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Problem Solving

Polya's problem-solving steps for children

Understand the problem, make a plan, carry it out and look back.

Quick answer

Polya's problem-solving steps are four simple steps that help you solve any maths problem: understand the problem, make a plan, carry out the plan, and look back. When you follow these steps, you can solve even tricky problems more easily.

Learning outcome

By the end of this page, you will know how to use Polya's four steps to solve any maths problem, and you'll be able to explain what you did to solve it. Success signs:
  • You can explain what the problem is asking
  • You can think of a way to solve it
  • You can carry out your plan and get an answer
  • You can check your answer makes sense

Why this matters

Problem-solving is one of the most important skills you can learn in maths. It helps you in school when you do homework, in real life when you need to share snacks or plan a trip, and in games when you need to figure out how to win. Polya's steps help you think clearly and find the right answer, no matter how tricky the problem is.

How it works

Polya's problem-solving steps are a way to think through any problem. Here are the four steps: 1. Understand the problem – What is the problem asking you to do? 2. Make a plan – What can you do to solve it? 3. Carry out the plan – Do what you planned and solve it. 4. Look back – Check if your answer is right and makes sense. Let's look at each step in detail.

Examples you can see

Let's try a problem together using Polya's steps. Problem: There are 12 children at a party. Each child gets 3 cookies. How many cookies are needed altogether? Step 1: Understand the problem - What do we know? There are 12 children. - What do we need to find out? How many cookies are needed if each child gets 3 cookies. Step 2: Make a plan - We can add 3 cookies, 12 times. - Or we can multiply 12 by 3. We will multiply because it's faster. Step 3: Carry out the plan - 12 × 3 = 36 Step 4: Look back - We have 12 children. - Each gets 3 cookies. - 12 × 3 = 36. - This makes sense. If we had 12 groups of 3, we would have 36 in total.

Try it as a mini adventure

The Cookie Quest You are a cookie chef and need to bake cookies for your class. There are 15 children in your class. You want to give each child 2 cookies. How many cookies do you need to bake? Step 1: Understand the problem - There are 15 children. - Each child gets 2 cookies. - You need to find the total number of cookies. Step 2: Make a plan - You can add 2 cookies, 15 times. - Or you can multiply 15 by 2. We will multiply. Step 3: Carry out the plan - 15 × 2 = 30 Step 4: Look back - 15 children. - Each gets 2 cookies. - 15 × 2 = 30. - This is right. 15 groups of 2 make 30. 4th time: ? cookies

Common mistakes

  • Mistake: Jumping straight to the answer without understanding what the problem is asking. Why it happens: Some children are excited to solve the problem and forget to read carefully. Fix: Always read the problem twice and ask, "What am I trying to find?"
  • Mistake: Not checking the answer after solving. Why it happens: Children think once they get an answer, it must be right. Fix: Always ask, "Does this answer make sense?"
  • Mistake: Choosing a wrong method to solve the problem. Why it happens: Children might think addition is always better than multiplication. Fix: Think about what makes the problem easier – sometimes multiplication is faster.

Parent and carer guide

Parents and carers can help children by asking questions instead of giving answers. Here's how:
  • Ask, "What do you know about this problem?"
  • Encourage your child to explain their plan before solving.
  • When they finish, ask, "Does your answer make sense?"
  • Let them try different ways to solve the problem.
  • Don't worry if they make mistakes – that's how they learn!

Practice questions

  1. There are 8 boxes. Each box has 5 toys. How many toys are there altogether?
  2. A teacher has 24 pencils. She wants to share them equally among 4 students. How many pencils does each student get?
  3. There are 10 rows of chairs. Each row has 6 chairs. How many chairs are there?
  4. There are 11 flowers in each vase. There are 3 vases. How many flowers are there in total?
  5. Tommy has 18 stickers. He wants to put them into 2 equal groups. How many stickers are in each group?
Answers:
  1. 8 × 5 = 40
  2. 24 ÷ 4 = 6
  3. 10 × 6 = 60
  4. 11 × 3 = 33
  5. 18 ÷ 2 = 9

FAQ

What is Polya's problem-solving method?

Polya's method is a way to solve problems by following four steps: understand the problem, make a plan, carry out the plan, and look back.

Why are Polya's steps important?

Polya's steps help you think clearly and find the right answer, no matter how tricky the problem is. They make solving problems easier and more fun.

Can I use Polya's steps for any problem?

Yes! Polya's steps work for any maths problem, whether it's adding, subtracting, multiplying, or dividing.

What if I get the wrong answer?

That's okay! The "look back" step helps you check your answer. If it's wrong, you can fix it by going back and trying again.

How can I remember Polya's steps?

You can remember them by thinking: "Understand, Plan, Do, Check." You can also make up a song or a story to help you remember!