats clever shortcuts.
Key ideas: solve one- step word problems using metric units
Metric stories keep units through every step. Grams stay grams and litres stay litres from start to finish. Mixing units mid story, like adding grams to kilograms, wrecks the total. Carry the unit word along each line of working. Diagrams versus equations is a free choice for perimeters. A labelled sketch stops missed sides. A compact equation like 2 x (5 + 3) is faster when numbers are friendly. Choose deliberately, then compute once.
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2 · Watch
En anglaisTake it off screen
Where it sits
Learn first
Optional connections
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.