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

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

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?

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?

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?

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

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

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

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

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?

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

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

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?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

An activity making various patterns with 2 x 1 rectangular tiles.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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?

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.

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?

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?

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.

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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 put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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!

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!

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.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

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

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

What happens when you try and fit the triomino pieces into these two grids?

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?

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?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

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?

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.

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

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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