# YEAR 3 MATHS FOCUS

## MEASUREMENT AND GEOMETRY

## TWO-DIMENSIONAL SPACE

OUTCOME

A student:

MA2-15MG: manipulates, identifies and sketches two-dimensional shapes, including special quadrilaterals, and describes their features

TEACHING POINTS | The special quadrilaterals are the parallelogram, rectangle, rhombus, square, trapezium and kite. |

Regular shapes have all sides equal and all angles equal. In Stage 2, students are expected to be able to distinguish between regular and irregular shapes and to describe a polygon as either regular or irregular, eg a regular pentagon has five equal sides and five equal angles. | |

It is important for students to have experiences with a variety of shapes in order to develop flexible mental images. Students need to be able to recognise shapes presented in different orientations. | |

When constructing polygons using materials such as straws of different lengths for sides, students should be guided to an understanding that: sometimes a triangle cannot be made from 3 straws; a figure made from 3 lengths, ie a triangle, is always flat; a figure made from 4 or more lengths need not be flat; a unique triangle is formed, if a triangle can be formed, from 3 given lengths; more than one two-dimensional shape can result if more than 3 lengths are used. | |

When using examples of Aboriginal rock carvings and other Aboriginal art, it is recommended that local examples be used wherever possible. Consult with local Aboriginal communities and education consultants for such examples. |

LANGUAGE | Students should be able to communicate using the following language: shape, two-dimensional shape (2D shape), circle, triangle, quadrilateral, parallelogram, rectangle, rhombus, square, trapezium, kite, pentagon, hexagon, octagon, regular shape, irregular shape, orientation, features, properties, side, parallel, pair of parallel sides, opposite, length, vertex (vertices), angle, right angle, symmetry, line (axis) of symmetry, rigid. |

The term ‘polygon’ (derived from the Greek words meaning ‘many angles’) refers to closed shapes with three or more angles and sides. While the angles are the focus for the general naming system used for shapes, polygons are more usually understood in terms of their sides. Students are not expected to use the term ‘polygon’. However, some students may explore other polygons and so benefit from being introduced to the collective term. Students could explore the language origins of the names of polygons. | |

The term ‘diamond’ is often used in everyday contexts when describing quadrilaterals with four equal sides. However, ‘diamond’ is not the correct geometrical term to name such quadrilaterals; the correct term is ‘rhombus’. |

## EXPECTATIONS OF ATTAINMENT

Compare and describe features of two-dimensional shapes, including the special quadrilaterals | manipulate, compare and describe features of two-dimensional shapes, including the special quadrilaterals: parallelograms, rectangles, rhombuses, squares, trapeziums and kites {Literacy} |

– determine the number of pairs of parallel sides, if any, of each of the special quadrilaterals {Reasoning} | |

use measurement to establish and describe side properties of the special quadrilaterals, eg the opposite sides of a parallelogram are the same length | |

identify and name the special quadrilaterals presented in different orientations, e.g. | |

– explain why a particular quadrilateral has a given name, eg ‘It is a parallelogram because it has four sides and the opposite sides are parallel’ {Communicating, Reasoning, Literacy} | |

– name a shape, given a written or verbal description of its features {Reasoning, Critical and creative thinking} | |

recognise the vertices of two-dimensional shapes as the vertices of angles that have the sides of the shape as their arms {Literacy} | |

identify right angles in squares and rectangles | |

group parallelograms, rectangles, rhombuses, squares, trapeziums and kites using one or more attributes, eg quadrilaterals with parallel sides and right angles | |

identify and describe two-dimensional shapes as either ‘regular’ or ‘irregular’, eg ‘This shape is a regular pentagon because it has five equal sides and five equal angles’ {Literacy} | |

– identify regular shapes in a group that includes irregular shapes, such as a regular pentagon in a group of pentagons, e.g. | |

– explain the difference between regular and irregular two-dimensional shapes {Communicating, Reasoning, Literacy} | |

– recognise that the name of a shape does not change if its size or orientation in space is changed {Reasoning} | |

draw representations of regular and irregular two-dimensional shapes in different orientations | |

construct regular and irregular two-dimensional shapes from a variety of materials, eg cardboard, straws, pattern blocks | |

– determine that a triangle cannot be constructed from three straws if the sum of the lengths of the two shorter straws is less than the length of the longest straw {Reasoning} | |

compare the rigidity of two-dimensional frames of three sides with the rigidity of those of four or more sides | |

– construct and manipulate a four-sided frame and explain how adding a brace can make a four-sided frame rigid {Communicating, Reasoning, Critical and creative thinking} |

Identify symmetry in the environment (ACMMG066) | identify lines of symmetry in pictures, artefacts, designs and the environment, e.g. Aboriginal rock carvings or Asian lotus designs {Critical and creative thinking, Aboriginal and Torres Strait Islander histories and cultures, Asia and Australia’s engagement with Asia, Intercultural understanding} |

identify and draw lines of symmetry on given shapes, including the special quadrilaterals and other regular and irregular shapes {Literacy} | |

– determine and explain whether a given line through a shape is a line of symmetry {Communicating, Reasoning, Critical and creative thinking Literacy} | |

– recognise and explain why any line through the centre of (and across) a circle is a line of symmetry {Communicating, Reasoning, Critical and creative thinking} |

To be added