One good turn
This is a level 3 geometry activity from the Figure It Out Series. It is focused on describing the rotational symmetry of shapes. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers’ notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Describe the rotational symmetry of shapes.
One good turn
Achievement objectives
GM3-6: Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object onto another.
Required materials
- a set of pattern blocks
- Figure It Out, Level 3, Geometry, "One good turn", page 21
See Materials that come with this resource to download:
- One good turn activity (.pdf)
Activity
Students need to recognise that each of the shapes in question 1 is made to a pattern. When students have made the various shapes, give them the opportunity to discuss the patterns they see. Encourage them to look for mirror lines in each shape and to recognise that some parts of the shape are mirror images or rotations of another part of the shape. This will help with visualisation.
Once students have made their shapes, have them either trace or draw these onto graph paper so that they can physically rotate the shapes and see how many times each shape maps onto itself. (The use of graph paper will help students be accurate in their drawing.)
The centre of rotation is the point that does not move when the shape is rotated. It is normally shown with a dot.
Rotational symmetry is the number of times a shape matches itself exactly during one complete turn.
This has rotational symmetry of order 3. The triangle matches itself exactly three times during one complete turn.
See also pages 4, 19, and 20 of the students’ booklet.
1.
a. Practical activity
b. i.
The figure fits onto itself every 1 / 4 turn about the centre (90°). It has rotational symmetry of order 4.
ii.
The figure fits onto itself every 1 / 3 turn about the centre (120°). It has rotational symmetry of order 3.
iii.
The figure fits onto itself every 1 / 4 turn about the centre (90°). It has rotational symmetry of order 4.
iv.
The figure fits onto itself every 1 / 3 turn about the centre (120°). It has rotational symmetry of order 3.
v.
The figure fits onto itself every 1 / 2 turn about the centre (180°). It has rotational symmetry of order 2.
vi.
The figure fits onto itself every 1 / 2 turn about the centre (180°). It has rotational symmetry of order 2.
vii.
The figure fits onto itself every 1 / 2 turn about the centre (180°). It has rotational symmetry of order 2.
2.
Practical activity
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