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Problem Solving

Problem-solving misconceptions

Fix habits such as grabbing numbers without understanding the question.

Quick answer

Problem-solving misconceptions happen when children rush to use numbers without understanding what the question is really asking. The key is to read the problem carefully, understand what is needed, and choose the right maths to solve it.

Learning outcome

By the end of this page, you will understand how to avoid common problem-solving mistakes and use a clear thinking process to solve maths problems correctly. Success signs:
  • You can read a word problem and explain what it is asking
  • You can choose the right maths operation (addition, subtraction, multiplication, or division)
  • You can check your answer to see if it makes sense
  • You can explain your thinking to someone else

Why this matters

Problem-solving is one of the most important maths skills you will learn. It helps you in school, in games, and in everyday life. When you solve problems well, you can:
  • Work out how many cookies you need to share with friends
  • Figure out how long it takes to walk to school
  • Plan your pocket money spending
  • Understand how far you can travel with a certain amount of fuel
  • Know how many pieces of a puzzle you need to complete
Even grown-ups use problem-solving every day – when they cook, plan a trip, or build something. The more you practice this skill, the easier it becomes.

How it works

Solving problems step by step helps you avoid mistakes. Here’s how to think through a problem like a maths detective:
  1. Read the whole problem carefully – don’t rush to the numbers!
  2. Ask yourself: What is the question really asking?
  3. Identify what you know – the facts and numbers
  4. Decide what operation to use – addition, subtraction, multiplication, or division
  5. Do the maths – solve it carefully
  6. Check your answer – does it make sense?

Examples you can see

Let’s look at some examples to see how this works. Example 1: The Cake Problem Sarah baked 24 cupcakes. She gave 8 to her friend. How many does she have left?
  • What do we know? Sarah had 24 cupcakes, gave away 8.
  • What do we need to find out? How many cupcakes are left.
  • What operation? Subtraction (taking away).
  • Calculation: 24 - 8 = 16
  • Check: 16 + 8 = 24, so it's right.
Example 2: The Party Problem There are 5 tables at a party. Each table has 6 children sitting around it. How many children are at the party?
  • What do we know? 5 tables, 6 children at each table.
  • What do we need to find out? Total number of children.
  • What operation? Multiplication (equal groups).
  • Calculation: 5 × 6 = 30
  • Check: 30 ÷ 5 = 6, so it's right.
Example 3: The Journey Problem A bus travels 120 km in 3 hours. How far does it travel in one hour?
  • What do we know? The bus travels 120 km in 3 hours.
  • What do we need to find out? Distance per hour.
  • What operation? Division (splitting equally).
  • Calculation: 120 ÷ 3 = 40
  • Check: 40 × 3 = 120, so it's right.

Try it as a mini adventure

Mini Adventure: The Lost Treasure Hunt You are going on a treasure hunt with your friends. You have a map with clues, and you must solve maths problems to find the treasure.
  1. First clue: You walk 5 steps forward, then 3 steps back. How many steps forward are you from your start?
  2. Second clue: There are 4 treasure chests, and each chest has 7 gold coins. How many coins are there in total?
  3. Third clue: The treasure is hidden 15 minutes away from the starting point. If you walk at 3 minutes per step, how many steps do you take?
  4. Fourth clue: You find 20 sweets to share equally among 4 friends. How many sweets does each friend get?
Try to solve each clue using the steps we learned. For each one, ask yourself:
  • What do I know?
  • What am I trying to find?
  • What maths should I use?
  • Is my answer sensible?

Common mistakes

Here are some common mistakes children make and how to fix them: Mistake 1: Grabbing numbers without reading the question.
  • Incorrect strategy: Seeing "12" and "4" in a problem and just adding them.
  • Why it happens: Rushing to get an answer without thinking.
  • Fix: Read the whole question first. Ask, “What is this problem really asking?”
Mistake 2: Choosing the wrong operation.
  • Incorrect strategy: Using multiplication when you need subtraction.
  • Why it happens: Not thinking about what the problem means.
  • Fix: Think about the situation. If things are being taken away, use subtraction. If things are being shared, think division.
Mistake 3: Not checking your answer.
  • Incorrect strategy: Writing down a number without checking if it makes sense.
  • Why it happens: Being in a hurry or not knowing how to check.
  • Fix: Ask, “Does my answer make sense?” For example, if you're adding and get a smaller number, something went wrong.
Mistake 4: Ignoring key words.
  • Incorrect strategy: Missing words like “more than,” “less than,” or “altogether.”
  • Why it happens: Not paying attention to important clues.
  • Fix: Underline or circle key words that tell you what to do.

Parent and carer guide

Parents and carers can help children improve their problem-solving skills in just a few minutes each day:
  • Ask questions: When your child solves a problem, ask, “What did you do first?” or “How do you know that’s right?”
  • Read together: Read word problems out loud and talk through what they mean.
  • Encourage thinking: Don’t give the answer right away. Let them try and guide them gently.
  • Use real life: Ask them to solve problems from daily life, like “If we have 3 bags of 4 apples, how many apples do we have?”
  • Check the process: Make sure they read the whole problem, not just the numbers.
What to watch for:
  • Children who rush to answer without reading
  • Children who guess the operation instead of thinking
  • Children who don’t double-check their work
What not to worry about:
  • It’s normal for children to make mistakes at first
  • They will get better with practice
  • It’s okay to ask for help or take time to think

Practice questions

  1. There are 10 books on a shelf. 3 are taken away. How many are left?
  2. A garden has 5 rows of flowers. Each row has 6 flowers. How many flowers are there?
  3. A runner completes 18 km in 3 hours. How far does he run in one hour?
  4. There are 24 pencils. They are shared equally among 4 children. How many does each child get?
  5. There are 15 balloons. 7 are popped. How many are left?
Answers:
  1. 10 - 3 = 7
  2. 5 × 6 = 30
  3. 18 ÷ 3 = 6
  4. 24 ÷ 4 = 6
  5. 15 - 7 = 8

FAQ

What is a problem-solving misconception?

A misconception is a wrong idea or way of thinking about a problem. In maths, this often means rushing to use numbers without understanding what the question is asking.

How can I tell if I understand a problem?

Ask yourself: What do I know? What do I need to find? What operation should I use? Does my answer make sense?

Why do I need to check my answer?

Checking helps you find mistakes and makes sure your answer is correct and sensible.

What should I do if I don’t understand a problem?

Read it again. Circle key words. Ask a grown-up or friend for help. Try to imagine the situation.

How can I practice problem-solving at home?

Use everyday situations like cooking, shopping, or playing games. Ask questions like, “How many more do we need?” or “If we split this evenly, how much does each person get?”