Students investigate the spatial properties of similar plane shapes and solids.
- Students distinguish between similar and non-similar shapes and objects and use ratio to quantify and describe the relationships between their measurable attributes (length, area, volume)
- Students are presented with pairs of shapesóone of the pairs is fixed, the other manipulable. Through manipulation of the shapes and using multiplication facts in ratio and scale situations, students manipulate shapes and solid representations on-screen to explore and develop recognition of similar and non-similar shapes.
Measures: similar shapes
Students work through examples that demonstrate that similar shapes are shapes that have the same angles and where the corresponding side-lengths are in proportion.
The shapes used are rectangles, squares, right angle triangles, isosceles triangles and equilateral triangles. The student is also presented with similar shapes in different orientations to make the task more challenging. Students receive a points score after ten attempts.
Measures: scaling up
Students scale up shapes to create similar plane shapes. Students are presented with simple shapes, asked to choose an enlargement scale factor and record their observations in a table. They must predict the area scales factor in the table before the larger shape is drawn. The shapes are rectangles, squares or triangles.
Measures: scaling down
Similar to 'scaling up' except students explore the relationships between side-length scale factor and area scale factor when reducing the size of a given shape.
Measures: similar solids
Students explore similar solids using cubes, triangular prisms, cylinders, cones and irregular shapes.
Measures: scaling up solids
Students scale up solids to create similar solids.
Measures: scaling down solids
Students scale down solids to create similar solids.
Measures: scaling surface area
Students identify the relationship between the side length scale factor and the surface area when scaling solids. They use this relationship to complete scaling tasks.
Students identify and describe the relationship between side lengths and volume when scaling up prisms. They use this relationship to complete scaling tasks.