In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

Dotty Six is a simple dice game that you can adapt in many ways.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

Use these four dominoes to make a square that has the same number of dots on each side.

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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?

What numbers would you put on this number line as it goes under the sea level?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

There are nasty versions of this dice game but we'll start with the nice ones...

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Four strategy dice games to consolidate pupils' understanding of rounding.

Try out these calculations. Are you surprised by the results?

Can you find any two-digit numbers that satisfy all of these statements?

How much can you read into a T-shirt?

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Can you work as a team to make doughnuts by matching these fractions, decimals and percentages?

Take three consecutive numbers and add them together. What do you notice?

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

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?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

How many solutions can you find to this sum? Each of the different letters stands for a different number.