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?

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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?

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

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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?

This package will help introduce children to, and encourage a deep exploration of, multiples.

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

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

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

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

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

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?

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

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

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

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

Got It game for an adult and child. How can you play so that you know you will always win?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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?

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.

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

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?

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

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

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

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

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?

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

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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?

A game that tests your understanding of remainders.

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

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Use the interactivities to complete these Venn diagrams.

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

An investigation that gives you the opportunity to make and justify predictions.

Number problems at primary level that may require determination.

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?