Advanced Multi-Step Problems · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Breaking Down Big Problems

Mathematics · Mathematical Thinking · ages 10-11
Name ______________________   Date ____________

  1. When solving a three-step ratio problem, what should you do first?

    • Multiply the ratio numbers by a random number
    • Add the ratio parts to find the total parts
    • Skip straight to the final answer

  2. Estimating first can help you spot a mistake in a decimal division answer.

    Circle one:   True   False

  3. In an algebra word problem, what is the 'unknown'?

    • A number you already know
    • The number you need to find, often shown as a letter like x
    • The units, such as pounds or kilograms

  4. Which estimate checks whether 19.8 / 4 is about 5?

    • 20 / 4 = 5
    • 19 x 4 = 76
    • 19.8 + 4 = 23.8
    • 4 / 20 = 0.2

  5. Maria calculates 38.7 ÷ 4.9 and gets 79. Rounding gives an estimate of 40 ÷ 5 = 8. Is Maria's answer reasonable?

    • Yes, it matches the estimate
    • No, it should be close to 8, not 79
    • No, it should be close to 200

  6. A recipe uses flour and sugar in the ratio 3:2. With 12 cups of flour, how many cups of sugar are needed?

    • 8 cups
    • 6 cups
    • 18 cups
    • 4 cups

  7. A number is doubled and then increased by 5, giving 17. What is the number?

    • 6
    • 11
    • 22
    • 5

  8. A juice recipe mixes orange and mango juice in a ratio of 5:3. Priya makes 40 litres in total. How many litres of orange juice does she need?

    Orangeparts5Mangoparts3

    Answer: ______________

  9. A shop sells pens in packs of 4 for £3. How much do 12 pens cost?

    • £9
    • £6
    • £36
    • £12

  10. To solve 'Ben has x pounds. He spends 12 pounds and has 25 pounds left', Priya writes x + 12 = 25. Is this equation set up correctly?

    • No, it should be 12 - x = 25
    • Yes, that's correct
    • No, it should be x - 12 = 25
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Breaking Down Big Problems W1-mt_FieL-vVTI_-s1

  1. Add the ratio parts to find the total parts · Adding the ratio parts gives you the total number of equal parts to work with next.
  2. True · A quick estimate shows roughly what size the answer should be, so a way-off answer stands out.
  3. The number you need to find, often shown as a letter like x · The unknown is what you're solving for, usually written as a letter such as x.
  4. 20 / 4 = 5 · 19.8 is near 20, and 20 / 4 = 5, so the answer should sit near 5.
  5. No, it should be close to 8, not 79 · The estimate is about 8, so an answer of 79 is far too big. Maria may have misplaced a decimal point.
  6. 8 cups · One part is 12 / 3 = 4 cups, and 2 parts give 8 cups of sugar.
  7. 6 · 2n + 5 = 17 gives 2n = 12, so n = 6.
  8. 25 · 40 ÷ (5 + 3) = 5 litres per part, so orange = 5 × 5 = 25 litres.
  9. £9 · 12 pens make 3 packs, and 3 packs at £3 each cost £9.
  10. No, it should be x - 12 = 25 · Ben starts with x, spends (subtracts) 12, and ends with 25, so the correct equation is x - 12 = 25.
Worksheet · LightMySky