Stage 3 -space and geometry – 2D
Identify quadrilaterals; recognise the properties of regular polygons; identify polygons that have rotational symmetry; use Microsoft Word to draw shapes and rotate shapes; use Microsoft Word to make enlargements and reductions of shapes
- identify quadrilaterals
- recognise the properties of regular polygons
- identify polygons that have rotational symmetry
- use Microsoft Word to draw shapes and rotate shapes
- use Microsoft Word to make enlargements and reductions of shapes
Activities to support the strategy
Activity 1: regular polygons
1. Discuss with the class the different features of two dimensional shapes.
Two dimensional shapes can have pairs of sides which are:
- equal in length
- unequal in length
and angles that are:
- equal in size
- acute, right, obtuse, straight, reflex
as well as the shapes being regular or irregular, having axes of symmetry and rotational symmetry.
2. Display a variety of quadrilaterals (polygons with four sides) on a whiteboard - square, rectangle, parallelogram, rhombus, trapezium, etc. Students name each quadrilateral and discuss for each one, whether the sides are equal in length and whether the angles are all the same size.
- How can we test if the sides are equal in length?
- How can we test if the angles are equal in size?
- Which shapes have sides that are parallel?
Students could also take turns to draw a variety of quadrilaterals on the whiteboard. Each quadrilateral that the students draw must be different from the previous ones. This way the students are recognising quadrilaterals in different orientations.
Read this definition of a regular polygon.
Squares are regular quadrilaterals. Examples of other regular shapes include regular pentagon, regular octagon and regular decagon.
Irregular shapes are shapes in which at least one side is not the same length as the other sides. Examples of irregular shapes include rectangle, trapezium and parallelogram.
Draw a square and a rectangle on the whiteboard or place the shapes on an overhead projector.
Only one of these shapes is a regular polygon, because only one has all sides equal in length and all angles equal in size.
- Which shape is a regular polygon?
- How do you know?
- What is this shape called?
3. Provide students with a table showing the different types of quadrilaterals. They complete this table by identifying the side and angle features of different quadrilaterals. Place a tick or cross to indicate if the quadrilateral is regular.
For the quadrilateral to be regular it must have a tick under four equal angles and four equal sides.
The students draw two of their own shapes for (e) and (f) in the table to match the description of the side and angle properties.
4. Provide students with an equilateral triangle cut out from coloured paper. They fold the triangle in different ways to find the lines of symmetry.
Students describe the shapes produced when they fold along a line of symmetry in an equilateral triangle.
Repeat with a paper square or another regular polygon, such as a pentagon, hexagon or octagon. A worksheet of regular shapes is provided.
Complete these sentences about regular polygons.
Activity 2 rotational symmetry
1. Explain to students:
- Some shapes have lines of symmetry. Shapes can also have turning symmetry or rotational symmetry.
- Rotational symmetry occurs when a shape, once rotated, matches the original shape. For example, a square can be rotated:
As it takes 4 turns to have square ABCD back in the same position, and the square matches on each turn, a square has rotational symmetry of order 4.
One way to test if an object has rotational symmetry is to trace around its outline onto A4 paper using a sharp pencil. The object is then rotated one full turn to discover if the outline of the object matches its outline on paper more than once as it is rotated.
Students use different materials to test for rotational symmetry.
- exercise book
- 50 cent coin
- school shoe
- a mug or glass
Trace around a school shoe, then lift the shoe and slowly turn it. Keep turning it around until it fits exactly inside the outline again.
How much did you have to turn the shoe until it fitted inside the outline again?
Did you have to rotate the shoe one full turn to make it fit?
The shoe matches only once with its outline in a full turn. This means the shoe has no rotational symmetry.
Trace the rectangular exercise book onto paper. Place the book in its outline then slowly turn it until it fits exactly inside the outline again.
The book can be rotated one half turn and its outline will match.
How many times will the book and its outline match in one full turn?
When the book is turned, did it match its outline two times in a full turn?
This book has rotational symmetry because it can fit exactly inside its outline after a half turn and all angles and sides match. The book matches more than once with its outline in a full turn. It has rotational symmetry of order 2.
- Trace around a 50 cent coin and test for rotational symmetry.
When you turned the coin did it match its outline many times in a full turn?
A 50 cent coin has rotational symmetry because it could match its outline more than once in a full turn. It has rotational symmetry of order 12.
- Trace around either the base or rim of a glass onto paper to test for rotational symmetry.
Before students turn the glass, they should use a pencil to mark both the glass and its outline at one point with matching dots. This will remind then how far the glass has been turned.
- When you turned the glass did it match its outline more than once in a full turn?
- How many times while you were turning the glass, did the glass match its outline?
- Is there any position where the glass did not match its outline on the paper?
A glass has rotational symmetry because it could match its outline more than once in a full turn.
2. Provide students with two copies of the worksheet 'Testing for Rotational Symmetry'. One copy can be on coloured cardboard and the other on paper. Students cut out the polygons on the cardboard worksheet only. Using the cardboard cut-outs they test each for rotational symmetry.
To do this they have to line up the star on each cut-out with the star on the matching polygon before they start to turn the cardboard cut-out. The star will remind them when they have completed a full rotation.
They complete the table 'Testing for Rotational Symmetry' after they have tested each polygon for rotational symmetry.
Students use the information in the table and write what they have learnt about rotational symmetry. e.g.
In pairs, play Concentration using drawings of shapes and descriptions of the features of the shapes.
Ask students to draw four shapes and write descriptions to match each of their drawings. Students should then play concentration between four pairs of students using their drawings and descriptions.
Activity 3: rotational symmetry using word
Students can use Microsoft Word to test for rotational symmetry. The following instructions are available for Microsoft Office 2003 and 2007.
1. Students can create a variety of different shapes using Word. They should label those which have rotational symmetry and those that do not. For the shapes with rotational symmetry they can determine the number of times the shape matches its outline during one full turn.
2. Students can also practise enlarging and reducing shapes they have drawn by clicking on a corner of a shape and dragging the shape in or out.
3. Students share their drawings with the class.
Activity 4: enlargement and reduction
These drawings have been enlarged and reduced. As a class, discuss what remains the same and what changes.
ACMMG114 Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries.
ACMMG115: Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original.
MA3-15MG Manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles and describes their properties.
- Scale Factor, The National Council of Teachers of Mathematics