Can you each work out the number on your card? What do you notice? How could you sort the cards?

Find all the numbers that can be made by adding the dots on two dice.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Can you find 2 butterflies to go on each flower so that the numbers on each pair of butterflies adds to the same number as the one on the flower?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

How would you count the number of fingers in these pictures?

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

There were 22 legs creeping across the web. How many flies? How many spiders?

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.

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

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

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?

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?

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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?

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

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

In this game for two players, the aim is to make a row of four coins which total one dollar.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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?

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?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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?

Investigate what happens when you add house numbers along a street in different ways.

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?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.