Making triangles

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.

Additional details
Year level(s)	Year 7, Year 8
Audience	Teacher
Purpose	Teaching resource
Format	Web page
Teaching strategies and pedagogical approaches	Mathematics investigation, Questioning, Explicit teaching, Concrete Representational Abstract model
Keywords	triangles, congruence, similarity, algorithms, Maths Hub lesson plan
Curriculum alignment
Curriculum connections	Critical and creative thinking
Strand and focus	Measurement, Space
Topics	Shapes and objects, Area, volume and surface area, Computational thinking
AC: Mathematics (V9.0) content descriptions	AC9M7SP02 Classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships AC9M8M01 Solve problems involving the area and perimeter of irregular and composite shapes using appropriate units AC9M8SP01 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 AC9M8SP04 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
Numeracy progression	Understanding geometric properties (P4, P7) Understanding units of measurement (P8) Proportional thinking (P6)
Copyright details
Organisation	Commonwealth of Australia
Copyright	© 2024 Commonwealth of Australia. Creative Commons BY 4.0.