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?
Can you make the birds from the egg tangram?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
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?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Here is a version of the game 'Happy Families' for you to make and play.
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?
Make a flower design using the same shape made out of different sizes of paper.
How many triangles can you make on the 3 by 3 pegboard?
What is the greatest number of squares you can make by overlapping three squares?
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?
Can you cut up a square in the way shown and make the pieces into a triangle?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
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.
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.
Follow these instructions to make a three-piece and/or seven-piece tangram.
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.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
What shape is made when you fold using this crease pattern? Can you make a ring design?
Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
These practical challenges are all about making a 'tray' and covering it with paper.
How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
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?
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?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
How can you put five cereal packets together to make different shapes if you must put them face-to-face?
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.
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?
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 ...
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 models can you find which obey these rules?
Can you visualise what shape this piece of paper will make when it is folded?
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
Use the tangram pieces to make our pictures, or to design some of your own!
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?
Reasoning about the number of matches needed to build squares that share their sides.
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.
How can you make a curve from straight strips of paper?
This practical activity involves measuring length/distance.
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?