How could you estimate the number of pencils/pens in these pictures?

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

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

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

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Buzzy Bee was building a honeycomb. She decided to decorate the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?

Can you hang weights in the right place to make the equaliser balance?

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

Complete the squares - but be warned some are trickier than they look!

This problem looks at how one example of your choice can show something about the general structure of multiplication.

Are these statements relating to odd and even numbers always true, sometimes true or never true?

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?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

An activity centred around observations of dots and how we visualise number arrangement patterns.

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Try this matching game which will help you recognise different ways of saying the same time interval.

What could the half time scores have been in these Olympic hockey matches?

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

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

This challenge is about finding the difference between numbers which have the same tens digit.

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

My coat has three buttons. How many ways can you find to do up all the buttons?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

This problem is designed to help children to learn, and to use, the two and three times tables.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.