What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
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?
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.
What is the greatest number of squares you can make by overlapping three squares?
Reasoning about the number of matches needed to build squares that share their sides.
Make a cube out of straws and have a go at this practical challenge.
Exploring and predicting folding, cutting and punching holes and making spirals.
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 ...
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Can you cut up a square in the way shown and make the pieces into a triangle?
What shape is made when you fold using this crease pattern? Can you make a ring design?
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?
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?
Make a flower design using the same shape made out of different sizes of paper.
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?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
How do you know if your set of dominoes is complete?
Can you create more models that follow these rules?
How many models can you find which obey these rules?
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?
Can you visualise what shape this piece of paper will make when it is folded?
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.
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
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?
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?
Can you make the birds from the egg tangram?
Follow these instructions to make a three-piece and/or seven-piece tangram.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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 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?
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.
In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
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?
Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.
This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.
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.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
How many triangles can you make on the 3 by 3 pegboard?
The challenge for you is to make a string of six (or more!) graded cubes.
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!