Expected level of development
Australian Curriculum Mathematics V9: AC9M7SP02
Numeracy Progression: Understanding geometric properties: P4
At this level, students build on their knowledge of two-dimensional shapes. They classify triangles according to their side length (scalene, isosceles, equilateral) and their angle properties (right, acute, obtuse). Students identify and describe different quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium and kite) in terms of their side length, parallel edges and equal angles. Students also investigate the angle sum of a triangle and quadrilateral.
By presenting shapes in different forms and orientations, students will become familiar with their properties and be able to sort them accordingly. Encourage students to use the correct vocabulary and to be precise in their explanations. (This will help when they meet proof in Year 10.) Using physical objects and dynamic geometry software will also aid students in their visualisation.
Teaching and learning summary:
- Connect and build on students’ prior knowledge of triangles.
- Classify triangles according to their angles and side lengths.
- Connect to and build on students’ knowledge of quadrilaterals.
- Classify quadrilaterals according to their properties.
- Investigate the sum of the interior angles in a triangle and a quadrilateral.
- Demonstrate how to solve problems involving the angles in a triangle or quadrilateral.
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Teaching strategies
A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Differentiation
Differentiation involves teachers creating lessons that are accessible and challenging for all students.
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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
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Making triangles
In this lesson, students investigate various combinations of three natural numbers to explore the concept of triangle inequality.
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Geometric patterns
In this lesson students use intuition and logic to establish the side and angle properties of triangles and special quadrilaterals.
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Celebrity quadrilaterals: algorithms
In this lesson students develop an understanding of how a decision tree algorithm works.
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Finding the angle sum of any polygon
A series of activities that explore the angle sum of polygons using dynamic geometry software to explain and demonstrate the properties of the angles in triangles and quadrilaterals.
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Classifying triangles
An explanation of how to classify triangles by looking at their angles and the lengths of their sides. The resource includes explanations, video, worked examples and questions.
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Sum of interior angles in a polygon
A series of student-based discovery activities that explore the sum of the interior angles of a polygon by deconstructing the polygons into triangles.
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Unit cubes and volume
Download this lesson plan that helps students to define and understand the concept of volume.
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