Advanced Multi-Step Problems
Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating reasonableness using estimation and inverse operations
What a learner can do afterwards
- Break down a three-step ratio problem into sub-problems and plan a solution pathway
- Identify which quantities are known/unknown in an algebraic word problem and set up equations
- Use estimation to check whether a decimal division answer is reasonable before finalising
1 · Read
Some problems mix a lot together: ratios, unknown numbers, fractions, decimals, even negative numbers. A problem like this can feel too big to start. The trick is to break it into smaller steps. First find what you already know, then spot what you still need to find, and plan your steps before you calculate anything. You already split big problems into steps. The number to find is the unknown, often called x.
A juice recipe mixes orange and mango juice in a ratio of 2:3. Priya makes 50 litres in total. Step 1: add the ratio parts, 2 + 3 = 5. Step 2: divide the total by the parts, 50 ÷ 5 = 10 litres per part. Step 3: multiply each part, orange = 2 × 10 = 20 litres, mango = 3 × 10 = 30 litres.
Once you have an answer, don't stop there. Round the numbers and estimate to see if your answer is about the right size. You can also work backwards with the inverse operation to test it. If 40 ÷ 8 = 5, then 5 × 8 should bring you back to 40.
Break a big problem into small steps, work through them in order, then check your answer with estimation or the inverse operation.
The rewritten readings were written for this dataset.
2 · Watch
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Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
16 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.