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
1 · Read
Some maths problems pack in a lot at once: big numbers, fractions, decimals, and percentages, all in one question. You meet them when you plan something real, like how much ribbon a school fair needs. Slow down. First, find what you already know. Then work out 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 3,914 × 6, round 3,914 to 4,000. Then 4,000 × 6 = 24,000. The calculated answer, 23,484, is close to that estimate, so it looks right.
When a percentage describes part of a whole, it should land between 0% and 100%. If your answer comes out as 140% or 250% for a part of a whole, 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.
More to read
Solve problems using the four operations
Big problems split into small problems. A three-step mix of conversion and multiplication splits into: convert units, multiply, then add. Solve one mini problem at a time. Write each answer with its unit before moving on. If step one gives grams and step two needs grams, the chain holds. Units that mismatch scream that a step went wrong.
Multi-step measurement problems
Estimate before calculating to build a safety net. 4,832 x 7 is near 5,000 x 7 = 35,000, so an exact answer of 33,824 passes the smell test. An answer of 3,382 would stink. Round one factor up and keep the other exact. The estimate takes seconds and catches slipped digits.
The locker problem
Some answers cannot make sense whatever the working says. A percentage over 100% with no bonus marks means a mistake, since you cannot score more than everything. Sanity checks close every problem. Ask: is the size plausible, are the units right, does the story allow it? A wrong-feeling answer deserves a recheck, not a box.
Explore more
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.