Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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

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.

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?

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?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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?

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

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

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

How many different shapes can you make by putting four right- angled isosceles triangles together?

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?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

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?

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.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Can you find out in which order the children are standing in this line?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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!

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?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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?

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

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

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?

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

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!

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

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?

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

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

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?

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?

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?

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?