Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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

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

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?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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?

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

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

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

There are nasty versions of this dice game but we'll start with the nice ones...

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

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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

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

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

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. . . .

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?

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!

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

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?

Investigate the different distances of these car journeys and find out how long they take.

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

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

These two group activities use mathematical reasoning - one is numerical, one geometric.

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Can you use the information to find out which cards I have used?

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.