Space and Geometry - Properties of Geometric Figures


Students can:

  • investigate similar figures
  • interpret scale drawings

Activities to support the strategy

Activity 1

1. Students collect an object which they are going to enlarge onto grid paper.

2. Direct students to place the object on cm grid paper and trace around the outline (see figure 1).

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The original leaf drawn is 8 cm long x 2.5 cm width.

3. Give students a sheet of 1 cm grid paper and transfer the shape of the object onto the 1 cm grid (see figure 2). Show students how to transfer the drawing, by using one square on the 1cm grid for a corresponding square used on the original drawing.

The finished diagram is now at a scale of 2 times (2x) the original size of the original drawing of the object.

4. Give students a sheet of cm grid paper.

Have them transfer the original shape of the object onto the smaller squares using the method modelled in Step 3 and shown in figure 3.

This drawing is now at a scale of (0.5x) the original size of the object.

Activity 2 – science

1. Direct students to collect leaf litter and carefully isolate the invertebrates such as slaters, ants, spiders, worms and cockroaches. Ask students to place an organism, e.g. a slater in a petri dish, measure the length of the organism (actual size is 1 cm body length).

2. Give students a cm grid paper and ask the students to draw the slater to actual size (see figure 4).

3. To increase the detail of structural characteristics observed:

  • ask students to place the petri dish with the slater under a binocular microscope
  • give students a piece of 1 cm grid paper and ask the students to enlarge their diagram in proportion so that it is drawn at a scale of 4x the original. Each square of the larger grid paper should have the same part of the body, drawn with greater detail (see figure 5)
  • make sure the student records the scale of the organism as a bar on the diagram.

4. Ask students to repeat this process for another organism such as an ant or worm and compare the structural features of each organism, listing similarities and differences.

These could include the number of antennae, legs, body parts, segmentation etc.

Activity 3

1.Using grid paper in different scales, have students enlarge diagrams such as cartoons and pictures by imposing grid lines over a picture then enlarging it piece by piece to create a scale diagram.

2. Ask students to bring in examples of plans and drawings found in the media or other learning areas.

3. Explore with students the use of similar and congruent figures in specific designs, architecture and art work. For example, works by Escher, Vasarely and Mondrian; or landscaping in European formal gardens.

Students can investigate similar figures using GeoGebra resources found in the Geometers Warehouse, Stage 4.


Australian curriculum

ACMMG220: Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar: using the properties of similarity and ratio, and correct mathematical notation and language, to solve problems involving enlargement (for example, scale diagrams)

NSW syllabus

MA5.1-11MG: Describes and applies the properties of similar figures and scale drawings.

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