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

Find out about Magic Squares in this article written for students. Why are they magic?!

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?

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

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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

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?

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

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?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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 find all the different triangles on these peg boards, and find their angles?

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?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

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?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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?

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?

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

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

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

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

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

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?

What two-digit numbers can you make with these two dice? What can't you make?

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

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

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

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?