My coat has three buttons. How many ways can you find to do up all the buttons?
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?
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?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
This challenge asks you to imagine a snake coiling on itself.
Can you find different ways of creating paths using these paving slabs?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.
These practical challenges are all about making a 'tray' and covering it with paper.
In how many ways can you stack these rods, following the rules?
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?
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.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
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.
Find all the ways of arranging the beads on this bracelet, using just two colours.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
This dice train has been made using specific rules. How many different trains can you make?
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?