A group activity using visualisation of squares and triangles.
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
Make a flower design using the same shape made out of different sizes of paper.
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?
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?
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!
What shape is made when you fold using this crease pattern? Can you make a ring design?
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?
Move four sticks so there are exactly four triangles.
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?
What is the greatest number of squares you can make by overlapping three squares?
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
Can you split each of the shapes below in half so that the two parts are exactly the same?
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.
Why do you think that the red player chose that particular dot in this game of Seeing Squares?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.
Reasoning about the number of matches needed to build squares that share their sides.
Can you fit the tangram pieces into the outline of this sports car?
Can you fit the tangram pieces into the outline of this goat and giraffe?
Watch this animation. What do you see? Can you explain why this happens?
An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?
Can you fit the tangram pieces into the outline of the rocket?
Can you fit the tangram pieces into the outline of this plaque design?
Can you fit the tangram pieces into the outline of these convex shapes?
Make a cube out of straws and have a go at this practical challenge.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Here's a simple way to make a Tangram without any measuring or ruling lines.
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?
Can you fit the tangram pieces into the outlines of the candle and sundial?
Can you fit the tangram pieces into the outlines of the watering can and man in a boat?
Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
Here are shadows of some 3D shapes. What shapes could have made them?