Year level: 8

Strand: Measurement / Number / Space

Lesson length: 60 mins

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. Suggestions are made throughout the lesson with respect to opportunities for exploration, questioning and reflection.

Achievement standard

Students use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angled triangles.

Students recognise irrational numbers and terminating or recurring decimals.

Students identify conditions for congruency and similarity in shapes and create and test algorithms designed to test for congruency and similarity.

Content description

• Students recognise irrational numbers in applied contexts, including square roots and π. AC9M8N01
• Students use Pythagoras’ theorem to solve problems involving the side lengths of right-angled triangles. AC9M8M06
• 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

• Understanding geometric properties (Level 7)
• Understanding units of measurement (Level 10)
• Multiplicative strategies (Level 9)
• Proportional thinking (Level 6)

Critical and creative thinking

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

Digital literacy

• Select and operate tools (Level 5)

The following suggestion is given as an assessment opportunity.

Exit ticket

• Question 1: What is the distance of the point (–7, 13) from the origin?
• Question 2: What is the length of the line segment connecting the points with coordinates (2, 8) and (10, 3)?

Answers:√ 218 = 14.76 (correct to two decimal places) √89= 9.43 (correct to two decimal places).

Some students may:

• not yet understand the meaning of a coordinate, and order of coordinates in an ordered pair
• confuse how to represent points from their coordinates in each quadrant, interpreting the negative sign correctly; the resource: Concept of Cartesian coordinates – GeoGebra can be used to help students gain fluency with interpreting coordinates and locating points on the Cartesian coordinate plane.

Prior to this lesson, it is expected students have knowledge of the:

• Cartesian coordinate plane, and the location of points using coordinates in all four quadrants
• spatial terms: point, coordinates, origin, axes, line segment, side, right-angle, quadrilateral, diagonal and their representation and labelling in diagrams
• measurement terms: distance, length, perimeter and area
• number terms and notations for integer, square and square root.

What you need:

• Lesson plan (Word)

• Teacher’s slides (PowerPoint)

• 1-cm-grid graph paper (Word)

• Scientific calculator