Year level: 8

Strand: Measurement / Number

Lesson length: 60 mins

This lesson is one in a series of lessons on Pythagoras theorem. Students work in small groups to investigate the application of Pythagoras’ theorem to problems in a practical or theoretical context. They apply the ‘context > representation > exploration > interpretation > investigation’ cycle to questions of interest or problems in a context involving right-angled triangles and lengths and communicate their findings to others.

### Achievement standard

By the end of Year 8, students recognise irrational numbers and terminating or recurring decimals. Students use Pythagoras’ theorem to solve measurement problems involving unknown lengths of right-angled triangles.

### 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

### General capabilities

Numeracy

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

Critical and creative thinking

• Interpret concepts and problems (Level 5)
• consider alternatives (Level 5)

Digital literacy

• Select and operate tools (Level 5)

The following assessment opportunities are suggested below.

• Display the Exit ticket (slide 14) and solutions (slide 15) from the teacher’s slides.
• Note: The key aspect of the exit ticket is the ability to read the information and construct a suitable right-angled triangle diagram. Students can either solve the problem using written working and a scientific calculator, or by using an online Pythagoras calculator. In this context a suitable level of accuracy is one decimal place.
• Assess each group on their presentation skills and their ability to logically explain the mathematical approach taken to investigate their respective investigation.

Some students may:

• find difficulty identifying key information from text
• misrepresent key information on a diagram
• not understand the notion of a variable in terms of systematically exploring a context.

It is expected that students have familiarity with:

• spatial terms including, side, right-angle, triangle, opposite, hypotenuse, square and their representation and labelling in diagrams
• measurement terms, including: 90 degrees, unit, cm, m, square cm, square m, length, area
• the number terms and notations for: square, square root, approximation, decimals and rounding.

Note: For the circle aspect of exploration Context 3, students would also need to be familiar with radius, diameter, semi-circle and formulas for the area of a circle.

## What you need:

• Lesson plan (Word)

• Teacher’s slides (PowerPoint)

• Scientific calculator