Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!
Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
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?
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?
This practical activity challenges you to create symmetrical designs by cutting a square into strips.
Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?
Follow these instructions to make a five-pointed snowflake from a square of paper.
Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!
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?
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?
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
Can you each work out what shape you have part of on your card? What will the rest of it look like?
It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!
Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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?
Can you deduce the pattern that has been used to lay out these bottle tops?
An activity making various patterns with 2 x 1 rectangular tiles.
Exploring and predicting folding, cutting and punching holes and making spirals.
Make a cube out of straws and have a go at this practical challenge.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
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 make the birds from the egg tangram?
These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?
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?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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?
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?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
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.
You'll need a collection of cups for this activity.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
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.
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?
How many models can you find which obey these rules?
Use the tangram pieces to make our pictures, or to design some of your own!
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?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?