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

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?

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?

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?

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?

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

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

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?

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

Can you make square numbers by adding two prime numbers together?

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.

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?

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 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?

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

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

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Have a go at balancing this equation. Can you find different ways of doing it?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Can you work out some different ways to balance this equation?

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

Number problems at primary level that may require resilience.

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?

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!

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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

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

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

How many different sets of numbers with at least four members can you find in the numbers in this box?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

An environment which simulates working with Cuisenaire rods.

"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 this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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

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?

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

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

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?