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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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?

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?"

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Find the values of the nine letters in the sum: FOOT + BALL = GAME

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Can you draw a square in which the perimeter is numerically equal to the area?

The clues for this Sudoku are the product of the numbers in adjacent squares.

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 this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Investigate the different ways you could split up these rooms so that you have double the number.