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Maths investigation starters

Open-ended tasks that invite children to notice, wonder and explain.

Quick answer

Maths investigation starters are open-ended tasks that help children notice patterns, ask questions, and explore maths in fun, creative ways. They encourage thinking, not just calculating.

Learning outcome

By the end of this page, you will understand how to use maths investigation starters to explore patterns, make predictions, and solve problems in your everyday life. Success signs:
  • You can ask your own maths questions about things you see around you
  • You can notice patterns in numbers, shapes, or objects
  • You can make predictions and test them
  • You can explain your thinking to others

Why this matters

Maths investigation starters help children think like mathematicians. They're not just about getting the right answer – they're about asking good questions, exploring ideas, and finding creative ways to solve problems. These skills help you in school, in games, and in real life when you need to figure out new things. Whether you're trying to share sweets equally, planning a party, or wondering how many steps it takes to get to school, these investigation skills help you think through problems step by step.

How it works

Investigation starters begin with a simple idea or question. They don't have one right answer. Instead, they invite you to:
  1. Notice – What do you see around you?
  2. Wonder – What questions come to mind?
  3. Explore – Try different ideas or ways to solve it
  4. Explain – Share what you found out
You can start with anything: a box of crayons, a group of toys, a pattern in the garden, or even a story you're reading. The best part? You get to choose how to explore it.

Examples you can see

Let's look at a few examples of maths investigation starters you can try at home or in class. Example 1: How many ways can you make 10? You can use objects like blocks or counters. Try making 10 in different ways:
  • 5 + 5 = 10
  • 3 + 7 = 10
  • 2 + 2 + 6 = 10
  • 10 + 0 = 10
Ask yourself: What other ways can you make 10? What happens if you use more than two numbers? Example 2: How many triangles can you find in a picture? Look at a drawing or a real object like a roof or a kite. Count how many triangles you can see. You might find:
  • 1 big triangle
  • 4 small triangles
  • 1 triangle inside a triangle
Try drawing your own shapes and seeing how many triangles you can find. Example 3: What happens when you roll a dice 10 times? Roll a dice 10 times and write down each number. Then ask:
  • How many times did you roll a 3?
  • What was the biggest number?
  • What was the smallest number?
Try rolling again and compare your results.

Try it as a mini adventure

Adventure: The Mystery Box You have a box with some toys inside. You can't see what's in it, but you can guess.
  1. First time: You reach in and pull out a toy. It's a red ball. What do you wonder?
  2. Second time: You pull out a blue cube. What do you notice?
  3. Third time: You pull out a green block. What pattern do you see?
  4. Fourth time: You pull out a yellow ball. What do you predict will come out next?
  5. Fifth time: You pull out a purple cube. What do you think is in the box?
Now, ask yourself: What did you notice? What questions did you have? How can you test your ideas?

Common mistakes

  • Mistake: Thinking you must always get the right answer. Why it happens: Some children think that maths is only about getting the right number. Fix: Investigation starters are about exploring ideas, not just finding the answer. It's okay to wonder, guess, and change your mind.
  • Mistake: Not asking questions. Why it happens: Some children are used to doing maths the same way every time. Fix: Start with "What do you notice?" or "What do you wonder?" to get your thinking going.
  • Mistake: Not sharing your ideas. Why it happens: Some children feel their ideas aren't good enough. Fix: Every idea is valuable. Even if it's not right, it helps you think more deeply.

Parent and carer guide

As a parent or carer, you can support your child by:
  • Asking open questions like, "What do you notice?" or "What do you wonder?"
  • Letting them explore and make mistakes – it's part of learning!
  • Encouraging them to explain their thinking, even if it's not perfect
  • Not focusing only on the answer, but on the process
  • Using everyday moments to start investigations: "How many ways can we share these cookies?" or "What shapes can you see in this room?"
It's okay if you don't know the answer. You can explore with your child. The goal is to have fun and learn together.

Practice questions

  1. How many different ways can you make 8 using addition?
  2. Look around your room. What shapes do you see?
  3. If you have 12 crayons, how many ways can you split them into two groups?
  4. Roll a dice 5 times. Record the numbers. What do you notice?
  5. How many triangles can you find in a picture of a house?
Answers:
  1. Examples: 4 + 4 = 8, 3 + 5 = 8, 2 + 6 = 8, 1 + 7 = 8, 0 + 8 = 8
  2. Examples: square, circle, triangle, rectangle, hexagon
  3. Examples: 1 and 11, 2 and 10, 3 and 9, 4 and 8, 5 and 7, 6 and 6
  4. Answers will vary. Look for patterns like how often numbers appear
  5. Examples: 1 big triangle for the roof, 4 small triangles for windows, etc.

FAQ

What is a maths investigation starter?

A maths investigation starter is an open-ended activity that invites children to explore numbers, shapes, or patterns. It's not about one right answer, but about asking questions and discovering new ideas.

Why are investigation starters helpful?

They help children think more deeply about maths, make connections between ideas, and build confidence in exploring problems. They also help with creativity and communication skills.

Can I use these at home?

Yes! You can use everyday objects like toys, food, or things around your house to start investigations. They're perfect for family time and learning together.

Are investigation starters good for all ages?

Yes! You can make them simple for younger children and more complex for older ones. The key is to let the child explore and ask questions.

How can I make my own investigation starters?

Look around your home or outside. Ask, "What do you notice?" or "What do you wonder?" Then let your child explore that idea. You can also use books, games, or art to inspire new questions.