There are lots of different methods to find out what the shapes are worth - how many can you find?

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you use this information to work out Charlie's house number?

Can you replace the letters with numbers? Is there only one solution in each case?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

This article for primary teachers suggests ways in which to help children become better at working systematically.

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?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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?

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Can you substitute numbers for the letters in these sums?

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.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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?

How many possible necklaces can you find? And how do you know you've found them all?

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

This task follows on from Build it Up and takes the ideas into three dimensions!

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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, focuses on 'open squares'. What would the next five open squares look like?

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

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

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?