NRICH Angles, Polygons and Geometrical Proof - Stage 3
This list supports teaching of angles, polygons and geometrical proof at Key Stage 3. It provides investigations, problems and games from NRICH as well as classroom activities on the STEM Learning website that compliment them.
Here are some favourite activities selected by the NRICH team.
- Square it In this game players take it in turn to click on a dot on a grid. The winner is the first to have four dots joined to form a square.
- Completing Quadrilaterals Students are challenged to complete quadrilaterals given one side of the shape and a given area.
- Triangles in Circles In this GeoGebra activity students are presented with a circle marked with 9 equally spaced points on the edge and one in the centre. The challenge is to draw as many different triangles as possible.
These are just a few of the activities on angles, polygons and geometrical proof that you can find on the NRICH curriculum pages.
The activities below, taken from the STEM Learning website, complement the NRICH activities above.
GAIM Activities: Investigations
Task 14, Triangles, presents a 3 by 3 pin board and requires students to make as many different triangles as possible. Teachers notes provide hints and possible extension activities.
Task 18, Roofs, explores how to draw quadrilateral shaped roofs on isometric paper.
Angle Properties
Smile Pack One, Worksheet 6 shows a hexagon with various diagonals and lines from the centre drawn on isometric paper. Students need to find all the angles.
Paper Magic: Folding Polygons
This is a series of activities and ideas where students use paper folding to investigate shape and angles. Shapes include equilateral triangle, rhombus, kite, regular pentagon, hexagon and other regular polygons. Further activities encourage students to explore angles, symmetries and tessellations.
Shape, Space and Measures 3
Pdf page 45 starts with an activity about a pentagon and the golden ratio. Students need to draw a regular pentagon in order to find a golden rectangle then follow an investigation leading to a spiral.
The next section (pdf page 47) has a set of five activities. The first three puzzles relate to polygons and special shapes within hexagons and quadrilaterals.
