Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

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

These pictures show squares split into halves. Can you find other ways?

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 five differently sized squares from the tangram pieces?

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

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

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?

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

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

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

Explore the triangles that can be made with seven sticks of the same length.

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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

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

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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?

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

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?

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

Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

Can you lay out the pictures of the drinks in the way described by the clue cards?

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

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

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

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 ...

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

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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?

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?

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

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?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

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 make the birds from the egg tangram?

The challenge for you is to make a string of six (or more!) graded cubes.