Stage 4
Outcomes
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Numbers and Algebra
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Computing with Integers
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MA4-4NA
Compares, orders and calculates with integers, applying a range of strategies to aid computation
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Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)
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Use an appropriate non-calculator method to divide two- and three-digit numbers by a two-digit number
Examples
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Use factors of a number to aid mental computation involving multiplication and division, eg to multiply a number by 12, first multiply the number by 6 and then multiply the result by 2
Examples
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Use an appropriate non-calculator method to divide two- and three-digit numbers by a two-digit number
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Compare, order, add and subtract integers (ACMNA280)
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Order integers
Examples
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Add and subtract integers using mental and written strategies
Play Activities 446Examples
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Order integers
- Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183)
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Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)
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MA4-4NA
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Fractions, Decimals and Percentages
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MA4-5NA
Operates with fractions, decimals and percentages
- Compare fractions using equivalence; locate and represent positive and negative fractions and mixed numerals on a number line (ACMNA152)
- Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153)
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Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)
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Determine the effect of multiplying or dividing by a number with magnitude less than one
Examples
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Multiply and divide decimals by powers of 10
Examples
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Multiply and divide decimals using written methods, limiting operators to two digits
Play Activities 209Examples
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Multiply and divide fractions and mixed numerals using written methods
Examples
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Multiply and divide fractions and decimals using a calculator
Examples
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Calculate fractions and decimals of quantities using mental, written and calculator methods
Examples
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Determine the effect of multiplying or dividing by a number with magnitude less than one
- Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155)
- Round decimals to a specified number of decimal places (ACMNA156)
- Investigate terminating and recurring decimals (ACMNA184)
- Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)
- Find percentages of quantities and express one quantity as a percentage of another, with and without the use of digital technologies (ACMNA158)
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Solve problems involving the use of percentages, including percentage increases and decreases, with and without the use of digital technologies (ACMNA187)
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Increase and decrease a quantity by a given percentage, using mental, written and calculator methods
Examples
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Interpret and calculate percentages greater than 100, eg an increase from $2 to $5 is an increase of 150%
Examples
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Solve a variety of real-life problems involving percentages, including percentage composition problems and problems involving money
Examples
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Increase and decrease a quantity by a given percentage, using mental, written and calculator methods
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MA4-5NA
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Financial Mathematics
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MA4-6NA
Solves financial problems involving purchasing goods
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MA4-6NA
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Ratios and Rates
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MA4-7NA
Operates with ratios and rates, and explores their graphical representation
- Recognise and solve problems involving simple ratios (ACMNA173)
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Solve a range of problems involving ratios and rates, with and without the use of digital technologies (ACMNA188)
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Interpret and calculate ratios that involve more than two numbers
Examples
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Solve a variety of real-life problems involving ratios, eg scales on maps, mixes for fuels or concrete
Examples
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Use rates to compare quantities measured in different units
Examples
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Solve a variety of real-life problems involving rates, including problems involving rate of travel (speed)
Examples
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Interpret and calculate ratios that involve more than two numbers
- Investigate, interpret and analyse graphs from authentic data (ACMNA180)
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MA4-7NA
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Algebraic Techniques
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MA4-8NA
Generalises number properties to operate with algebraic expressions
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Algebraic Techniques 1
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Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)
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Develop the concept that pronumerals (letters) can be used to represent numerical values
Examples
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Recognise and use equivalent algebraic expressions, eg y + y + y + y = 4y
Examples
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Use algebraic symbols to represent mathematical operations written in words and vice versa, eg the product of x and y is xy, x + y is the sum of x and y
Examples
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Develop the concept that pronumerals (letters) can be used to represent numerical values
- Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)
- Simplify algebraic expressions involving the four operations (ACMNA192)
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Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)
- Algebraic Techniques 2
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Algebraic Techniques 1
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MA4-8NA
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Indices
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MA4-9NA
Operates with positive-integer and zero indices of numerical bases
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MA4-9NA
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Equations
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MA4-10NA
Uses algebraic techniques to solve simple linear and quadratic equations
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Solve simple linear equations (ACMNA179)
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Solve simple linear equations using concrete materials, such as the balance model or cups and counters, stressing the notion of performing the same operation on both sides of an equation
Examples
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Solve linear equations that may have non-integer solutions, using algebraic techniques that involve up to two steps in the solution process
Examples
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Solve simple linear equations using concrete materials, such as the balance model or cups and counters, stressing the notion of performing the same operation on both sides of an equation
- Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194)
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Solve simple linear equations (ACMNA179)
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MA4-10NA
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Linear Relationships
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MA4-11NA
Creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane
- Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)
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Describe translations, reflections in an axis, and rotations of multiples of 90 degrees on the Cartesian plane using coordinates (ACMMG181)
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Use the notation P' to name the 'image' resulting from a transformation of a point P on the Cartesian plane
Examples
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Plot and determine the coordinates for P' resulting from translating P one or more times
Examples
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Plot and determine the coordinates for P' resulting from reflecting P in either the x- or y-axis
Examples
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Plot and determine the coordinates for P' resulting from rotating P by a multiple of 90 degrees about the origin
Examples
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Use the notation P' to name the 'image' resulting from a transformation of a point P on the Cartesian plane
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Plot linear relationships on the Cartesian plane, with and without the use of digital technologies (ACMNA193)
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Use objects to build a geometric pattern, record the results in a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
Examples
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Recognise a given number pattern (including decreasing patterns), complete a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
Examples
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Use a rule generated from a pattern to calculate the corresponding value for a larger number
Examples
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Form a table of values for a linear relationship by substituting a set of appropriate values for either of the pronumerals and graph the number pairs on the Cartesian plane, eg given y = 3x + 1, form a table of values using x = 0, 1 and 2 and then graph t
Examples
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Extend the line joining a set of points on the Cartesian plane to show that there is an infinite number of ordered pairs that satisfy a given linear relationship
Examples
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Derive a rule for a set of points that has been graphed on the Cartesian plane
Examples
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Use objects to build a geometric pattern, record the results in a table of values, describe the pattern in words and algebraic symbols, and represent the relationship on a number grid
- Solve linear equations using graphical techniques (ACMNA194)
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MA4-11NA
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Computing with Integers
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Measurement and Geometry
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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
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Length
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Statistics and Probability
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Data Collection and Representation
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MA4-19SP
Collects, represents and interprets single sets of data, using appropriate statistical displays
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MA4-19SP
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Single Variable Data Analysis
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MA4-20SP
Analyses single sets of data using measures of location, and range
- Calculate mean, median, mode and range for sets of data and interpret these statistics in the context of data (ACMSP171)
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Describe and interpret data displays using mean, median and range (ACMSP172)
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Calculate measures of location (mean, median and mode) and the range for data represented in a variety of statistical displays, including frequency distribution tables, frequency histograms, stem-and-leaf plots and dot plots
Examples
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Draw conclusions based on the analysis of data displays using the mean, median and/or mode, and range
Examples
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Calculate measures of location (mean, median and mode) and the range for data represented in a variety of statistical displays, including frequency distribution tables, frequency histograms, stem-and-leaf plots and dot plots
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MA4-20SP
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Probability
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MA4-21SP
Represents probabilities of simple and compound events
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Probability 1
- Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167)
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Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)
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Assign a probability of 0 to events that are impossible and a probability of 1 to events that are certain to occur
Examples
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Assign probabilities to simple events by reasoning about equally likely outcomes, eg the probability of randomly drawing a card of the diamond suit from a standard pack of 52 playing cards is 13/25 = 1/4
Examples
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Solve probability problems involving single-step experiments using cards, dice, spinners, etc
Examples
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Assign a probability of 0 to events that are impossible and a probability of 1 to events that are certain to occur
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Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)
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Establish that the sum of the probabilities of all of the possible outcomes of a single-step experiment is 1
Examples
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Calculate the probability of a complementary event using the fact that the sum of the probabilities of complementary events is 1, eg the probability of 'rolling a 6' when rolling a die is 1/6, therefore the probability of the complementary event, 'not rol
Examples
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Establish that the sum of the probabilities of all of the possible outcomes of a single-step experiment is 1
- Probability 2
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Probability 1
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MA4-21SP
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Data Collection and Representation