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 | Algorithms, Area, volume and surface area, Computational thinking, Shapes and objects |
| 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. |
Related resources
-
Polygons and objects (10 lessons)
In this sequence of 10 lessons, students prove angle sum rules, classify quadrilaterals, draw 3D views in 2D, and apply volume and geometric reasoning to problems.
Resource details -
Pythagoras: Cartesian coordinate plane
This lesson is one in a series of lessons on Pythagoras' theorem. Students calculate the distance between any two points on the Cartesian coordinate plane using Pythagoras’ theorem and then develop a set of steps that outline the process. It combines the use of Pythagoras’ theorem with the Cartesian coordinate plane and the use of coordinates to specify position, form line segments, shapes of triangles and determine their perimeters.
Resource details -
Celebrity quadrilaterals: Algorithms
In this lesson, students develop an understanding of how a decision tree algorithm works using a game. They apply this understanding to create their own algorithm to classify special quadrilaterals by their properties.
Resource details -
Geometric patterns
As geometric explorers, students use intuition and logic to establish the side and angle properties of triangles and special quadrilaterals.
Resource details -
Algorithms: Year 8 – planning tool
This planning resource for Year 8 is for the topic of Algorithms.
Resource details -
Shapes and objects: Year 8 – planning tool
This planning resource for Year 8 is for the topic of Shapes and objects.
Resource details -
Volume and surface area: Year 8 – planning tool
This planning resource for Year 8 is for the topic of Volume and surface area.
Resource details