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vocabulary

Problem-solving vocabulary

Child-friendly definitions and examples for words such as strategy, explain, prove, estimate, reasonable and systematic.

Quick answer

Problem-solving vocabulary helps you understand what to do when you're solving maths problems. Words like strategy, explain, prove, estimate, reasonable, and systematic help you think clearly and talk about your maths thinking.

Learning outcome

By the end of this page, you will be able to use maths problem-solving words to describe how you solve problems and explain your thinking. Success signs:
  • You can say what strategy you used to solve a problem
  • You can explain your thinking clearly to someone else
  • You can prove your answer is correct
  • You can make a good estimate before solving
  • You can check if your answer is reasonable

Why this matters

Knowing problem-solving vocabulary helps you become a better mathematician. When you can talk about your thinking, you learn more and help others understand your ideas. These words are used in school, in games, and in everyday life when you need to figure things out. Understanding these words makes solving problems easier and more fun.

How it works

Problem-solving vocabulary helps you think step-by-step. When you solve a problem, you need to:
  1. Choose a strategy (how you'll solve it)
  2. Explain your thinking
  3. Prove your answer is right
  4. Estimate first to check if your answer makes sense
  5. Work systematically so you don't miss anything

Examples you can see

Let's look at each word with examples you can imagine and use. Strategy means the plan you use to solve a problem. For example, if you have 12 apples and want to share them equally among 4 friends, your strategy might be to divide 12 by 4. Explain means to tell someone how you think and why you did something. If someone asks how you solved 8 + 7, you might explain, "I counted 8 and then counted on 7 more: 9, 10, 11, 12, 13, 14, 15." Prove means to show something is true. If you think 6 × 5 = 30, you can prove it by drawing 6 groups of 5 objects or by counting 5, 10, 15, 20, 25, 30. Estimate means to make a good guess. If you have 27 marbles and your friend has 31, you can estimate that together you have about 60 marbles. Reasonable means your answer makes sense. If you think 7 × 8 = 15, that's not reasonable because 7 × 8 should be much more than 15. Systematic means to do things in order and not miss anything. If you're looking for all the ways to make 10 with two numbers, you work systematically: 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5.

Try it as a mini adventure

Adventure: The Mystery of the Missing Sweets You are a detective solving a mystery! There were 24 sweets in a jar. Some were eaten, and now there are 9 sweets left. You need to find out how many sweets were eaten. Step 1: What strategy will you use? (Counting back, subtraction, drawing a picture) Step 2: Explain your thinking. (I counted back from 24 to 9, or I did 24 - 9) Step 3: Prove your answer is correct. (I can check: 9 + 15 = 24) Step 4: Estimate first. (I think it's about 10 sweets, maybe a bit more) Step 5: Work systematically. (I'll list all the ways to make 24 with two numbers)

Common mistakes

  • Mistake: Thinking "explain" means "tell the answer quickly"
    Why it happens: Kids think they just need to say the number.
    Fix: Practice explaining your thinking step-by-step, like "First I did this, then I did that."
  • Mistake: Using "prove" only when you're right
    Why it happens: Some kids think you only prove when you're sure.
    Fix: Proving means showing your work, even if you're not sure. It helps you check your answer.
  • Mistake: Not estimating before solving
    Why it happens: Kids jump straight to solving without thinking.
    Fix: Always ask "Does my answer make sense?" before finishing.
  • Mistake: Not working systematically
    Why it happens: Kids get excited and forget to check all possibilities.
    Fix: Use a list or chart to make sure you don't miss anything.

Parent and carer guide

Parents, you can help your child learn problem-solving vocabulary in 5-10 minutes:
  • Ask your child to explain how they solved a problem
  • Encourage them to estimate before calculating
  • Ask them to prove their answer by checking it another way
  • Have them list their steps when solving problems
  • Use these words in daily conversations: "strategy", "explain", "prove", "estimate", "reasonable", "systematic"
What to say: "Can you explain how you found that answer?" "What strategy did you use?" "Can you check your answer another way?" "Does your answer seem reasonable?" What not to worry about: Don't expect perfect answers. Focus on good thinking, not just right answers.

Practice questions

  1. What strategy would you use to solve 9 + 6? What is your answer?
  2. Explain how you know 5 × 7 = 35.
  3. Estimate the sum of 23 + 18. What is your estimate?
  4. Prove that 12 ÷ 3 = 4.
  5. Is 15 + 17 = 32 reasonable? Why or why not?
Answers:
  1. Strategy: Count on from 9. Answer: 15
  2. I can count 7, 14, 21, 28, 35, or I can think of 5 groups of 7
  3. Estimate: 20 + 20 = 40
  4. I can draw 12 circles and group them into 3 equal groups of 4
  5. Yes, because 15 + 15 = 30, and 17 is a bit more than 15, so 32 is reasonable

FAQ

What does "strategy" mean in maths?

Strategy means the plan or way you choose to solve a problem. It's like your game plan for finding the answer.

Why do I need to explain my thinking?

Explaining helps you understand what you did and helps others learn from you. It also helps you find mistakes.

How can I prove my answer is correct?

You can prove it by checking with a different method, drawing a picture, or using what you know about numbers.

What is a good estimate?

A good estimate is a smart guess that's close to the real answer. It helps you check if your answer makes sense.

How do I work systematically?

Working systematically means doing things in order and checking that you've done everything. It helps you not miss anything.