Year level: 7 / 8

Strand: Space / Measurement

Lesson length: 60 mins

Students study the concept of triangle inequality, which determines if three positive numbers can serve as the side lengths of a triangle. This principle states that a triangle is possible if the largest of the three numbers is smaller than the sum of the other two. To explore this, students experiment with various combinations of three natural numbers. They investigate whether these numbers can form a triangle and, when they do, students classify and construct the corresponding triangle. Additionally, they learn to calculate the perimeter of these triangles.

This lesson also reviews content from Year 7 to enable students to successfully engage in four related lessons that explore the Year 8 Pythagoras theorem content.

Achievement standard

Students classify polygons according to their features and create an algorithm designed to sort and classify shapes (Year 7).

They identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity (Year 8).

Content description

Note: this lesson primarily is primarily for the Year 8 level however it also reviews related Year 7 content, listed in the first dot point below.

• Students classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships. AC9M7SP02
• They solve problems involving the area and perimeter of irregular and composite shapes using appropriate units. AC9M8M01
• Students identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations. AC9M8SP01
• They design, create and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works. AC9M8SP04

General capabilities

Numeracy

• Properties of shapes and object (Level 4)
• Understanding units of measurement (Level 9)
• Understanding geometric properties (Level 7)
• Proportional thinking (Level 6)

Critical and Creative Thinking

• Draw conclusions and provide reasons (Level 5)
• Interpret problems and concepts (Level 5)
• Evaluate actions and outcomes (Level 5)
• Consider alternatives (Level 5)

Digital literacy

• Select and operate tools (Level 5)

The following suggestion is given as an assessment opportunity.

• Download the teacher’s slides and go to slide 16, a table with several sets of 3 numbers.
• Students answer ‘Yes’ or ‘No’ as to whether they can be used to form the sides of a triangle or not.
• Students classify the type of triangle and calculate its perimeter when this is the case.
• Students might assume that any set of three positive numbers can form a triangle. To address this misconception, teachers can provide carefully crafted activities. These activities might include experimenting with different numeric combinations that both can and cannot form triangles, or reviewing a selection of pre-constructed examples and counterexamples. Such methods help enhance students' understanding of triangle formation.
• Visualising triangles based on given side lengths can be challenging for students. To support their learning, hands-on activities with preconstructed line segments (concrete manipulatives) of various lengths can be effective. Students can experiment by combining sets of three segments to form triangles. Additionally, digital tools offering virtual manipulatives can further aid in visualising these shapes.
• Recalling the definitions of different types of triangles might be difficult for students. A helpful solution could be a classroom poster featuring a classification flowchart with examples of each triangle type. Also, concrete models of triangles, such as those made from cardboard or plastic, can be effective in reinforcing the characteristics and differences of various triangle types.

Prior to this lesson, it is expected that students have:

• familiarity with the spatial terms point, line, angle, side and triangle, and their representation and labelling in diagrams
• knowledge of the classification of triangles as equilateral, isosceles or scalene according to the number of sides of equal length
• familiarity with the measurement terms degree, unit, cm, perimeter
• familiarity with the number terms positive, integer, inequality.

What you need:

• Lesson plan (Word)

• Teacher’s slides (PowerPoint)

• Student investigation worksheet (Word)