Where is inverse thinking hiding in Topmarks Hit the Button times table questions?

Quick answer

When you play Topmarks Hit the Button and see a multiplication question like "6 × 7 = ?", the inverse thinking is hiding in how you can also think of it as "7 × 6 = ?" or even as a division problem like "42 ÷ 6 = ?" or "42 ÷ 7 = ?". This shows that multiplication and division are connected, and understanding one helps you understand the other.

Learning outcome

By the end of this page, you will understand how inverse thinking helps you solve multiplication and division problems, and how Topmarks Hit the Button uses this to help you learn your times tables.

• You can solve multiplication problems using division facts.
• You can find missing numbers in multiplication and division equations.
• You can use the same facts to solve both multiplication and division questions.
• You can see how multiplication and division are connected in real life.

Why this matters

Learning inverse thinking is like having a secret superpower! It helps you solve maths problems more quickly and easily. When you know your multiplication tables, you also know your division facts – it's like having two sides of the same coin. This is especially helpful when you're playing games like Topmarks Hit the Button, where you have to think fast. Understanding how multiplication and division are connected helps you do better in school and in everyday life.

How it works

Let’s imagine you are playing Topmarks Hit the Button and the question is "6 × 7 = ?". You might know that 6 × 7 = 42. But inverse thinking means you can also think of it as:

1. 7 × 6 = 42 (because multiplication is commutative)
2. 42 ÷ 6 = 7 (because division is the opposite of multiplication)
3. 42 ÷ 7 = 6 (same idea, just flipped)

This means that if you know one fact, you can use it to solve other problems. It’s like knowing one door opens to a room, and the other door also opens to the same room – just from a different side.

Examples you can see

Let’s look at a few examples of how inverse thinking works in Topmarks Hit the Button:

These examples show that if you know one multiplication fact, you also know two division facts. This is the magic of inverse thinking!

Try it as a mini adventure

Imagine you are a detective in a maths mystery. You are given a clue: “There are 42 cookies, and they are shared equally among 6 friends. How many cookies does each friend get?”

1. First, you think: “42 cookies shared by 6 friends” – that’s a division problem!
2. Then you remember: “6 × 7 = 42”
3. So, 42 ÷ 6 = 7
4. Each friend gets 7 cookies!

This is how inverse thinking helps you solve the mystery quickly. You used a multiplication fact to solve a division problem. Try it with different numbers – can you find a mystery where 36 cookies are shared by 9 friends?

Common mistakes

• Mistake: Thinking that 42 ÷ 6 = 7 and 42 ÷ 7 = 6 are different problems.
  Why it happens: Not understanding that division is the opposite of multiplication.
  Fix: Practice with arrays or groups. For example, if you have 42 objects and split them into 6 equal groups, each group has 7 objects. If you split them into 7 equal groups, each group has 6 objects.
• Mistake: Forgetting that 6 × 7 = 42 and 7 × 6 = 42 are the same.
  Why it happens: Not knowing that multiplication is commutative.
  Fix: Use physical objects like counters or blocks to show that 6 groups of 7 is the same as 7 groups of 6.
• Mistake: Not realising that 32 ÷ 8 = 4 means that 4 × 8 = 32.
  Why it happens: Not seeing the connection between multiplication and division.
  Fix: Use a multiplication chart or times table grid to see how multiplication and division are related.

Parent and carer guide

As a parent or carer, you can help your child by:

• Playing Topmarks Hit the Button together and asking questions like, “How did you know that?” or “Can you think of a division fact that matches this?”
• Using real-life examples like sharing snacks or arranging plates to show how multiplication and division are connected.
• Encouraging your child to say the multiplication and division facts out loud to build memory.
• Using visual aids like arrays or groups to show how the same numbers can be used in different ways.
• Not worrying if they get the answer wrong at first – inverse thinking is a skill that takes time to build.

Practice questions

1. What is 8 × 5? What division facts can you make from this?
2. If 9 × 6 = 54, what is 54 ÷ 9?
3. How many groups of 4 make 24? What multiplication fact does this show?
4. What is 12 × 3? What division facts can you make from this?
5. Find a division fact that matches 7 × 8 = 56.

Answers:

1. 8 × 5 = 40. Division facts: 40 ÷ 8 = 5 and 40 ÷ 5 = 8
2. 54 ÷ 9 = 6
3. 6 groups of 4 make 24. Multiplication fact: 6 × 4 = 24
4. 12 × 3 = 36. Division facts: 36 ÷ 12 = 3 and 36 ÷ 3 = 12
5. 56 ÷ 7 = 8 or 56 ÷ 8 = 7

FAQ

What is inverse thinking in maths?

Inverse thinking means using the opposite operation to solve a problem. For example, if you know 6 × 7 = 42, then you also know 42 ÷ 6 = 7 and 42 ÷ 7 = 6.

Why is inverse thinking helpful?

It helps you solve problems faster and understand how multiplication and division are connected. It’s a powerful tool that makes maths easier and more fun.

Can I use inverse thinking in everyday life?

Yes! For example, if you have 24 candies and want to share them equally among 4 friends, you can think: “24 ÷ 4 = 6,” meaning each friend gets 6 candies.

How can I practice inverse thinking?

You can practice by playing games like Topmarks Hit the Button, solving word problems, and using arrays or physical objects to show how multiplication and division work together.

What if I forget a multiplication fact?

You can use inverse thinking to help. If you forget 6 × 7, you can think: “What number times 6 gives 42?” That helps you remember that 6 × 7 = 42.