Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

How would you count the number of fingers in these pictures?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

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

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

How could you estimate the number of pencils/pens in these pictures?

Daisy and Akram were making number patterns. Daisy was using beads that looked like flowers and Akram was using cube bricks. First they were counting in twos.

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

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?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Here is a version of the game 'Happy Families' for you to make and play.

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

Can you work out how many apples there are in this fruit bowl if you know what fraction there are?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

25 students are queuing in a straight line. How many are there between Julia and Jenny?

How many legs do each of these creatures have? How many pairs is that?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

What could these drawings, found in a cave in Spain, represent?

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

Can you deduce the pattern that has been used to lay out these bottle tops?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?

What do you see as you watch this video? Can you create a similar video for the number 12?

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?