Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

What shape is made when you fold using this crease pattern? Can you make a ring design?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Make a flower design using the same shape made out of different sizes of paper.

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Can you visualise what shape this piece of paper will make when it is folded?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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?

Can you put these shapes in order of size? Start with the smallest.

Can you deduce the pattern that has been used to lay out these bottle tops?

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

What do these two triangles have in common? How are they related?

Exploring and predicting folding, cutting and punching holes and making spirals.

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Make a cube out of straws and have a go at this practical challenge.

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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?

Can you split each of the shapes below in half so that the two parts are exactly the same?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

In this activity focusing on capacity, you will need a collection of different jars and bottles.

For this activity which explores capacity, you will need to collect some bottles and jars.