This is part of our collection of favourite rich tasks arranged by topic.
If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.
1 out of 3
How good are you at estimating angles?
1 out of 3
A game for 2 or more people, based on the traditional card game Rummy.
1 out of 3
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
1 out of 3
Can you find triangles on a 9-point circle? Can you work out their angles?
1 out of 3
Can you find the squares hidden on these coordinate grids?
1 out of 3
How many questions do you need to identify my quadrilateral?
1 out of 3
Join pentagons together edge to edge. Will they form a ring?
1 out of 3
We started drawing some quadrilaterals - can you complete them?
1 out of 3
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
1 out of 3
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
2 out of 3
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
2 out of 3
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
2 out of 3
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
2 out of 3
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
2 out of 3
A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?
2 out of 3
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
2 out of 3
What's special about the area of quadrilaterals drawn in a square?
2 out of 3
Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?
3 out of 3
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
1 out of 3
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
1 out of 3
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
1 out of 3
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
1 out of 3
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.
2 out of 3
Can you make sense of these three proofs of Pythagoras' Theorem?
2 out of 3
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.
