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?

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.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

What is the best way to shunt these carriages so that each train can continue its journey?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Can you find all the different triangles on these peg boards, and find their angles?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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. . . .

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

What could the half time scores have been in these Olympic hockey matches?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!