Year level: 7

Strand: Measurement

Lesson length: 60 mins

In this lesson, students will engage in various activities to explore angles between parallel lines in a navigational context. They will measure angles using traditional hand and finger techniques, construct parallel and perpendicular lines and establish laws of angle properties using algebraic formulas.

This lesson is based on activities from the Stellar navigation and mathematics resource from Ngarrngga. The project aims to empower all teachers to integrate Aboriginal and Torres Strait Islander histories and cultures in their teaching. Find more resources at https://www.ngarrngga.org/.

### Achievement standard

• Students can apply knowledge of angle relationships between parallel lines to solve problems.
• Students can describe the relationship between angles using algebraic formulas.

### Content description

Identify corresponding, alternate and co-interior relationships between angles formed when parallel lines are crossed by a transversal; use them to solve problems and explain reasons (AC9M7M04)

General capabilities

Numeracy

• Understanding geometric properties (PL6)

Critical and Creative Thinking

• Interpret concepts and problems (PL5)
• Draw conclusions and provide reasons (PL5)

Cross-curriculum priority

• Aboriginal and Torres Strait Islander Histories and Cultures (A_TSICP1)
• First Nations communities of Australia maintain a deep connection to, and responsibility for, Country/Place and have holistic values and belief systems that are connected to the land, sea, sky and waterways

Two assessment opportunities are presented below, with further suggestions for differentiation.

• Star map activities submitted for student portfolios.
• Download and handout the Geometric assessment and spend a few minutes explaining what students should do. This can be completed in the remaining time in your lesson or completed for homework. Slide 16 shows an example of a student worked example for one identified reason and argument. Further student examples are available for download. Students submit answers to this task.

Differentiation (enabling and developing): note the assessment can be modified to suit groups or individual students.

Differentiation (Extension): Angles Inside website

Some students may:

• mistakenly believe that the length of the lines that form an angle determines the size of the angle itself. For example, they might think that a larger angle is created by longer lines.
• experience difficulty in using a protractor accurately incorrectly starting their measure from 180° instead of 0°, and not lining up the rays of the angle correctly. Direct instruction and observation will help correct this misunderstanding and support the above misunderstanding.
• have learned about angles by rote learning. This can hinder students' ability to link geometric concepts. When students memorise properties without understanding the relationships between them, they may struggle to apply their knowledge flexibly. Focus on understanding rather than memorisation of these properties.

Student can:

• demonstrate that the angle sum of a triangle is 180˚ and can use this to solve problems
• identify that angles at a point add to 360° and that vertically opposite angles are equal
• identify interior angles in shapes to calculate angle sum
• use angle properties to identify and calculate unknown angles in familiar two-dimensional shapes
• can bisect/transverse a line or angle is to cut it in half.

The meaning of the terms perpendicular, bisect, intersection, corresponding angles, transversal and notation, are found on the Version 9 mathematics glossary .

## What you need:

• Lesson plan (Word

• Teacher's slides (PowerPoint)

• Star map worksheet (Word)

• Geometric activity (Word)

• Geometric assessment (Word)

• Teacher star map (Word)

• Student examples (PDF)

• Students need coloured pencils and a protractor.