Search results

Sort by

Result list

VC2M7N02

represent natural numbers in expanded notation using powers of 10, and as products of powers of prime numbers using exponent notation

Elaborations
- relating the sequences 10, 100, 1000, 10 000 … and 10¹, 10², 10³, 10⁴ …
- applying and explaining the connections between place value and expanded notations, for example, $7000 = 7 \times 10^{3}$ and $3750 = 3 \times 10^{3} + 7 \times 10^{2} + 5 \times 10^{1}$
- applying knowledge of factors to strategies for expressing natural numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees, for example, $48 = 6 \times 8 = 2 \times 3 \times 2 \times 2 \times 2 = 3^{1} \times 2^{4} = 3 \times 2^{4}$
- developing familiarity with the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and powers of 2; the sequence 1, 3, 9, 27, 81, 243, 729 and powers of 3; and the sequence 1, 5, 25, 125, 625 and powers of 5
- solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorisation
VC2M7N02 | Mathematics | Mathematics Version 2.0 | Level 7 | Number
Mathematics Version 2.0: Foundation Level description

In Foundation, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian Early Years Learning and Development Framework (VEYLDF). Students engage in a range of approaches to the...

Level description | Mathematics | Mathematics Version 2.0
Mathematics Version 2.0: Level 9 achievement standards

By the end of Level 9, students recognise and use rational and irrational numbers to solve problems.
Students extend and apply the exponent laws with positive integers and the zero exponent to variables. They expand binomial products and factorise monic quadratic expressions. They...

Level description | Mathematics | Mathematics Version 2.0 | Level 9
VC2M9A02

simplify algebraic expressions, apply the distributive law to expand algebraic expressions including binomial products, and factorise monic quadratic expressions

Elaborations
- expanding combinations of binomials such as $(x + 7) (x + 8), (x + 7) (x - 8),$ $(x - 7) (x + 8), (x - 7) (x - 8)$ to identify expansion and factorisation patterns related to $(x + a) (x + b) = x^{2} + (a + b) x + a b$ , where $a$ and $b$ are integers
- using manipulatives such as algebra tiles or area models to expand or factorise algebraic expressions with readily identifiable binomial factors; for example, $(x + 1) (x + 3) = x^{2} + 4 x + 3$ , ${(x - 5)}^{2} = x^{2} - 10 x + 25$ or ${(x - 3)}^{2} + 4 = x^{2} - 6 x + 9 + 4 = x^{2} - 6 x + 13$
- recognising the relationship between expansion and factorisation, and using digital tools to systematically explore the factorisation of $x^{2} + m x + n$ where $m$ and $n$ are integers
VC2M9A02 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra
VC2M10AA10

experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

Elaborations
- applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as $f (x) = 2 x^{2} - 3 x - 7$
- applying transformations to the graph of $x^{2} + y^{2} = 1$
- identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
- identifying intervals on the real number line over which a given quadratic function is positive or negative
- using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay
VC2M10AA10 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra
VC2M4N01

recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals

Elaborations
- using a bar to represent the whole, dividing it into 10 equal pieces with each piece representing 0.1 or one-tenth of the whole length and understanding that 2 pieces are 0.2 or two-tenths of the whole
- using materials to show the multiplicative relationship between the whole, tenths and hundredths; for example, using a bundle of 10 straws to represent the whole, one straw as the tenth, and cutting the tenth into 10 parts to show the hundredths; or using deci-pipes to represent tenths
- recognising that one is the same as ten-tenths and one-tenth is the same as ten-hundredths and using this relationship to rename decimals; for example, renaming 0.25 as two-tenths and five-hundredths or twenty-five-hundredths
- making models of measurement attributes to show the relationship between the base unit and parts of the unit, for example, 1.5 metres is one metre and five-tenths of the next metre; 1.75 units is one unit and seventy-five-hundredths of the next unit
- counting large quantities of mixed notes and coins, writing the total using dollars and cents, and recognising the cents as parts of the next dollar
- comparing the way money and measures are read and said, and explaining how they are the same and different; for example, explaining that $2.75 is said ‘two dollars seventy-five’ and 2.75 metres is said ‘two point seven five metres’, and recognising that the 7 means seven-tenths and the 5 means five-hundredths in both
VC2M4N01 | Mathematics | Mathematics Version 2.0 | Level 4 | Number
VC2M1N05

use mathematical modelling to solve practical problems involving additive situations, including simple money transactions; represent the situations with diagrams, physical and virtual materials; use calculation strategies to solve the problem

Elaborations
- modelling problems involving addition and subtraction presented in stories, using a Think Board to represent the problem, solving the problem using physical materials and explaining the connections between any materials used, the Think Board diagram and the numbers within the story
- modelling simple money problems involving addition and subtraction using whole dollar amounts; for example, setting up a shop and role-playing practical problems of buying and selling goods, using addition and subtraction with play money and prices in whole dollar amounts; or solving the problem ‘I had $14 and was given $15 for my birthday’ using addition to answer the problem
- modelling a variety of different additive situations to solve practical problems; for example, keeping track of the number of people on a bus as it stops to pick up and drop off passengers or the number of people entering a lift
VC2M1N05 | Mathematics | Mathematics Version 2.0 | Level 1 | Number
Mathematics Version 2.0: Level 2 description

In Level 2, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian Early Years Learning and Development Framework (VEYLDF). Students engage in a range of approaches...

Level description | Mathematics | Mathematics Version 2.0
VC2M10AA03

simplify combinations of linear expressions with rational coefficients and the solution of related equations

Elaborations
- simplifying sums and differences of linear expressions of the form $\frac{a x + b}{c}$ where
  $a$ and $b$ are integers, and $c$ is a non-zero integer, for example, $\frac{6 x - 11}{2} - \frac{7 x}{4} + \frac{9 - 5 x}{3} = \frac{- 5 x - 30}{12}$
- solving equations involving sums and differences of linear expressions with rational coefficients, for example, $\frac{- 2 x}{3} + \frac{4}{9} = \frac{11}{5} (7 x - 1)$ $\Rightarrow - 30 x + 20 = 693 x - 99$ $\Rightarrow x = \frac{119}{723}$ , and verifying the solution
VC2M10AA03 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra
VC2M9A06

use mathematical modelling to solve applied problems involving change, including financial contexts involving simple interest; formulate problems, choosing to use either linear or quadratic functions or other simple variations; interpret solutions in terms of the context; evaluate the model and...

Elaborations
- modelling practical contexts using linear functions such as cooking times that include resting or cooling times, or water leakage from water tanks, using tables and graphs or digital tools and algebraically
- modelling measurement situations and determining the perimeter and areas of rectangles where the length, $l$ , of the rectangle is a linear function of its width, $w$ ; for example, $l = w, l = w + 5, l = 3 w, l = 2 w + 7$
- modelling practical contexts (for example, area, paths of projectiles, parabolic mirrors, satellite dishes) using simple quadratic functions, tables and graphs (hand drawn or using digital tools) and, algebraically, interpreting features of the graphs such as the turning point and intercepts in context; for example, area, paths of projectiles, parabolic mirrors, satellite dishes
- modelling and solving problems involving financial contexts using linear functions, for example, combinations of purchases of different items when they have a set amount of money to spend, profit/loss situations and trade quotes involving call-out fees
- modelling situations involving change, for example, change in daily temperature during the ski season, fluctuation of speed above and below the speed limit, and acceleration and deceleration of a car coming to and moving off from a set of traffic lights
- modelling the hunting techniques of Aboriginal and Torres Strait Islander Peoples using quadratic functions and exploring the effect of increasing the number of hunters to catch more prey
VC2M9A06 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra
VC2M9P02

calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’, inclusive ‘or’ and exclusive ‘or’

Elaborations
- understanding that relative frequencies from large data sets or long-run experiments can provide reliable measures of probability and can be used to make predictions of decisions
- using Venn diagrams or two-way tables to estimate frequencies of events involving ‘and’ and ‘or’ questions
VC2M9P02 | Mathematics | Mathematics Version 2.0 | Level 9 | Probability
VC2M10ST03

construct two-way tables and discuss possible relationship between categorical variables

Elaborations
- using two-way tables to investigate and comparing the survey responses to questions involving five-point Likert scale against 2 different categories of respondents, for example, junior students’ responses compared to senior students’ responses to a survey question
- recording data in two-way tables and using percentages and proportions to identify patterns and associations in the data
- conducting a litter survey around the school, considering the relationship between different categorical variables such as the day of the week (as canteen specials might lead to different types of litter) or the weather (due to hot days leading to more icy poles and cold drinks being sold)
VC2M10ST03 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics
VC2M10ST05

plan and conduct statistical investigations of situations that involve bivariate data, including where the independent variable is time; evaluate and report findings with consideration of limitations of any inferences

Elaborations
- designing statistical investigations that collect bivariate data over time through observation, experiment or measurement; graphing, interpreting and analysing data; and reporting within the context of the statistical investigation question
- investigating and comparing anecdotal claims with data collected from well-constructed surveys, including those concerning climate, housing affordability and natural resources, with consideration of data validity and limitations of interpolation or extrapolation
- using a statistical investigation to address the question ‘Is there a relationship between vaccines and immunity from a virus?’
- investigating biodiversity changes in Australia before and after colonisation by comparing related bivariate numerical data, discussing and reporting on associations
VC2M10ST05 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics
VC2M7N01

describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems

Elaborations
- investigating squares of natural numbers from one to 20, and connecting them to visual representations such as dots arranged in a square pattern
- using the square and square root notation, and the distributive property and area diagrams, to calculate the squares of two-digit numbers; for example, $43^{2} = {(40 + 3)}^{2} = 40^{2} + 2 \times 40 \times 3 + 3^{2} = 1600 + 240 + 9 = 1849$
- determining between which 2 consecutive natural numbers the square root of a given number lies; for example, 43 is between the square numbers 36 and 49 so $\sqrt[]{43}$ is between $\sqrt[]{36} and \sqrt[]{49}$ and therefore between 6 and 7
- generating a list of perfect square numbers and describing any emerging patterns, for example, the last digit of perfect square numbers, or the difference between consecutive square numbers, and recognising the constant second difference
- using the relationship between perfect square numbers and their square roots to determine the perimeter of a square tiled floor using square tiles; for example, an area of floor with 144 square tiles has a perimeter of 48 tile lengths
VC2M7N01 | Mathematics | Mathematics Version 2.0 | Level 7 | Number
VC2M9ST05

plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

Elaborations
- planning and conducting an investigation using questions together with analysis of a secondary data set collected from online databases such as the Australian Bureau of Statistics
- planning and conducting an investigation relating to consumer spending habits; and modelling market research on what teenagers are prepared to spend on technology compared to clothing, with consideration of sample techniques and potential sources of bias
- investigating where would be the best location for a tropical fruit plantation, by conducting a statistical investigation comparing different variables such as the annual rainfall in various parts of Australia, Indonesia, New Guinea and Malaysia, land prices and associated farming costs
- posing statistical questions; collecting, representing and interpreting data from different sources in relation to reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians; and considering the relationships between variables
VC2M9ST05 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics
VC2M4N09

use mathematical modelling to solve practical problems that involve additive and multiplicative situations, including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate...

Elaborations
- modelling and solving a range of practical additive problems using materials, part-part-whole diagrams and/or a bar model, and writing addition and/or subtraction number sentences, based on whether a part or the whole is missing; and explaining how each number in their number sentence is connected to the situation
- modelling practical problems with division, interpreting and representing the situation using a diagram or array to represent what is unknown (the number of groups, or the number per group); and writing a division number sentence to represent the situation and choosing an efficient calculation strategy
- modelling practical problems involving money (such as a budget for a large event) that require either addition, subtraction, multiplication or division and justifying the choice of operation in relation to the situation
- modelling and solving multiplication problems involving money, such as buying 5 toy scooters for $96 each, using efficient mental strategies and written jottings to keep track if needed; for example, rounding $96 up to $100 and subtracting 5 × $4 = $20, so 5 × $96 is the same as 5 × $100 less $20, giving the answer $500 − $20 = $480
- modelling situations by formulating comparison problems using number sentences, comparison models and arrays; for example, ‘Ariana read 16 books for the “readathon”; Maryam read 4 times as many books. How many books did Maryam read?’ using the expression 4 × 16 and using place value partitioning, basic facts and an array, thinking 4 × 10 = 40 and 4 × 6 = 24, so 4 × 16 can be written as 40 + 24 = 64
VC2M4N09 | Mathematics | Mathematics Version 2.0 | Level 4 | Number
VC2M6N08

approximate numerical solutions to problems involving rational numbers and percentages, using appropriate estimation strategies

Elaborations
- using familiar fractions, decimals and percentages to approximate calculations, such as 0.3 of 180 is about $\frac{1}{3}$ of 180, or 52% is about $\frac{1}{2}$
- choosing appropriate estimation strategies including rounding to the nearest whole number, knowledge of multiples of 2, 5 or 10 and partitioning numbers, in contexts such as measuring or cost per unit
- recognising the effect of rounding on calculations involving fractions or decimals and saying what numbers the answer will be between
- recognising the usefulness of estimation to check calculations for contexts such as dividing wood into a number of lengths, calculating cost per unit, reducing a recipe or dividing the cost of dinner for a group into individual amounts
- verifying solutions by estimating percentages in suitable contexts, such as discounts, using common percentages of 10%, 25%, 30%, 50% and 1%
- investigating estimation strategies to make decisions about steam cooking in ground ovens by Aboriginal and/or Torres Strait Islander Peoples, including catering for different numbers of people and resources needed for cooking
VC2M6N08 | Mathematics | Mathematics Version 2.0 | Level 6 | Number
VC2M3P02

conduct repeated chance experiments; identify and describe possible outcomes, record the results, and recognise and discuss the variation

Elaborations
- identifying the possible outcomes of a chance experiment, creating a tally chart to record results, carrying out a few trials and tallying the results for each trial, and then responding to the questions ‘How did your results vary for each trial?’ and ‘How do the results vary across the class?’
- conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, or using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials
VC2M3P02 | Mathematics | Mathematics Version 2.0 | Level 3 | Probability
VC2M7SP02

classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships

Elaborations
- using strips of paper with parallel sides to make triangles and quadrilaterals, and contrasting the rigidity of triangles with the flexibility of quadrilaterals
- constructing triangles with 3 given side lengths and discussing the question ‘Can any 3 lengths be used to form the sides of a triangle?’
- identifying and communicating about side and angle properties of scalene, isosceles, equilateral, right-angled, acute and obtuse triangles using geometric conventions
- describing, comparing and contrasting squares, rectangles, rhombuses, parallelograms, kites and trapeziums, explaining the relationships between these shapes
VC2M7SP02 | Mathematics | Mathematics Version 2.0 | Level 7 | Space
VC2M6N09

use mathematical modelling to solve practical problems involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and using efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and...

Elaborations
- modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation, for example, purchasing items during a sale
- modelling situations involving earning money and budgeting, asking questions such as ‘Can I afford it?’, ‘Do I need it?’ and ‘How much do I need to save for it?’ and developing a savings plan or budget for an upcoming event or personal purchase
- modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals
VC2M6N09 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

Result list

VC2M7N02

Elaborations

Mathematics Version 2.0: Foundation Level description

Mathematics Version 2.0: Level 9 achievement standards

VC2M9A02

Elaborations

VC2M10AA10

Elaborations

VC2M4N01

Elaborations

VC2M1N05

Elaborations

Mathematics Version 2.0: Level 2 description

VC2M10AA03

Elaborations

VC2M9A06

Elaborations

VC2M9P02

Elaborations

VC2M10ST03

Elaborations

VC2M10ST05

Elaborations

VC2M7N01

Elaborations

VC2M9ST05

Elaborations

VC2M4N09

Elaborations

VC2M6N08

Elaborations

VC2M3P02

Elaborations

VC2M7SP02

Elaborations

VC2M6N09

Elaborations

Refine results by Area

Refine results by Subject

Refine results by Level

Refine results by Type