### FOCUS AREA 3 : Spatial visualisation, geometric reasoning and mapping A student understands and applies concepts of 2D shapes and 3D objects, angles and position

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ASPECTS OF NUMERACY FOCUS AREA 3

early in STAGE 5
A student:

end of STAGE 5
A student:

APPLYING CONCEPTS OF 3D OBJECTS
• Uses knowledge of 3D objects to create composite shapes and designs

APPLYING CONCEPTS OF 2D SHAPES
• Uses trigonometry to find sides and angles in right-angled triangles (angles measured to nearest degree)
• Applies trigonometry to solve problems involving right-angled triangles, including the use of angles of elevation and depression, from a given diagram

• Uses trigonometry to find sides and angles in right-angled triangles (including angles measured to nearest minute or second)
• Applies trigonometry to solve word problems involving right-angled triangles, including the use of three-figure bearings and angles of elevation and depression

APPLYING CONCEPTS OF ANGLES AND GEOMETRY
• Identifies similar figures and describes their properties informally
• Uses scale factors and proportion statements to determine unknown lengths in similar figures
• Uses scales on maps, plans and drawings

• Uses deductive reasoning with congruent triangles
• Verifies properties of isosceles and equilateral triangles and special quadrilaterals using congruent triangles
• Uses conditions for triangles to be similar
• Uses results for the sum of exterior and interior angles in polygons

UNDERSTAND POSITION, MAPS AND GRID REFERENCES
• Graphs linear relationships using gradient-intercept form
• Uses bearings on a map measured in degrees and minutes of latitude and longitude

• Graphs linear relationships, quadratics and cubic curves, exponentials, hyperbolas and circles

KLA APPLICATION AND CONSIDERATIONS

GEOGRAPHY

• Locates places using maps, coordinates measured in degrees and minutes, compass bearings, six point map references
• Represents spatial distributions and geographical phenomena on maps at different scales conforming to cartographic conventions

HISTORY

• Outlines the expansion of European settlement on a map of Aboriginal Australia to 1900

HISTORY

• Uses information from maps and globes as evidence in constructing historical narratives

SCIENCE

• Investigates quantitatively, features of waves including frequency, wavelength and speed and relates this to musical instruments