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

Big Problems, One Step at a Time

Mathematics · Mathematical Thinking · ages 9-10
Name ______________________   Date ____________

  1. A 3-step problem mixes kilometres and metres. What is the best first move?

    • Convert all lengths to the same unit
    • Multiply everything first
    • Guess the answer
    • Add the numbers ignoring units

  2. A sale promises 120% off with no bonus conditions. Ali says that makes no sense. Is Ali right?

    Circle one:   True   False

  3. When you start a complex multi-step problem, what should you figure out first?

    • What you know and what you need to find
    • The final answer straight away
    • The biggest number in the problem

  4. A percentage answer over 100% can still be correct when it's meant to describe part of a whole.

    Circle one:   True   False

  5. Estimate 4,832 x 7 by rounding.

    • 3,500
    • 35,000
    • 350,000
    • 3,500,000

  6. Mia calculates that 120% of her classmates picked pizza as their favourite lunch. What does that tell her?

    • She made a mistake somewhere in her calculation
    • Pizza is extremely popular
    • She forgot to add a few classmates

  7. A baker makes 3 cakes using 250 g of flour each, plus 500 g of icing. How many grams in total?

    Answer: ______________

  8. Beth estimates 4,832 x 7 as 5,000 x 7 = 35,000 and says 33,824 looks right. Is Beth right?

    Circle one:   True   False

  9. A school orders 15 packs of pencils. Each pack has 24 pencils. The pencils are then shared equally among 9 classes. Which order of steps solves this?

    • Divide packs by classes, then multiply by pencils per pack
    • Multiply packs by pencils per pack, then divide by classes
    • Add the packs and classes, then multiply by pencils per pack

  10. A test with no bonus marks is reported as 110%. What should you think?

    • It is a top score to celebrate
    • It beats everyone else
    • It must be a mistake
    • It means full marks exactly
LightMySky · lightmysky.comW1-mt_GpltXPoaoc-s1

Answer key

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

Big Problems, One Step at a Time W1-mt_GpltXPoaoc-s1

  1. Convert all lengths to the same unit · Matching units first keeps every later step valid.
  2. True · Ali is right: over 100% off is nonsense here.
  3. What you know and what you need to find · Naming what's known and unknown helps you plan your steps before you calculate.
  4. False · A whole is 100% at most. An answer above that means a step in the working went wrong.
  5. 35,000 · 5,000 x 7 = 35,000.
  6. She made a mistake somewhere in her calculation · A group of classmates is a whole, so the answer can't go over 100%. Mia should recheck her steps.
  7. 1250 · 3 x 250 + 500 = 1250 g.
  8. True · Beth is right: 33,824 sits near 35,000.
  9. Multiply packs by pencils per pack, then divide by classes · Find the total pencils first (15 × 24 = 360), then divide by 9 classes to share them out.
  10. It must be a mistake · Over 100% with no bonus is impossible, so it must be a mistake.
Worksheet · LightMySky