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?

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

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

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

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?

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

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.

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?

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?

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

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

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

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?

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?

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?

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?

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

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

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

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

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

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

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

Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?

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.

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

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

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

How do you know whether you will reach these numbers when you count in steps of six from zero?

This task focuses on distances travelled by the asteroid Florence. It's an opportunity to work with very large numbers.

How would you put these journey lengths in order? Give a bit of a place value challenge with subtractions set out not as a calculation.

Find as many different ways of representing this number of dots as you can.

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

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

This task gives an opportunity to perform some subtractions in a slightly realistic situation.