Multi-Step Problem Solving
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
The lesson
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 that is 5 metres by 4 metres. He wants to plant flowers on 3/5 of it. First, Sam finds the area: 5 x 4 = 20 square metres. Before multiplying by the fraction, he guesses that 3/5 should be a bit more than half. Then he checks: 3/5 of 20 is 12 square metres, and 12 is indeed a bit more than half of 20, which is 10.
For a perimeter problem, you can sketch the shape and label each side, or write an equation and add the side lengths. Either way works, so pick whichever helps you see the steps clearly. Always check your final answer against your first estimate: if they don't roughly match, look back over your steps.
Break a problem into steps, plan your order, estimate before you calculate, and check your answer makes sense.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.