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Maths Without Realising

Maths detective: rolling dice

A mini detective challenge where children spot probability and addition while rolling dice.

Quick answer

When you roll dice, you're using maths without even realising it! You're adding numbers, predicting outcomes, and understanding chance – all part of being a maths detective.

Learning outcome

By the end of this page, you will be able to spot the maths in rolling dice and use addition and probability to solve simple detective puzzles. Success signs:
  • You can add the numbers on two dice to find the total
  • You can predict which totals are more likely when rolling two dice
  • You can explain how dice help you solve simple maths problems
  • You can play a dice game and notice the maths happening

Why this matters

Rolling dice isn't just for games – it's a way to learn maths! Whether you're playing a board game, predicting how many points you'll score, or planning a party, dice help you understand numbers, chance, and problem-solving. As a maths detective, you're always looking for numbers hiding in everyday life.

How it works

When you roll dice:
  1. You get random numbers from 1 to 6
  2. When you roll two dice, you add the numbers together
  3. Some totals are more likely than others
  4. You can use dice to solve puzzles or play games

Examples you can see

Let’s imagine you’re a detective solving a mystery. You roll two dice to find out how many steps you need to go to find the treasure. Example 1: Rolling one die If you roll a die and get a 4, that’s just one number. Example 2: Rolling two dice If you roll two dice and get a 3 and a 5, you add them: 3 + 5 = 8. So you need to take 8 steps. Example 3: Adding dice totals When you roll two dice, the smallest total is 1 + 1 = 2, and the biggest is 6 + 6 = 12. Here’s a table showing all possible totals when rolling two dice:
Die 1 Die 2 Total
1 1 2
1 2 3
1 3 4
1 4 5
1 5 6
1 6 7
2 1 3
2 2 4
2 3 5
2 4 6
2 5 7
2 6 8
3 1 4
3 2 5
3 3 6
3 4 7
3 5 8
3 6 9
4 1 5
4 2 6
4 3 7
4 4 8
4 5 9
4 6 10
5 1 6
5 2 7
5 3 8
5 4 9
5 5 10
5 6 11
6 1 7
6 2 8
6 3 9
6 4 10
6 5 11
6 6 12

Try it as a mini adventure

Adventure: The Dice Detective Mission You are a detective on a mission to find a lost treasure. You must roll dice to figure out how many steps to take. Here’s your adventure: 1st time: Roll two dice. If you get 5 and 3, take 5 + 3 = 8 steps. 2nd time: Roll again. If you get 2 and 6, take 2 + 6 = 8 steps. 3rd time: Roll again. If you get 4 and 4, take 4 + 4 = 8 steps. 4th time: Roll again. If you get 1 and 5, take 1 + 5 = 6 steps. 5th time: Roll again. If you get 6 and 2, take 6 + 2 = 8 steps. Now, which total did you get most often? You might notice that 7 is the most common total, because there are more ways to make 7 than any other number.

Common mistakes

  • Mistake: Thinking that rolling a 1 and a 6 gives you 16. Why it happens: Children sometimes confuse the dice numbers with a two-digit number. Fix: Remember that 1 + 6 = 7, not 16. Roll two dice and add the numbers, not put them side by side.
  • Mistake: Thinking all totals are equally likely. Why it happens: Children might not notice that some numbers can be made in more ways. Fix: Roll dice several times and count how many times each total comes up. You’ll see that 7 comes up more often than 2 or 12.
  • Mistake: Forgetting that rolling a 1 and a 1 gives 2, not 1. Why it happens: Children might think the dice show 1 and 1, so the total is 1. Fix: Remember that 1 + 1 = 2. Two dice showing 1 each make 2.

Parent and carer guide

As a parent or carer, you can help your child become a maths detective by:
  • Playing dice games together, like rolling dice and adding the numbers
  • Asking questions like: “What’s the biggest number you can get? What’s the smallest?”
  • Noticing when your child adds numbers from dice in games or daily life
  • Encouraging them to record their rolls and totals to see patterns
  • Not worrying if they make mistakes – they’re learning!
You can also play the detective game with them:
  • Roll dice and ask them to add the numbers
  • Try to guess which number will come up most often
  • Count how many times each number appears in a set of rolls

Practice questions

  1. Roll two dice. You get 3 and 4. What is the total?
  2. You roll two dice. You get 5 and 5. What is the total?
  3. You roll two dice. You get 1 and 6. What is the total?
  4. Which total is most likely when rolling two dice?
  5. Which total is least likely when rolling two dice?
Answers:
  1. 3 + 4 = 7
  2. 5 + 5 = 10
  3. 1 + 6 = 7
  4. 7
  5. 2 or 12

FAQ

How many different totals can you get when rolling two dice?

You can get totals from 2 to 12. That’s 11 different totals.

Why is 7 the most common total?

There are more ways to make 7 than any other number. For example, 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1 all make 7.

Can you use dice to play maths games?

Yes! You can play games where you roll dice and add the numbers, or subtract them, or even multiply them.

What if I roll the same number twice?

That’s fine! If you roll two 3s, you add them: 3 + 3 = 6. You’re still using addition.

Do I need to know all the dice combinations?

No, but it helps to know that 7 is the most common and that 2 and 12 are the least common totals.