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

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

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Use the interactivities to complete these Venn diagrams.

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

A game in which players take it in turns to choose a number. Can you block your opponent?

Use the interactivity to sort these numbers into sets. Can you give each set a name?

Can you complete this jigsaw of the multiplication square?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

If you have only four weights, where could you place them in order to balance this equaliser?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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

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

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

A game that tests your understanding of remainders.

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Can you find the chosen number from the grid using the clues?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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?

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

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

56 406 is the product of two consecutive numbers. What are these two numbers?

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?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

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

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?