Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
These practical challenges are all about making a 'tray' and covering it with paper.
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?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
What do these two triangles have in common? How are they related?
Try continuing these patterns made from triangles. Can you create your own repeating pattern?
How many triangles can you make on the 3 by 3 pegboard?
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?
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.
Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
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.
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
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?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
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.
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?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
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?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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 is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
Can you put these shapes in order of size? Start with the smallest.
A group of children are discussing the height of a tall tree. How would you go about finding out its height?
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?
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you create more models that follow these rules?
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?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
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?
Explore the triangles that can be made with seven sticks of the same length.
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?
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?
These pictures show squares split into halves. Can you find other ways?
We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you make the birds from the egg tangram?
Can you split each of the shapes below in half so that the two parts are exactly the same?
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?