National Young Mathematicians' Award activities

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

This problem looks at how one example of your choice can show something about the general structure of multiplication.

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

This task challenges you to create symmetrical U shapes out of rods and find their areas.

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

We can make 'wire cages' by using rods as the edges of cuboids. Can you work out what the volume of each wire cage will be? How many rods will you use?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

This challenge combines addition, multiplication, perseverance and even proof.

This task combines spatial awareness with addition and multiplication.

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

How will you decide which way of flipping over and/or turning the grid will give you the highest total?

In how many ways can you stack these rods, following the rules?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

This dice train has been made using specific rules. How many different trains can you make?

These practical challenges are all about making a 'tray' and covering it with paper.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?