Measurement and Geometry
Outcomes
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Length
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MA4-12MG
Calculates the perimeters of plane shapes and the circumferences of circles
- Find perimeters of parallelograms, trapeziums, rhombuses and kites (ACMMG196)
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Investigate the relationship between features of circles, such as the circumference, radius and diameter; use formulas to solve problems involving circumference (ACMMG197)
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Develop and use the formulas to find the circumferences of circles in terms of the diameter d or radius r:
Circumference of a circle = pi x d
Circumference of a circle = 2 x pi x r
Examples
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Find the perimeters of simple composite figures consisting of two shapes, including quadrants and semicircles
Examples
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Develop and use the formulas to find the circumferences of circles in terms of the diameter d or radius r:
Circumference of a circle = pi x d
Circumference of a circle = 2 x pi x r
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MA4-12MG
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Area
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MA4-13MG
Uses formulas to calculate the areas of quadrilaterals and circles, and converts between units of area
- Choose appropriate units of measurement for area and convert from one unit to another (ACMMG195)
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Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (ACMMG159)
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Develop and use the formulas to find the areas of rectangles and squares:
Area of a rectangle = lb where l is the length and b is the breadth (or width) of the rectangle
Area of square = s squared where s is the side length of the square
Examples
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Find the areas of simple composite figures that may be dissected into rectangles, squares, parallelograms and triangles
Examples
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Develop and use the formulas to find the areas of rectangles and squares:
Area of a rectangle = lb where l is the length and b is the breadth (or width) of the rectangle
Area of square = s squared where s is the side length of the square
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Find areas of trapeziums, rhombuses and kites (ACMMG196)
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Develop, with or without the use of digital technologies, and use the formula to find the areas of kites and rhombuses:
Area of rhombus/kite = 1/2xy where x and y are the lengths of the diagonals
Examples
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Develop and use the formula to find the areas of trapeziums:
Area of trapezium = 1/2h (a + b) where h is the perpendicular height and a and b are the lengths of the parallel sides
Examples
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Select and use the appropriate formula to find the area of any of the special quadrilaterals
Examples
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Solve a variety of practical problems relating to the areas of triangles and quadrilaterals
Examples
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Develop, with or without the use of digital technologies, and use the formula to find the areas of kites and rhombuses:
Area of rhombus/kite = 1/2xy where x and y are the lengths of the diagonals
- Investigate the relationship between features of circles, such as the area and the radius; use formulas to solve problems involving area (ACMMG197)
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MA4-13MG
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Volume
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MA4-14MG
Uses formulas to calculate the volumes of prisms and cylinders, and converts between units of volume
- Draw different views of prisms and solids formed from combinations of prisms (ACMMG161)
- Choose appropriate units of measurement for volume and convert from one unit to another (ACMMG195)
- Develop the formulas for the volumes of rectangular and triangular prisms and of prisms in general; use formulas to solve problems involving volume (ACMMG198)
- Calculate the volumes of cylinders and solve related problems (ACMMG217)
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MA4-14MG
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Time
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MA4-15MG
Performs calculations of time that involve mixed units, and interprets time zones
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Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone (ACMMG199)
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Add and subtract time mentally using bridging strategies, eg from 2:45 to 3:00 is 15 minutes and from 3:00 to 5:00 is 2 hours, so the time from 2:45 until 5:00 is 15 minutes + 2 hours = 2 hours 15 minutes
Examples
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Solve a variety of problems involving duration, including where times are expressed in 12-hour and 24-hour notation, that require the use of mixed units (years, months, days, hours and/or minutes)
Examples
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Add and subtract time mentally using bridging strategies, eg from 2:45 to 3:00 is 15 minutes and from 3:00 to 5:00 is 2 hours, so the time from 2:45 until 5:00 is 15 minutes + 2 hours = 2 hours 15 minutes
- Solve problems involving international time zones
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Solve problems involving duration, including using 12-hour and 24-hour time within a single time zone (ACMMG199)
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MA4-15MG
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Right-Angled Triangles (Pythagoras)
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MA4-16MG
Applies Pythagoras' theorem to calculate side lengths in right-angled triangles, and solves related problems
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MA4-16MG
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Properties of Geometrical Figures
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MA4-17MG
Classifies, describes and uses the properties of triangles and quadrilaterals, and determines congruent triangles to find unknown side lengths and angles
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Properties of Geometrical Figures 1
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Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)
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Recognise and classify types of triangles on the basis of their properties (acute-angled triangles, right-angled triangles, obtuse-angled triangles, equilateral triangles, isosceles triangles and scalene triangles)
Examples
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Investigate the properties of special quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapeziums and kites), including whether: the opposite sides are parallel, the opposite sides are equal, the adjacent sides are perpendicular, the opposi
Examples
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Recognise and classify types of triangles on the basis of their properties (acute-angled triangles, right-angled triangles, obtuse-angled triangles, equilateral triangles, isosceles triangles and scalene triangles)
- Identify line and rotational symmetries (ACMMG181)
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Demonstrate that the angle sum of a triangle is 180 degrees and use this to find the angle sum of a quadrilateral (ACMMG166)
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Justify informally that the interior angle sum of a triangle is 180 degrees, and that any exterior angle equals the sum of the two interior opposite angles
Examples
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Use the angle sum results for triangles and quadrilaterals to determine unknown angles in triangles and quadrilaterals, giving reasons
Examples
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Justify informally that the interior angle sum of a triangle is 180 degrees, and that any exterior angle equals the sum of the two interior opposite angles
- Use the properties of special triangles and quadrilaterals to solve simple numerical problems with appropriate reasoning
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Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)
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Properties of Geometrical Figures 1
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MA4-17MG
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Angle Relationships
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MA4-18MG
Identifies and uses angle relationships, including those related to transversals on sets of parallel lines
- Use the language, notation and conventions of geometry
- Recognise the geometrical properties of angles at a point
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Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163)
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Identify and name pairs of parallel lines using the symbol for 'is parallel to'
Examples
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Define and identify 'transversals', including transversals of parallel lines
Examples
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Identify, name and measure alternate angle pairs, corresponding angle pairs and co-interior angle pairs for two lines cut by a transversal
Examples
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Recognise the equal and supplementary angles formed when a pair of parallel lines is cut by a transversal
Examples
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Identify and name pairs of parallel lines using the symbol for 'is parallel to'
- Solve simple numerical problems using reasoning (ACMMG164)
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MA4-18MG