Chapter 8 Geometry: Properties of shapes; position and direction.

Chapter Summary This chapter shows how the ideas of visualistaion, categorisation and describing positionunderpin geometry. There is a focus on noticing and describing the properties of shapes The chapter describes the importance of developing the language of position.

Starting point One of the group read the following whilst the rest of the group close their eyes. Create a large red rectangle that you can see clearly in your mind’s eye. Stand it on its end so that you can see it standing on its shortest side. Then slowly rotate it so that it is laying on one of the longest sides. Now rotate it again so that it is balancing on a corner. Move the rectangle round and round in your mind’s eye and make a decision about which way round you want finally to picture the rectangle and stop it in that orientation. Now imagine a small, blue right-angled triangle that will fit inside the rectangle. Picture it inside the rectangle and slide it so that the right angle fits exactly into one corner of the rectangle. Imagine another small, blue right-angled triangle, which can be a different size from the first one you thought of. Slide into one of the other corners of the rectangle. Notice the red shape that is left inside the rectangle. Open you eyes and sketch your visualisation. Compare your drawings.

Developing geometric thinking Van Hiele Levels Level 0: Visualisation Level 1: Analysis Level 2: Informal deduction Level 3: Deduction Level 4: Rigour

Polygons

Triangles Draw 3 different triangles on 3 small pieces of paper. In groups of 4 or 5 classify all your triangles in a least 3 different ways. Make sure that as a group you have some equilateral, isosceles, scalene and right angled triangles.

Shapes in the environment Go for a walk around the building in which you are working. Sketch 4 or 5 shapes that you find. Include at least one you do not know the name of. When you get back describe the shapes to each other. Carry out research to decide on a name for the shape that you do not know the name of.

Three dimensional shapes Look around the room. Name as many three dimensional shapes as you can. List as many properties of each shapes as you can.

Transformations A transformation is the process of moving or transforming a shape on a grid. Transformations can take the form of: Translation Reflection Rotation

Symmetry Reflective Symmetry: List 3 things in the room which have reflective of line symmetry. Rotational Symmetry: List 3 things in the room which have rotational symmetry.

Observing the teaching of geometry Watch the video on the companion website of the teaching of geometry: What shapes would you use if you were going to use this activity? What questions would you ask? What vocabulary would you model to your pupils