Writing maths explanations
Use because, therefore and diagrams to communicate reasoning.
Quick answer
When you solve a maths problem, you can write down your thinking using words like "because", "therefore", and drawings to show how you figured it out. This helps others understand your maths ideas.Learning outcome
By the end of this page, you will be able to write clear maths explanations that show how you solved a problem, using words like "because", "therefore", and drawings. Success signs:- You can explain your maths thinking with words and pictures
- You use "because" to show your reasons
- You use "therefore" to show your answer
- You can show your thinking in a clear way that others can follow
Why this matters
Writing maths explanations helps you think more clearly and helps others understand how you solved a problem. When you explain your thinking, it helps you learn better and helps teachers and friends see what you know. It’s like telling a story about your maths adventure!How it works
Writing a maths explanation is like being a detective. You find the answer, then you explain how you found it. Here are the steps:- Find the problem – Read the question carefully
- Think about how to solve it – Decide what maths you need
- Work it out – Do the maths
- Write your explanation – Use words like "because" and "therefore"
- Draw a picture – Show your thinking with a diagram
Examples you can see
Let’s look at a problem and how to write an explanation. Problem: There are 3 boxes of pencils. Each box has 4 pencils. How many pencils are there altogether? Step 1: I need to find the total number of pencils. Step 2: I can use multiplication because I have equal groups. Step 3: 3 boxes with 4 pencils in each box means 3 × 4 = 12 pencils. Step 4: I can draw a picture to show this. Step 5: Therefore, there are 12 pencils altogether. Here’s how to write it:Explanation:
I have 3 boxes of pencils. Each box has 4 pencils. I need to find the total number of pencils. Because I have equal groups, I can use multiplication. 3 × 4 = 12. Therefore, there are 12 pencils altogether.
Another example:
Problem: Sarah has 15 stickers. She gives 6 to her friend. How many does she have left?
Explanation:
Sarah starts with 15 stickers. She gives 6 to her friend. I need to subtract to find how many she has left. 15 − 6 = 9. Therefore, Sarah has 9 stickers left.
Try it as a mini adventure
Adventure: The Lost Treasure Hunt You are on a treasure hunt with your friends. You need to solve maths clues to find the treasure. Here's your first clue:Clue: There are 5 treasure chests. Each chest has 3 gold coins. How many gold coins are there in total?
Your mission:
- Draw a picture of the treasure chests and coins
- Write your explanation using "because" and "therefore"
- Write your answer
Example answer:
I have 5 treasure chests. Each chest has 3 gold coins. I need to find the total number of coins. Because I have equal groups, I can use multiplication. 5 × 3 = 15. Therefore, there are 15 gold coins in total.
Common mistakes
- Mistake: Not using words like "because" and "therefore"
- Why it happens: Children think writing an explanation is not needed
- Fix: Explain that writing words helps others understand your thinking
- Mistake: Not drawing a picture to show the problem
- Why it happens: Children think pictures are not important
- Fix: Draw a simple picture to show the groups or the problem
- Mistake: Writing the answer without showing the working
- Why it happens: Children want to get the answer quickly
- Fix: Always show your steps with words and pictures
Parent and carer guide
Parents and carers can help by:- Asking your child to explain their thinking
- Encouraging them to use "because" and "therefore"
- Letting them draw pictures to show their problem-solving
- Reading their explanations together
- Practising with simple problems at home
Try this at home:
Give your child a simple problem like "There are 4 apples and 3 oranges. How many fruits are there?" Ask them to write an explanation using words like "because" and "therefore".
What to say:
- "Can you show me how you worked it out?"
- "Why did you use addition?"
- "Can you draw a picture to show that?"
What not to worry about:
- Not every explanation has to be perfect
- It's okay to make mistakes – that's how we learn
- Encourage creativity in how they show their thinking
Practice questions
- Problem: There are 6 bags. Each bag has 2 marbles. How many marbles are there?
- Problem: I have 12 crayons. I give 5 to my sister. How many do I have left?
- Problem: There are 4 rows of chairs. Each row has 5 chairs. How many chairs are there?
- Problem: There are 10 cookies. 3 are eaten. How many are left?
- Problem: 7 children each have 3 toy cars. How many toy cars are there?
Answers:
- Because I have 6 equal groups of 2 marbles, I use multiplication. 6 × 2 = 12. Therefore, there are 12 marbles.
- Because I start with 12 crayons and give away 5, I use subtraction. 12 − 5 = 7. Therefore, I have 7 crayons left.
- Because I have 4 rows with 5 chairs in each row, I use multiplication. 4 × 5 = 20. Therefore, there are 20 chairs.
- Because I start with 10 cookies and eat 3, I use subtraction. 10 − 3 = 7. Therefore, 7 cookies are left.
- Because I have 7 children with 3 toy cars each, I use multiplication. 7 × 3 = 21. Therefore, there are 21 toy cars.
FAQ
What does it mean to explain my maths?
It means telling others how you solved a problem. You can use words, pictures, or both to show your thinking.
Why do I need to explain my maths?
Explaining helps you understand your own thinking. It also helps others see what you know and how you solved the problem.
Can I use drawings to explain?
Yes! Drawing pictures helps you show your thinking. It makes it easier for others to understand how you solved the problem.
What are the words "because" and "therefore" for?
"Because" helps you explain your reason. "Therefore" helps you show your answer. These words make your explanation clear.
Do I have to write full sentences?
No, but you should write enough so others can understand how you solved the problem. Short sentences are okay!