NSW Syllabuses

# Mathematics K–10 - Stage 3 - Measurement and Geometry Two-Dimensional Space

## Two-Dimensional Space 1

### Outcomes

#### A student:

• MA3-1WM

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

• MA3-2WM

selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

• MA3-3WM

gives a valid reason for supporting one possible solution over another

• MA3-15MG

manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

### Content

• Students:
• Classify two-dimensional shapes and describe their features
• manipulate, identify and name right-angled, equilateral, isosceles and scalene triangles
• recognise that a triangle can be both right-angled and isosceles or right-angled and scalene (Reasoning)
• compare and describe features of the sides of equilateral, isosceles and scalene triangles
• explore by measurement side and angle properties of equilateral, isosceles and scalene triangles
• explore by measurement angle properties of squares, rectanglesparallelograms and rhombuses
• select and classify a two-dimensional shape from a description of its features
• recognise that two-dimensional shapes can be classified in more than one way, eg a rhombus can be more simply classified as a parallelogram (Communicating, Reasoning)
• identify and draw regular and irregular two-dimensional shapes from descriptions of their side and angle properties
• use tools such as templates, rulers, set squares and protractors to draw regular and irregular two-dimensional shapes (Communicating, Problem Solving)
• explain the difference between regular and irregular shapes (Communicating)
• use computer drawing tools to construct a shape from a description of its side and angle properties (Communicating, Problem Solving)
• use the terms 'translate', 'reflect' and 'rotate' to describe the movement of two-dimensional shapes
• rotate a graphic or object through a specified angle about a particular point, including by using the rotate function in a computer drawing program (Communicating)
• describe the effect when a two-dimensional shape is translated, reflected or rotated, eg when a vertical arrow is rotated 90°, the resulting arrow is horizontal
• recognise that the properties of shapes do not change when shapes are translated, reflected or rotated (Reasoning)
• identify and quantify the total number of lines (axes) of symmetry (if any exist) of two-dimensional shapes, including the special quadrilaterals and triangles
• identify shapes that have rotational symmetry and determine the 'order' of rotational symmetry
• construct designs with rotational symmetry, with and without the use of digital technologies (Communicating, Problem Solving)
• Apply the enlargement transformation to familiar two-dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)
• make enlargements of two-dimensional shapes, pictures and maps, with and without the use of digital technologies
• overlay an image with a grid composed of small squares (eg 5 mm by 5 mm) and create an enlargement by drawing the contents of each square onto a grid composed of larger squares (eg 2 cm by 2 cm) (Communicating, Problem Solving)
• investigate and use functions of digital technologies that allow shapes and images to be enlarged without losing the relative proportions of the image (Problem Solving)
• compare representations of shapes, pictures and maps in different sizes, eg student drawings enlarged on a photocopier
• measure an interval on an original representation and its enlargement to determine how many times larger than the original the enlargement is (Problem Solving, Reasoning)

### Background Information

A shape has rotational symmetry if a tracing of the shape, rotated part of a full turn around its centre, matches the original shape exactly.

The order of rotational symmetry refers to the number of times a figure coincides with its original position in turning through one full rotation, eg

'Scalene' is derived from the Greek word skalenos, meaning 'uneven'; our English word 'scale' is derived from the same word. 'Isosceles' is derived from the Greek words isos, meaning 'equals', and skelos, meaning 'leg'. 'Equilateral' is derived from the Latin words aequus, meaning 'equal', and latus, meaning 'side'. 'Equiangular' is derived from aequus and another Latin word, angulus, meaning 'corner'.

### Language

Students should be able to communicate using the following language: shape, two-dimensional shape (2D shape), triangle, equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, features, properties, side, parallel, pair of parallel sides, opposite, length, vertex (vertices), angle, right angle, line (axis) of symmetry, rotational symmetry, order of rotational symmetry, translate, reflect, rotate, enlarge.

A 'feature' of a shape or object is a generally observable attribute of a shape or object. A 'property' of a shape or object is an attribute that requires mathematical knowledge to be identified.

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

When working towards the outcome MA3‑15MG the sub-elements (and levels) of Understanding geometric properties (UGP2-UGP4) 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:

• MA3-1WM

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

• MA3-2WM

selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations

• MA3-15MG

manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties

### Content

• Students:
• Investigate the diagonals of two-dimensional shapes
• identify and name 'diagonals' of convex two-dimensional shapes
• recognise the endpoints of the diagonals of a shape as the vertices of the shape (Communicating)
• determine and draw all the diagonals of convex two-dimensional shapes
• compare and describe diagonals of different convex two-dimensional shapes
• use measurement to determine which of the special quadrilaterals have diagonals that are equal in length (Problem Solving)
• determine whether any of the diagonals of a particular shape are also lines (axes) of symmetry of the shape (Problem Solving)
• Identify and name parts of circles
• create a circle by finding points that are all the same distance from a fixed point (the centre)
• identify and name parts of a circle, including the centre, radius, diameter, circumference, sector, semicircle and quadrant
• identify whether a two-dimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90° once and then reflected once'
• construct patterns of two-dimensional shapes that involve translations, reflections and rotations using computer software
• predict the next translation, reflection or rotation in a pattern, eg 'The arrow is being rotated 90° anti-clockwise each time'
• choose the correct pattern from a number of options when given information about a combination of transformations (Reasoning)

### Background information

When drawing diagonals, students need to be careful that the endpoints of their diagonals pass through the vertices of the shape.

### Language

Students should be able to communicate using the following language: shape, two-dimensional shape (2D shape), circle, centre, radius, diameter, circumference, sector, semicircle, quadrant, triangle, equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, diagonal, vertex (vertices), line (axis) of symmetry, translate, reflect, rotate, clockwise, anti-clockwise.

A diagonal of a two-dimensional shape is an interval joining two non-adjacent vertices of the shape. The diagonals of a convex two-dimensional shape lie inside the figure.

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

When working towards the outcome MA3‑15MG the sub-elements (and levels) of Number patterns and algebraic thinking (NPA3) and Understanding geometric properties (UGP4) 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.