Angles 1
Outcomes
A student:

 MA31WM
describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

 MA316MG
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 twodimensional 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 subelements (and levels) of Understanding geometric properties (UGP5) describe observable behaviours that can aid teachers in making evidencebased decisions about student development and future learning.
The progression subelements and indicators can be viewed by accessing the National Numeracy Learning Progression.
Angles 2
Outcomes
A student:

 MA31WM
describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions

 MA316MG
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 subelements (and levels) of Understanding geometric properties (UGP6) describe observable behaviours that can aid teachers in making evidencebased decisions about student development and future learning.
The progression subelements and indicators can be viewed by accessing the National Numeracy Learning Progression.