Complex Multi-Step Problems
Make sense of complex multi-step problems involving large numbers, fractions, decimals, and percentages by analysing what is known and unknown, planning multi-step strategies, and evaluating reasonableness through estimation and inverse operations
What a learner can do afterwards
- Break a three-step problem involving unit conversion and multiplication into sub-problems and solve systematically
- Estimate 4,832 × 7 as roughly 5,000 × 7 = 35,000 to check a calculated answer of 33,824
- Identify that a percentage answer over 100% doesn't make sense in context
The lesson
Some maths problems pack in a lot at once: big numbers, fractions, decimals, and percentages, all in one question. Slow down. First, find what you already know. Then work out exactly what the question wants you to find. Once you know that, split the problem into smaller steps you can solve one at a time.
A shop orders 8 boxes of ribbon. Each box holds 12 rolls, and each roll is 250 cm long. First: 8 × 12 = 96 rolls. Next: 96 × 250 = 24,000 cm. Last: 24,000 ÷ 100 = 240 m of ribbon in total.
Before you trust a big calculation, round the numbers first. To check 4,832 × 7, round 4,832 to 5,000. Then 5,000 × 7 = 35,000. The calculated answer, 33,824, is close to that estimate, so it looks right.
A percentage describes part of a whole, so it should land between 0% and 100%. If your answer comes out as 140% or 250%, stop. Somewhere in your working, a step went wrong.
Find what you know, break the problem into steps, then check your answer with an estimate or a quick sense check.
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.