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

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

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

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

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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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?

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

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

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

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

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

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?

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?

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

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?

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?

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

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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

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

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 magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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?

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 players. Practises subtraction or other maths operations knowledge.

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?

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?

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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

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 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?

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

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!

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?