Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
In this matching game, you have to decide how long different events take.
What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Can you find all the different ways of lining up these Cuisenaire rods?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
You need to find the values of the stars before you can apply normal Sudoku rules.
Find out what a "fault-free" rectangle is and try to make some of your own.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
How many different triangles can you make on a circular pegboard that has nine pegs?
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.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Can you find all the different triangles on these peg boards, and find their angles?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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. . . .
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?