Problem Solving
Low floor high ceiling tasks
Design tasks that everyone can start and many can extend.
Quick answer
Low floor high ceiling tasks are maths problems that everyone can start working on, no matter their skill level, but that can be extended and made more challenging for those who want to go further.Learning outcome
By the end of this page, you will understand how to find and create maths problems that everyone can enjoy and learn from, no matter how good at maths you are.Why this matters
Low floor high ceiling tasks help children feel confident in maths and show that maths is more than just getting the right answer. They help children see that they can explore, question, and extend their thinking. These tasks are great for school, at home, and in games. They help children grow their problem-solving skills and build a love of maths that lasts a lifetime.How it works
Low floor high ceiling tasks have two parts: Low floor means the problem is easy to understand and start. You don’t need to know a lot of maths to begin. High ceiling means you can take the problem further and make it harder if you want to. You can find new patterns, make up your own questions, or explore different solutions. These tasks are like a ladder: everyone can start on the bottom step, but clever children can climb higher and higher.Examples you can see
Let’s look at a simple example: Task: How many ways can you make 10? Low floor: You can start by counting 10 fingers or drawing 10 apples. High ceiling: You can try to find all the ways to add numbers to get 10, or you can make it about money, like how many coins can make 10p, or even how many ways to split 10 sweets between 2 friends. Here’s another one: Task: Build a tower with blocks Low floor: You can just stack 3 blocks. High ceiling: You can make towers with 100 blocks, find the tallest one, or make patterns with the blocks. Let’s try a more mathematical example: Task: Find the area of a garden Low floor: You can count squares on a grid to find the area of a small garden. High ceiling: You can measure a real garden, find the area of a garden with a pond in it, or find the area of a garden with different shapes like rectangles and triangles.Try it as a mini adventure
Let’s go on a “Shape Hunt” adventure! Adventure: Find shapes in your house 1st time: Look around your house and find 3 shapes (like a square table, a circular plate, a triangular roof). 2nd time: Try to find 5 shapes, and write down how many sides each one has. 3rd time: Now try to find shapes that have the same number of sides (like 3 triangles, or 4 squares). 4th time: Can you make a new shape by combining 2 or more shapes? Draw it and describe it. 5th time: Challenge yourself to find shapes in your garden or outside. 6th time: If you can, find a shape that has more than 6 sides (like a hexagon or octagon). 7th time: Share your shape hunt with a friend or family member and tell them what you found.Common mistakes
Mistake 1: Thinking that low floor means easy. Why it happens: Some children think if a problem is easy to start, it must be easy to finish. Fix: A low floor task is just the beginning. It’s about starting with a simple idea and then finding ways to make it more interesting. Mistake 2: Not extending tasks further. Why it happens: Some children finish a task quickly and then stop, not seeing the fun in making it harder. Fix: Try asking “What if?” or “How else?” after finishing a task. This helps you think of new ways to make it more interesting. Mistake 3: Thinking there’s only one way to solve a problem. Why it happens: Children often believe there is only one correct answer or method. Fix: Show that there are often many ways to solve a problem. Try solving the same problem in different ways.Parent and carer guide
As a parent or carer, you can help your child enjoy low floor high ceiling tasks in 5-10 minutes by: 1. Asking open-ended questions: Instead of “What is the answer?”, ask “How did you solve it?” or “Can you think of another way?” 2. Encouraging creativity: Let your child make up their own versions of the task. For example, if the task is about shapes, let them create a new shape and explain it. 3. Not rushing: Let your child explore and take time to think. This helps them understand better. 4. Celebrating effort: Focus on how your child tried different ways to solve the problem, not just if the answer was right. 5. Making it fun: Use games, drawing, or stories to make the task more exciting. What not to do: Don’t tell your child the answer or make it about getting the right number. Focus on the process of thinking and solving.Practice questions
Here are 5 short practice questions to try: 1. How many ways can you make 8? Answer: 0 + 8, 1 + 7, 2 + 6, 3 + 5, 4 + 4, 5 + 3, 6 + 2, 7 + 1, 8 + 0 2. How many different rectangles can you make with 12 blocks? Answer: 1x12, 2x6, 3x4 3. Can you find 3 things in your room that are circular? Answer: (Any 3 circular objects like a plate, a coin, a clock) 4. How many ways can you split 6 sweets between 2 friends? Answer: 0 and 6, 1 and 5, 2 and 4, 3 and 3 5. Can you find a shape with 5 sides? Answer: (Any 5-sided shape like a pentagon, a slice of pizza, or a stop sign)FAQ
What is a low floor high ceiling task?
A low floor high ceiling task is a maths problem that is easy to start but can be made more difficult and extended for more advanced learners.
Why are these tasks good for children?
They help all children feel confident in maths, encourage creativity, and allow children to explore and extend their thinking in ways that match their abilities.
Can you give me more examples of low floor high ceiling tasks?
Yes! Examples include: finding all the ways to make 10, building with blocks, drawing shapes, measuring different objects, or sorting items by size or colour.
How can I make my own low floor high ceiling tasks?
Start with a simple idea, like “How many ways can you make 5?” Then think of ways to make it more complex, like using money, shapes, or real-life situations.
Are these tasks good for school?
Yes! They help children learn to think, explore, and solve problems in different ways, which is a key skill in maths and life.