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Organisation of content into year levels is advisory. Teachers will continue to make professional judgements about when to introduce content based on children’s prior learning and achievement. *National Consistency in Curriculum Outcomes, Statement of Learning Early adolescence: Mathematics/Space – Students describe and analyse mathematically the spatial features of objects, environments and movements. Typical sequence of content: Year 8 Year 9 Year 10 Represent spatial ideas Represent location Directional language Directional language and symbols Directional language, symbols and methods instructions for moving and locating objects (eg distance, direction and common map grids) directional language for paths, regions and locations (eg equidistant, bisect, parallel and perpendicular) directional language, symbols and methods of representation in maps and plans (eg degrees of turn, compass directions, keys, bearings, distance, scale and coordinates) Interpret and make maps which represent distance and direction, showing a sense of scale Interpret and make maps and plans representing size and position accurately Interpret and make maps using bearings and precise measurement key features on a map or path so that others can use them (eg providing a tour map of their school for visitors) following and providing directions from one location to another on a variety of maps and plans with reference to key features, distance and orientation* (Mathematics) (eg writing a set of directions to assist a visually-impaired peer find his or her way around a part of the yard) more precision in map making including use of bearings from 0 to 360 interpreting maps to find their way around the actual environment (eg using a plan of the library to find a particular book) using drawing equipment when representing paths and regions* (ICT) (eg computer software, templates, protractors, compasses and rulers) sketching paths and regions, given a set of special constraints (eg a path traced out by the valve of a bicycle wheel) using grids and coordinates, scale, and true bearings to read, interpret and follow maps* (Mathematics) (eg orienteering) solving problems involving a series of distances and bearings © Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007 1 Organisation of content into year levels is advisory. Teachers will continue to make professional judgements about when to introduce content based on children’s prior learning and achievement. *National Consistency in Curriculum Outcomes, Statement of Learning Typical sequence of content: Year 8 Year 9 Year 10 Represent arrangements Represent orientation through topological diagrams Produce diagrams with essential features of location and orientation Visualise and sketch own networks and use networks to determine best path drawing and using topological maps to show place and position but not distance (eg stations on a railway line) paths and regions described in everyday language (eg shading the region mowed when the electric draw cord is x metres) why distance is not represented on a network (eg explaining that they cannot tell from their network which drink fountains are closer) tracing pathways through networks (eg a milk round) drawing and using diagrams to represent and analyse relationships* (Mathematics) (eg The Konigsberg Bridge Problem) drawing and using networks that represent information from a variety of real life situations (eg delivery routes) network diagrams usually do not show distance or direction, unlike conventional maps network diagrams show the order of, and paths between locations investigating the traversablility of a network using network diagrams available within their community (eg using an airline map to plan a tour of the north-west by a country and western singer) ‘best’ paths and locations (eg finding the best location for a recycling depot) Represent shape Shape and structure to make simple 3D models Precision in producing models Make complex models based on drawings matching the faces of an object with parts of its net (eg finding the number opposite a six on the net of a die) what the essential details are when constructing figures and objects (eg matching lengths and angles) making models from oblique, orthogonal and isometric drawings making a box to match a provided wooden block by drawing around each of its faces to make a net designing nets or constructing 3D objects from isometric diagrams* (Mathematics) (eg a soccer ball from the net of its stitching pattern involving a tessellation of pentagons and hexagons) © Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007 2 Organisation of content into year levels is advisory. Teachers will continue to make professional judgements about when to introduce content based on children’s prior learning and achievement. *National Consistency in Curriculum Outcomes, Statement of Learning Typical sequence of content: Year 8 Year 9 Year 10 Represent shape (continued) cutting suitable lengths to make a skeleton of a provided 3D shape (eg cutting straws to the correct lengths to make a triangular prism) distinguishing suitable nets for various polyhedra from a random set* (Mathematics) copying lengths and angles and constructing parallels, perpendiculars, angle and line bisectors and various angles* (Mathematics) drawing cross-sections of prisms, pyramids and spheres* (Mathematics) Common conventions for drawing angles, 2D shapes and 3D objects Conventions to produce orthogonal, oblique, perspective and isometric drawings Use geometric tools and technology to make accurate drawings drawing polyhedra, prisms, pyramids, cylinders and cones* (Mathematics) (eg showing front, side and top views and cross-sections) conventions for oblique or perspective drawings when drawing common 3D shapes* (Mathematics/ICT) using geometric equipment to construct accurate drawings (eg parallel, perpendicular, various angles and bisectors construct polygons, circles, and ellipses from diagrams or given dimensions) drawing polyhedra, prisms, pyramids, cylinders and cones and composite shapes formed from them constructing accurate two-dimensional representations of three dimensional objects using geometric shapes* (Mathematics/ICT) (eg an isometric drawing or front-side-top view or a single point perspective drawing of an hourglass) drawing a figure from a different position or orientation without the aid of a model drawing two-dimensional shapes in terms of boundary, angle and scale* (Mathematics) determining which properties are preserved by the representation and which are not* (Mathematics) (eg angle, length and area) using drawing equipment or computer drawing software to copy and design (eg using logotypes and other patterns) using compass and ruler and computer software in constructions (eg constructing the bisector of an angle) using geometric tools and techniques, such as mirrors, templates and computer software, to make accurate drawings* (Mathematics/ICT) using mathematical properties to check accuracy (eg checking the lengths of the diagonals of a rectangle) © Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007 3 Organisation of content into year levels is advisory. Teachers will continue to make professional judgements about when to introduce content based on children’s prior learning and achievement. *National Consistency in Curriculum Outcomes, Statement of Learning Typical sequence of content: Year 8 Year 9 Year 10 Represent transformations Recognise and visualise transformation and symmetry and produce spatial sequences Combine two transformations and produce symmetrical patterns Describe properties of transformations to reproduce drawings and complex patterns the language of transformation (eg ‘Rotate it at right angles around the centre and slide it to the left’) producing symmetrical designs* (Mathematics/ICT) (eg folding paper or using mirrors or computer graphics) carrying out a translation, rotation or reflection using coordinates, tracing paper, geometric drawing equipment or a computer package (eg rotate triangle ABC about B, 60° clockwise) translation, rotation or reflection can affect the position or orientation of a shape or object the effect of a translation, rotation, reflection, dilation and distortion on the shape of an object* (Mathematics) producing a reflection, translation or rotation of a figure on a coordinate grid and describing it (eg ‘I reflected it using the line that passes through [0, 3] and [4, 0] as the mirror line’) representing dilations and distortions of a shape or object by a whole number or unit fraction scale factor (eg doubling width but not height) finding the centres, axes and planes of symmetry in shapes or objects* (Mathematics) using properties of transformations to accurately produce a symmetric arrangement (eg reflecting a figure through a mirror line oblique to it) using transformations to design tessellations technologies which employ transformation language or properties* (ICT) (eg swings or projectors) finding the centres, axes and planes of symmetry in figures Enlargements and reductions Predict the effects of enlargements and reductions using a grid to enlarge and reduce a figure and to make distortions (eg doubling widths but not heights) enlarging and reducing figures using projections enlarging models made with cubes to a small whole number scale (eg given a model made of 6 cubes, produce one enlarged by a scale factor of 3) © Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007 4 Organisation of content into year levels is advisory. Teachers will continue to make professional judgements about when to introduce content based on children’s prior learning and achievement. *National Consistency in Curriculum Outcomes, Statement of Learning Typical sequence of content: Year 8 Year 9 Year 10 Reason geometrically Geometric language Geometric language to refine descriptions Geometric language to solve problems appropriate geometric language (eg using face and edge rather than side) identifying, describing and classifying a broad range of 2D shapes and 3D objects* (Mathematics) properties of shapes to produce informal arguments about tessellations, symmetry and transformations (eg all triangles tessellate since a triangle and its reflection form a parallelogram and all parallelograms tessellate) parallel and perpendicular lines and planes in figures and objects (eg in a triangular prism) using counter-examples to test descriptions Generate and classify shapes Generate and classify shapes based on geometric properties Identify and use properties of triangles, rectangles and circles identifying polygons, circles and ellipses* (Mathematics) identifying different representations of three dimensional shapes and objects* (Mathematics) (eg cylinders, cones, platonic solids, packages and containers) testing descriptions by using counter-examples (eg ‘polygons with four equal sides are squares’ becomes ‘four-sided polygons with equal sides and equal angles are squares’) classifying triangles and quadrilaterals in terms of side, diagonal and angle* (Mathematics) showing front, side and top views of cross-sections of three-dimensional shapes* (Mathematics/ICT) using congruent and similar triangles to solve geometric problems* (Mathematics) similarity and congruence to solve mathematical and practical problems (eg ‘I know that this side equals this side – what else do I need to know in order to say that the two triangles are congruent’?) © Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007 5 Organisation of content into year levels is advisory. Teachers will continue to make professional judgements about when to introduce content based on children’s prior learning and achievement. *National Consistency in Curriculum Outcomes, Statement of Learning Typical sequence of content: Year 8 Year 9 Year 10 Reason geometrically (continued) Make simple conjectures about familiar shapes Informal arguments about familiar shapes Generalisations about triangles why certain types of shapes will or will not tessellate (eg ‘We think that all parallelograms will tile. This is because you can always slide them together to make long strips and then push the strips together’) making deductions related to geometric properties of shapes* (Mathematics) (eg when two straight lines intersect, opposite angles are equal) generalising conditions for congruent triangles exploring demonstrations and informal proofs of general propositions* (Mathematics) (eg the sum of angles in a plane triangle is always 180°; if corresponding angles are equal then alternate angles are equal) applying tests for congruent triangles Classify angles Explore and use angle relationships Identify and use angle relationships recognising and describing acute, obtuse, right and straight angles applying angle properties related to parallel, perpendicular and transversal lines* (Mathematics) angles which are congruent, supplementary and complementary, and using angle relationships in intersecting, parallel and perpendicular lines and triangles to find the size of angles practical checks for whether lines and surfaces are parallel, perpendicular, vertical or horizontal (eg checking that two walls are parallel, that the diagonals of a rectangle are congruent and bisect each other) © Department of Education and Training Western Australia, Early adolescence: Mathematics/Space scope and sequence, December 2007 6