Angles

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Definition

An angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.

Imagine that the ray OB is rotated about the point O until it lies along OA. The amount of turning is called the size of the angle AOB. (NSW Mathematics K-10 Syllabus)

Teaching and learning activities

The resources below provide targeted teaching strategies to support student improvement in this skill.

Each downloadable lesson activity includes:

learning intentions
a list of required resources
a step-by-step lesson sequence
printable classroom materials

Select the download all icon to download all available activities or select each activity separately.

Identifying anglesEstimate and measure angles in degrees up to one revolution. They will identify and classify angles in the environment.

Finding anglesRecognise, identify and label angles found in a picture of Sydney Harbour.

Investigating angle sumDiscover angle sum of triangles and quadrilaterals, and identifying unknown angles in the environment.

Finding unknown anglesStudents calculate unknown angles of triangles and quadrilaterals from the environment

Download all (ZIP)Download the resource pack containing all activities.

PLAN2 Areas of focus

An Areas of focus template has been created in PLAN2 to support targeted teaching of Text structure in your learning area.

Search for the DoE template titled ‘DoE HSCMinStd Writing: Text structure’ in the Areas of focus template library tab within the Plan menu, and customise it for your students’ needs.

For more information about using PLAN2 Areas of focus templates with this resource, visit the Using this resource with PLAN2 page.

Relevance to the numeracy test marking

The feedback for a Level 3 performance in the HSC minimum standard online numeracy test states:

Individuals performing at this level typically “select appropriate strategies from a variety of everyday mathematical processes in familiar and some less familiar contexts.”

Students are also able to identify and estimate common angles.

Connections with ACSF Level 3 descriptors

The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how identifying and estimating common angles are assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.

Numeracy Indicator 3.09: Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts

Focus area: Explicitness and Complexity of mathematical information

Level 3 performance features:

interprets and comprehends a range of everyday mathematical information that is embedded in familiar and routine texts

Numeracy Indicator 3.10: Selects from and uses a variety of developing mathematical and problem solving strategies in a range of familiar and some less familiar contexts

Focus area: Mathematical knowledge and skills: measurement and geometry

Level 3 performance features:

identifies and estimates common angles, e.g. as a rotation with a full turn = 360° and recognition of right angles as 90°.

Connections with Numeracy Learning Progression:

The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to angles are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.

Element: Measurement and Geometry

Sub-element: Understanding geometric properties (UGP)

UGP2 — Angles

identifies angles in the environment (e.g. an angle formed when a door is opened; identifies there are four angles in a square)

UGP3 — Angles

compares angles to a right angle, classifying them as greater than, less than or equal to a right angle

UGP4 — Angles

estimates, compares and constructs angles (e.g. uses a ruler and protractor to construct a 45˚ angle; compares the size of angles in the environment and estimates their size)
describes angles in the environment according to their size as acute, obtuse, right, straight, reflex or a revolution and identifies them in shapes and objects (e.g. identifies slope as angles in the environment such as the ramp outside of the school block)

UGP6 — Angles

uses angle properties to identify perpendicular and parallel lines
demonstrates that the angle sum of a triangle is 180˚ and uses this to solve problems
identifies interior angles in shapes to calculate angle sum
uses angle properties to identify and calculate unknown angles in familiar two-dimensional shapes

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