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?

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

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?

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

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

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?

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

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

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?

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.

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

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?

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?

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

What two-digit numbers can you make with these two dice? What can't you make?

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

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

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?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

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

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

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

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

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?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

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

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

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

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

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

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

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

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?

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?

"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 ...?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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

Can you fill in the empty boxes in the grid with the right shape and colour?