NSW Syllabuses

# Mathematics K–10 - Stage 2 - Measurement and Geometry Angles

## Angles 1

### Outcomes

#### A student:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-16MG

identifies, describes, compares and classifies angles

### Content

• Students:
• Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)
• identify 'angles' with two arms in practical situations, eg the angle between the arms of a clock
• identify the 'arms' and 'vertex' of an angle
• describe informally an angle as the 'amount of turning' between two arms
• recognise that the length of the arms does not affect the size of the angle (Reasoning)
• compare angles directly by placing one angle on top of another and aligning one arm
• identify 'perpendicular' lines in pictures, designs and the environment
• use the term 'right angle' to describe the angle formed when perpendicular lines meet
• describe examples of right angles in the environment (Communicating, Problem Solving)
• identify right angles in two-dimensional shapes and three-dimensional objects (Communicating)

### Background Information

In Stage 2, students need informal experiences of creating, identifying and describing a range of angles. This will lead to an appreciation of the need for a formal unit to measure angles.

Paper folding is a quick and simple means of generating a wide range of angles for comparison and copying.

The arms of the angles above are different lengths. However, the angles are the same size, as the amount of turning between the arms is the same. Students may mistakenly judge one angle to be greater in size than another on the basis of the length of the arms of the angles in the diagram.

### Language

Students should be able to communicate using the following language: angle, amount of turning, arm, vertex, perpendicular, right angle.

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

When working towards the outcome MA2‑16MG the sub-elements (and levels) of Understanding geometric properties (UGP2) 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:

• MA2-1WM

uses appropriate terminology to describe, and symbols to represent, mathematical ideas

• MA2-3WM

checks the accuracy of a statement and explains the reasoning used

• MA2-16MG

identifies, describes, compares and classifies angles

### Content

• Students:
• Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)
• compare angles using informal means, such as by using an 'angle tester'
• recognise and describe angles as 'less than', 'equal to', 'about the same as' or 'greater than' a right angle
• classify angles as acute, right, obtuse, straightreflex or a revolution
• describe the size of different types of angles in relation to a right angle, eg acute angles are less than a right angle (Communicating)
• relate the turn of the hour hand on a clock through a right angle or straight angle to the number of hours elapsed, eg a turn through a right angle represents the passing of three hours (Reasoning)
• identify the arms and vertex of the angle in an opening, a slope and/or a turn where one arm is visible and the other arm is invisible, eg the bottom of an open door is the visible arm and the imaginary line on the floor across the doorway is the other arm
• create, draw and classify angles of various sizes, eg by tracing along the adjacent sides of shapes
• draw and classify the angle through which the minute hand of a clock turns from various starting points (Communicating, Reasoning)

### Background Information

A simple 'angle tester' can be made by placing a pipe-cleaner inside a straw and bending the straw to form two arms. Another angle tester can be made by joining two narrow straight pieces of card with a split-pin to form the rotatable arms of an angle.

### Language

Students should be able to communicate using the following language: angle, arm, vertex, right angle, acute angle, obtuse angle, straight angle, reflex angle, angle of revolution.

The use of the terms 'sharp' and 'blunt' to describe acute and obtuse angles, respectively, is counterproductive in identifying the nature of angles. Such terms should not be used with students as they focus attention on the external points of an angle, rather than on the amount of turning between the arms of the angle.

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

When working towards the outcome MA2‑16MG the sub-elements (and levels) of Understanding geometric properties (UGP2) 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.