NSW Syllabuses

# Mathematics K–10 - Stage 1 - Measurement and Geometry Two-Dimensional Space

## Two-Dimensional Space 1

### Outcomes

#### A student:

• MA1-1WM

describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

• MA1-3WM

supports conclusions by explaining or demonstrating how answers were obtained

• MA1-15MG

manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons

• Students:
• Recognise and classify familiar two-dimensional shapes using obvious features (ACMMG022)
• identify vertical and horizontal lines in pictures and the environment and use the terms 'vertical' and 'horizontal' to describe such lines
• relate the terms 'vertical' and 'horizontal' to 'portrait' and 'landscape' page orientation, respectively, when using digital technologies (Communicating)
• identify parallel lines in pictures and the environment and use the term 'parallel' to describe such lines
• recognise that parallel lines can occur in orientations other than vertical and horizontal (Reasoning)
• give everyday examples of parallel lines, eg railway tracks (Reasoning)
• manipulate, compare and describe features of two-dimensional shapes, including triangles, quadrilaterals, pentagons, hexagons and octagons
• describe features of two-dimensional shapes using the terms 'side' and 'vertex' (Communicating)
• sort two-dimensional shapes by a given attribute, eg by the number of sides or vertices
• explain the attribute used when sorting two-dimensional shapes (Communicating, Reasoning)
• identify and name two-dimensional shapes presented in different orientations according to their number of sides, including using the terms 'triangle', 'quadrilateral', 'pentagon', 'hexagon' and 'octagon', eg
• recognise that the name of a shape does not change when the shape changes its orientation in space, eg a square turned on its vertex is still a square
(Communicating, Reasoning)
• select a shape from a description of its features (Reasoning)
• recognise that shapes with the same name may have sides of equal or different lengths (Reasoning)
• recognise that rectangles and squares are quadrilaterals
• identify and name shapes embedded in pictures, designs and the environment, eg in Aboriginal art
• use computer drawing tools to outline shapes embedded in a digital picture or design (Communicating)

### Background Information

Manipulation of a variety of real objects and shapes is crucial to the development of appropriate levels of visualisation, language and representation.

The skills of discussing, representing and visualising three-dimensional objects and two-dimensional shapes are developing in Stage 1 and must be fostered through practical activities and communication. It is important that students have experience involving a broad range and variety of objects and shapes in order to develop flexible mental images and language.

Students need to be able to recognise shapes presented in different orientations. They need to develop an understanding that changing the orientation of a shape does not change its features or its name. In addition, students should have experiences identifying both regular and irregular shapes, although it is not expected that students understand or distinguish between regular and irregular shapes in Stage 1. Regular shapes have all sides and all angles equal.

Many shapes used in Aboriginal art are used with specific meanings. Local Aboriginal communities and many education consultants can provide examples. Further exploration of such meanings could be incorporated in students' studies within the Creative Arts Key Learning Area.

### Language

Students should be able to communicate using the following language: shape, circle, triangle, quadrilateral, square, rectangle, pentagon, hexagon, octagon, orientation, features, side, vertex (vertices), vertical, horizontal, portrait (orientation), landscape (orientation), parallel.

The term 'vertex' (plural: vertices) refers to the point where two straight sides of a two-dimensional shape meet (or where three or more faces of a three-dimensional object meet).

The term 'shape' refers to a two-dimensional figure. The term 'object' refers to a three-dimensional figure.

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

When working towards the outcome MA1‑15MG 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.

## Two-Dimensional Space 2

### Outcomes

#### A student:

• MA1-1WM

describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols

• MA1-15MG

manipulates, sorts, represents, describes and explores two-dimensional shapes, including quadrilaterals, pentagons, hexagons and octagons

• Students:
• Describe and draw two-dimensional shapes, with and without the use of digital technologies (ACMMG042)
• use the term 'two-dimensional' to describe plane (flat) shapes
• make representations of two-dimensional shapes in different orientations using concrete materials
• combine and split single shapes and arrangements of shapes to form new shapes, eg create a hexagon from six triangles (Communicating)
• draw and name two-dimensional shapes in different orientations, with and without the use of digital technologies
• recognise that the name of a shape does not change if its size or orientation in space is changed (Reasoning)
• Investigate the effect of one-step slides and flips, with and without the use of digital technologies (ACMMG045)
• identify a one-step slide or flip of a single shape and use the terms 'slide' and 'flip' to describe the movement of the shape
• perform a one-step slide or flip with a single shape
• recognise that sliding or flipping a shape does not change its size or features (Reasoning)
• describe the result of a one-step slide or flip of a shape, eg 'When I flip the shape, it is the same but backwards' (Communicating)
• record the result of performing one-step slides and flips, with and without the use of digital technologies
• copy and manipulate a shape using the computer functions for slide and flip (Communicating)
• make designs with line symmetry using paper-folding, pattern blocks, drawings and paintings
• recognise the connection between line symmetry and performing a flip (Reasoning)
• Identify and describe half-turns and quarter-turns (ACMMG046)
• identify full-, half- and quarter-turns of a single shape and use the terms 'turn', 'full-turn', 'half-turn' and 'quarter-turn' to describe the movement of the shape
• identify and describe amounts of turn using the terms 'clockwise' and 'anti-clockwise'
• perform full-, half- and quarter-turns with a single shape
• recognise that turning a shape does not change its size or features (Reasoning)
• describe the result of a turn of a shape, eg 'When the shape does a half-turn, it is the same but upside-down' (Communicating)
• record the result of performing full-, half- and quarter-turns of a shape, with and without the use of digital technologies
• copy and manipulate a shape using the computer function for turn (Communicating)
• determine the number of half-turns required for a full-turn and the number of quarter-turns required for a full-turn
• connect the use of quarter- and half-turns to the turn of the minute hand on a clock for the passing of quarter- and half-hours (Communicating, Reasoning)

### Background Information

In Stage 1, students need to have experiences involving directions and turning. Discussions about what represents a 'full-turn', a 'half-turn' and a 'quarter-turn' will be necessary. Relating this information to students physically may be helpful, eg by playing games such as 'Simon Says' with Simon saying to make turns.

Digital technologies such as computer drawing tools may use the terms 'move', 'rotate' and 'flip horizontal', or various other terms, to describe transformations. The icons for these functions may assist students in locating the required transformations.

### Language

Students should be able to communicate using the following language: shape, two-dimensional shape (2D shape), circle, triangle, quadrilateral, square, rectangle, pentagon, hexagon, octagon, orientation, features, symmetry, slide, flip, turn, full-turnhalf-turn, quarter-turn, clockwise, anti-clockwise.

In Stage 1, students refer to the transformations of shapes using the terms 'slide', 'flip' and 'turn'. While in Stage 2, students are expected to use the terms 'translate', 'reflect' and 'rotate', respectively.

Linking the vocabulary of half-turns and quarter-turns to students' experiences with clocks may be of benefit.

A shape is said to have line symmetry if matching parts are produced when it is folded along a line of symmetry. Each part represents the 'mirror image' of the other.

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

When working towards the outcome MA1‑15MG the sub-elements (and levels) of Interpreting fractions (InF1) and Understanding geometric properties (UGP2-UPG4) 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.