YEAR 5 MATHS FOCUS
MEASUREMENT AND GEOMETRY
2D Space
Learning Experiences
2D Space
TWO-DIMENSIONAL SPACE
OUTCOME
A student:
MA3-15MG:
manipulates, classifies and draws two-dimensional shapes, including equilateral, isosceles and scalene triangles, and describes their properties
TEACHING POINTS | 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. If the order of rotational symmetry is 1, the shape does not have rotational symmetry. e.g.
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| 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. |
EXPECTATIONS OF ATTAINMENT
Classify two-dimensional shapes and describe their features | manipulate, identify and name right-angled, equilateral, isosceles and scalene triangles {Literacy} |
| – recognise that a triangle can be both right-angled and isosceles or right-angled and scalene {Reasoning, Critical and creative thinking} | |
| 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 {Critical and creative thinking} | |
| explore by measurement angle properties of squares, rectangles, parallelograms and rhombuses {Critical and creative thinking} | |
| select and classify a two-dimensional shape from a description of its features {Literacy} | |
| – recognise that two-dimensional shapes can be classified in more than one way, e.g. a rhombus can be more simply classified as a parallelogram {Communicating, Reasoning, Critical and creative thinking} | |
| identify and draw regular and irregular two-dimensional shapes from descriptions of their side and angle properties {Literacy} | |
| – use tools such as templates, rulers, set squares and protractors to draw regular and irregular two-dimensional shapes {Communicating, Problem Solving, Critical and creative thinking} | |
| – 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, Information and communication technology capability} |
Describe translations, reflections and rotations of two-dimensional shapes (ACMMG114) | 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, Information and communication technology capability} | |
| 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, Critical and creative thinking} |
Identify line and rotational symmetries (ACMMG114) | 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, Information and communication technology capability} |
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 {Information and communication technology capability} |
| – 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, Critical and creative thinking} | |
| – 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, Information and communication technology capability} | |
| 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, Critical and creative thinking} |
Learning Experiences
To be added