An environment which simulates working with Cuisenaire rods.

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

If you have only four weights, where could you place them in order to balance this equaliser?

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Use the number weights to find different ways of balancing the equaliser.

This challenge extends the Plants investigation so now four or more children are involved.

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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

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?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Here is a chance to play a version of the classic Countdown Game.

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

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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.

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

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?