Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

How many trapeziums, of various sizes, are hidden in this picture?

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

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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

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

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

This challenge is about finding the difference between numbers which have the same tens digit.

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.

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

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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?

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

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

My coat has three buttons. How many ways can you find to do up all the buttons?

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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

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?

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?

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

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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.

Can you fill in the empty boxes in the grid with the right shape and colour?

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

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

Can you find the chosen number from the grid using the clues?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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?

Investigate the different ways you could split up these rooms so that you have double the number.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Find all the numbers that can be made by adding the dots on two dice.

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

These practical challenges are all about making a 'tray' and covering it with paper.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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?

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?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.