Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

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?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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

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

Number problems at primary level that require careful consideration.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

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?

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?

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?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

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

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?

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!

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

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

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.

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. . . .

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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

This number has 903 digits. What is the sum of all 903 digits?

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?

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. . . .

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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?

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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

Can you find different ways of creating paths using these paving slabs?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.