NSW Syllabuses

# Mathematics K–10 - Stage 3 - Measurement and Geometry Angles

## Angles 1

### Outcomes

#### A student:

• MA3-1WM

describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

• MA3-16MG

measures and constructs angles, and applies angle relationships to find unknown angles

• Students:
• Estimate, measure and compare angles using degrees (ACMMG112)
• identify the arms and vertex of an angle where both arms are invisible, such as for rotations and rebounds
• recognise the need for a formal unit for the measurement of angles
• record angle measurements using the symbol for degrees (°)
• measure angles of up to 360° using a protractor
• explain how a protractor is used to measure an angle (Communicating)
• explore and explain how to use a semicircular protractor to measure a reflex angle (Communicating, Reasoning)
• extend the arms of an angle where necessary to facilitate measurement of the angle using a protractor (Problem Solving)
• Construct angles using a protractor (ACMMG112)
• construct angles of up to 360° using a protractor
• identify that a right angle is 90°, a straight angle is 180° and an angle of revolution is 360°
• identify and describe angle size in degrees for each of the classifications acute, obtuse and reflex
• use the words 'between', 'greater than' and 'less than' to describe angle size in degrees (Communicating)
• compare the sizes of two or more angles in degrees, eg compare angles in different two-dimensional shapes
• estimate angles in degrees and check by measuring

### Background Information

A circular protractor calibrated from 0° to 360° may be easier for students to use to measure reflex angles than a semicircular protractor calibrated from 0° to 180°.

### Language

Students should be able to communicate using the following language: angle, arm, vertex, protractor, degree.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA3‑16MG the sub-elements (and levels) of Understanding geometric properties (UGP5) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.

## Angles 2

### Outcomes

#### A student:

• MA3-1WM

describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

• MA3-16MG

measures and constructs angles, and applies angle relationships to find unknown angles

• Students:
• Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)
• identify and name angle types formed by the intersection of straight lines, including right angles, 'angles on a straight line', 'angles at a point' that form an angle of revolution, and 'vertically opposite angles'
• recognise right angles, angles on a straight line, and angles of revolution embedded in diagrams (Reasoning)
• identify the vertex and arms of angles formed by intersecting lines (Communicating)
• recognise vertically opposite angles in different orientations and embedded in diagrams (Reasoning)
• investigate, with and without the use of digital technologies, adjacent angles that form a right angle and establish that they add to 90°
• investigate, with and without the use of digital technologies, adjacent angles on a straight line and establish that they form a straight angle and add to 180°
• investigate, with and without the use of digital technologies, angles at a point and establish that they form an angle of revolution and add to 360°
• use the results established for adjacent angles that form right angles, straight angles and angles of revolution to find the size of unknown angles in diagrams
• explain how the size of an unknown angle in a diagram was calculated (Communicating, Reasoning)
• investigate, with and without the use of digital technologies, vertically opposite angles and establish that they are equal in size
• use the equality of vertically opposite angles to find the size of unknown angles in diagrams

### Background Information

Students should be encouraged to give reasons when finding unknown angles.

### Language

Students should be able to communicate using the following language: angle, right angle, straight angle, angles on a straight line, angle of revolution, angles at a point, vertically opposite angles.

Two angles at a point are called adjacent if they share a common arm and a common vertex, and lie on opposite sides of the common arm.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA3‑16MG the sub-elements (and levels) of Understanding geometric properties (UGP6) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.