# Mathematics

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## Level 4

### Level 4 Description

In Level 4, students extend the number system to simple decimal fractions, and broaden their use of measures and scales.

Students model, represent and order numbers to tens of thousands, and extend...

### Level 4 Content Descriptions

#### Statistics and Probability

##### Chance
1. Describe possible everyday events and order their chances of occurring (VCMSP175)
2. Identify everyday events where one cannot happen if the other happens (VCMSP176)
3. Identify events where the chance of one will not be affected by the occurrence of the other (VCMSP177)
##### Data representation and interpretation
1. Select and trial methods for data collection, including survey questions and recording sheets (VCMSP178)
2. Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values (VCMSP179)
3. Evaluate the effectiveness of different displays in illustrating data features including variability (VCMSP180)

### Level 4 Achievement Standard

Number and Algebra

Students recall multiplication facts to 10 x 10 and related division facts. They choose appropriate strategies for calculations involving multiplication and division, with and without the use of digital technology, and estimate answers accurately enough for the context. Students solve simple purchasing problems with and without the use of digital technology. They locate familiar fractions on a number line, recognise common equivalent fractions in familiar contexts and make connections between fractions and decimal notations up to two decimal places. Students identify unknown quantities in number sentences. They use the properties of odd and even numbers and describe number patterns resulting from multiplication. Students continue number sequences involving multiples...

## Level 5

### Level 5 Description

In Level 5, students extend decimal fractions to thousandths, and explore the ideas of factors, multiples and divisibility.

Students use estimation and rounding for all four operations, with and...

### Level 5 Content Descriptions

#### Statistics and Probability

##### Chance
1. List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (VCMSP203)
2. Recognise that probabilities range from 0 to 1 (VCMSP204)
##### Data representation and interpretation
1. Pose questions and collect categorical or numerical data by observation or survey (VCMSP205)
2. Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (VCMSP206)
3. Describe and interpret different data sets in context (VCMSP207)

### Level 5 Achievement Standard

Number and Algebra

Students solve simple problems involving the four operations using a range of strategies including digital technology. They estimate to check the reasonableness of answers and approximate answers by rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students order decimals and unit fractions and locate them on a number line. Students add and subtract fractions with the same denominator. They find unknown quantities in number sentences and continue patterns by adding or subtracting fractions and decimals.

Measurement and Geometry

Students use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles and volume, and capacity of rectangular prisms. They...

## Level 6

### Level 6 Description

In Level 6, students work with prime, composite, square and triangular numbers and carry out mental, written and technology based computation to solve whole number problems involving all four operations...

### Level 6 Content Descriptions

#### Statistics and Probability

##### Chance
1. Describe probabilities using fractions, decimals and percentages (VCMSP232)
2. Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (VCMSP233)
3. Compare observed frequencies across experiments with expected frequencies (VCMSP234)
##### Data representation and interpretation
1. Construct, interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (VCMSP235)
2. Interpret secondary data presented in digital media and elsewhere (VCMSP236)
3. Pose and refine questions to collect categorical or numerical data by observation or survey (VCMSP237)

### Level 6 Achievement Standard

Number and Algebra

Students recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers. They solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts. Students locate fractions and integers on a number line and connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students calculate a simple fraction of a quantity and calculate common percentage discounts on sale items, with and without the use of digital technology. They make connections between the powers of 10 and the multiplication and division of decimals. Students add, subtract and multiply decimals...

## Level 7

### Level 7 Description

In Level 7, students work with powers of whole numbers, use index notation, represent numbers as products of powers of prime numbers, and investigate square roots of perfect squares. They use number...

### Level 7 Content Descriptions

#### Statistics and Probability

##### Chance
1. Construct sample spaces for single-step experiments with equally likely outcomes (VCMSP266)
2. Assign probabilities to the outcomes of events and determine probabilities for events (VCMSP267)
##### Data representation and interpretation
1. Identify and investigate issues involving numerical data collected from primary and secondary sources (VCMSP268)
2. Construct and compare a range of data displays including stem-and-leaf plots and dot plots (VCMSP269)
3. Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (VCMSP270)
4. Describe and interpret data displays using median, mean and range (VCMSP271)

### Level 7 Achievement Standard

Number and Algebra

Students solve problems involving the order, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving all four operations with fractions, decimals, percentages and their equivalences, and express fractions in their simplest form. Students compare the cost of items to make financial decisions, with and without the use of digital technology. They make simple estimates to judge the reasonableness of results. Students use variables to represent arbitrary numbers and connect the laws and properties of number to algebra and substitute numbers into algebraic expressions. They assign ordered pairs to given points on the Cartesian plane...

## Level 8

### Level 8 Description

In Level 8, students consolidate their proficiency with the four arithmetic operations, and combinations of these, for general computation involving natural numbers, integers and rational numbers...

### Level 8 Content Descriptions

#### Statistics and Probability

##### Chance
1. Identify complementary events and use the sum of probabilities to solve problems (VCMSP294)
2. Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and' (VCMSP295)
3. Represent events in two-way tables and Venn diagrams and solve related problems (VCMSP296)
##### Data representation and interpretation
1. Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation (VCMSP297)
2. Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (VCMSP298)
3. Explore the variation of means and proportions of random samples drawn from the same population (VCMSP299)
4. Investigate the effect of individual data values including outliers, on the range, mean and median (VCMSP300)

### Level 8 Achievement Standard

Number and Algebra

Students use efficient mental and written strategies to make estimates and carry out the four operations with integers, and apply the index laws to whole numbers. They identify and describe rational and irrational numbers in context. Students estimate answers and solve everyday problems involving profit and loss rates, ratios and percentages, with and without the use of digital technology. They simplify a variety of algebraic expressions and connect expansion and factorisation of linear expressions. Students solve linear equations and graph linear relationships on the Cartesian plane.

Measurement and Geometry

Students convert between units of measurement for area and for volume. They find the perimeter and area of parallelograms, rhombuses and kites. Students name the...

## Level 9

### Level 9 Description

In Level 9, students develop familiarity with a broader range of non-linear and linear functions and relations, and related algebra and graphs.

Students apply index laws with integer indices to a...

### Level 9 Content Descriptions

#### Statistics and Probability

##### Chance
1. List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (VCMSP321)
2. Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (VCMSP322)
3. Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians (VCMSP323)
##### Data representation and interpretation
1. Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (VCMSP324)
2. Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (VCMSP325)
3. Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (VCMSP326)

### Level 9 Achievement Standard

Number and Algebra

Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw linear and non-linear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without...

## Level 10

### Level 10 Description

In Level 10, students extend their use of mathematical models to a wide range of familiar and unfamiliar contexts, involving the use of all types of real numbers. They recognise the role of logical...

### Level 10 Content Descriptions

#### Statistics and Probability

##### Chance
1. Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (VCMSP347)
2. Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language (VCMSP348)
##### Data representation and interpretation
1. Determine quartiles and interquartile range and investigate the effect of individual data values, including outliers on the interquartile range (VCMSP349)
2. Construct and interpret box plots and use them to compare data sets (VCMSP350)
3. Compare shapes of box plots to corresponding histograms and dot plots and discuss the distribution of data (VCMSP351)
4. Use scatter plots to investigate and comment on relationships between two numerical variables (VCMSP352)
5. Investigate and describe bivariate numerical data, including where the independent variable is time (VCMSP353)
6. Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (VCMSP354)

### Level 10 Achievement Standard

Number and Algebra

Students recognise the connection between simple and compound interest. They solve problems involving linear equations and inequalities, quadratic equations and pairs of simultaneous linear equations and related graphs, with and without the use of digital technology. Students substitute into formulas, find unknown values, manipulate linear algebraic expressions, expand binomial expressions and factorise monic and simple non-monic quadratic expressions, with and without the use of digital technology. They represent linear, quadratic and exponential functions numerically, graphically and algebraically, and use them to model situations and solve practical problems.

Measurement and Geometry

Students solve and explain surface area and volume problems relating to composite...