Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

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?

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?

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

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

An activity centred around observations of dots and how we visualise number arrangement patterns.

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?

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

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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

This activity involves rounding four-digit numbers to the nearest thousand.

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

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?

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?

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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...

Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of 3 dominoes?

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

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

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

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Here's a very elementary code that requires young children to read a table, and look for similarities and differences.

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

There are six numbers written in five different scripts. Can you sort out which is which?

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

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

A task which depends on members of the group noticing the needs of others and responding.

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