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

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

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?

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?

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

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 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.

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

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 make square numbers by adding two prime numbers together?

An environment which simulates working with Cuisenaire rods.

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?

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

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?

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?

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

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

"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 ...?

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

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

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

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

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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?

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

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!

Can you complete this jigsaw of the multiplication square?

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?

Number problems at primary level that may require determination.

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

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?

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

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.

Number problems at primary level to work on with others.

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.

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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?

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

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.

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?

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

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

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

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Given the products of adjacent cells, can you complete this Sudoku?

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

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?