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

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

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

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.

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?

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

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?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

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

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

Here is a version of the game 'Happy Families' for you to make and play.

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?

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

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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?

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

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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

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

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

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 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?

Use the tangram pieces to make our pictures, or to design some of your own!

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?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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 make the birds from the egg tangram?

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

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

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?

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 ...

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

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?

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

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

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