Numbers and Algebra
Outcomes
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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