# Mathematics

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## Level 3

### Level 3 Description

In Level 3, students increasingly use mathematical terms and symbols to describe computations, measurements and characteristics of objects.

Students recognise, model and order numbers to at least...

### Level 3 Content Descriptions

#### Number and Algebra

##### Number and place value
1. Investigate the conditions required for a number to be odd or even and identify odd and even numbers (VCMNA129)
2. Recognise, model, represent and order numbers to at least 10 000 (VCMNA130)
3. Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (VCMNA131)
4. Recognise and explain the connection between addition and subtraction (VCMNA132)
5. Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (VCMNA133)
6. Recall multiplication facts of two, three, five and ten and related division facts (VCMNA134)
7. Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (VCMNA135)
##### Fractions and decimals
1. Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (VCMNA136)
##### Money and financial mathematics
1. Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (VCMNA137)
##### Patterns and algebra
1. Describe, continue, and create number patterns resulting from performing addition or subtraction (VCMNA138)
2. Use a function machine and the inverse machine as a model to apply mathematical rules to numbers or shapes (VCMNA139)

#### Measurement and Geometry

##### Using units of measurement
1. Measure, order and compare objects using familiar metric units of length, area, mass and capacity (VCMMG140)
2. Tell time to the minute and investigate the relationship between units of time (VCMMG141)
##### Shape
1. Make models of three-dimensional objects and describe key features (VCMMG142)
##### Location and transformation
1. Create and interpret simple grid maps to show position and pathways (VCMMG143)
2. Identify symmetry in the environment (VCMMG144)
3. Identify and describe slides and turns found in the natural and built environment (VCMMG145)
##### Geometric reasoning
1. Identify angles as measures of turn and compare angle sizes in everyday situations (VCMMG146)

#### Statistics and Probability

##### Chance
1. Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (VCMSP147)
##### Data representation and interpretation
1. Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (VCMSP148)
2. Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (VCMSP149)
3. Interpret and compare data displays (VCMSP150)

### Level 3 Achievement Standard

Number and Algebra

Students count and order numbers to and from 10 000. They recognise the connection between addition and subtraction, and solve problems using efficient strategies for multiplication with and without the use of digital technology. Students recall addition and multiplication facts for single-digit numbers. They represent money values in various ways and correctly count out change from financial transactions. Students model and represent unit fractions for halves, thirds, quarters, fifths and eighths, and multiples of these up to one. They classify numbers as either odd or even, continue number patterns involving addition or subtraction, and explore simple number sequences based on multiples.

Measurement and Geometry

Students use metric units for length, area, mass and capacity. They tell time to the nearest minute. Students identify symmetry in natural and constructed environments. They use angle size as a measure of turn in real situations and make models of three-dimensional objects. Students match positions on maps with given information and create simple maps.

Statistics and Probability

Students carry out simple data investigations for categorical variables. They interpret and compare data displays. Students conduct chance experiments, list possible outcomes and recognise variations in results.

## 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

#### Number and Algebra

##### Number and place value
1. Investigate and use the properties of odd and even numbers (VCMNA151)
2. Recognise, represent and order numbers to at least tens of thousands (VCMNA152)
3. Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (VCMNA153)
4. Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (VCMNA154)
5. Recall multiplication facts up to 10 × 10 and related division facts (VCMNA155)
6. Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (VCMNA156)
##### Fractions and decimals
1. Investigate equivalent fractions used in contexts (VCMNA157)
2. Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (VCMNA158)
3. Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (VCMNA159)
##### Money and financial mathematics
1. Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (VCMNA160)
##### Patterns and algebra
1. Explore and describe number patterns resulting from performing multiplication (VCMNA161)
2. Solve word problems by using number sentences involving multiplication or division where there is no remainder (VCMNA162)
3. Use equivalent number sentences involving addition and subtraction to find unknown quantities (VCMNA163)
4. Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions (VCMNA164)

#### Measurement and Geometry

##### Using units of measurement
1. Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (VCMMG165)
2. Compare objects using familiar metric units of area and volume (VCMMG166)
3. Convert between units of time (VCMMG167)
4. Use am and pm notation and solve simple time problems (VCMMG168)
##### Shape
1. Compare the areas of regular and irregular shapes by informal means (VCMMG169)
2. Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (VCMMG170)
3. Explain and compare the geometric properties of two-dimensional shapes and three-dimensional objects (VCMMG171)
##### Location and transformation
1. Use simple scales, legends and directions to interpret information contained in basic maps (VCMMG172)
2. Create symmetrical patterns, pictures and shapes with and without digital technologies (VCMMG173)
##### Geometric reasoning
1. Compare angles and classify them as equal to, greater than or less than a right angle (VCMMG174)

#### 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

#### Number and Algebra

##### Number and place value
1. Identify and describe factors and multiples of whole numbers and use them to solve problems (VCMNA181)
2. Use estimation and rounding to check the reasonableness of answers to calculations (VCMNA182)
3. Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (VCMNA183)
4. Solve problems involving division by a one digit number, including those that result in a remainder (VCMNA184)
5. Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (VCMNA185)
6. Recognise, represent and order numbers to at least hundreds of thousands (VCMNA186)
##### Fractions and decimals
1. Compare and order common unit fractions and locate and represent them on a number line (VCMNA187)
2. Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (VCMNA188)
3. Recognise that the place value system can be extended beyond hundredths (VCMNA189)
4. Compare, order and represent decimals (VCMNA190)
##### Money and financial mathematics
1. Create simple financial plans (VCMNA191)
##### Patterns and algebra
1. Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (VCMNA192)
2. Use equivalent number sentences involving multiplication and division to find unknown quantities (VCMNA193)
3. Follow a mathematical algorithm involving branching and repetition (iteration) (VCMNA194)

#### Measurement and Geometry

##### Using units of measurement
1. Choose appropriate units of measurement for length, area, volume, capacity and mass (VCMMG195)
2. Calculate the perimeter and area of rectangles and the volume and capacity of prisms using familiar metric units (VCMMG196)
3. Compare 12- and 24-hour time systems and convert between them (VCMMG197)
##### Shape
1. Connect three-dimensional objects with their nets and other two-dimensional representations (VCMMG198)
##### Location and transformation
1. Use a grid reference system to describe locations. Describe routes using landmarks and directional language (VCMMG199)
2. Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (VCMMG200)
3. Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (VCMMG201)
##### Geometric reasoning
1. Estimate, measure and compare angles using degrees. Construct angles using a protractor (VCMMG202)

#### 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

#### Number and Algebra

##### Number and place value
1. Identify and describe properties of prime, composite, square and triangular numbers (VCMNA208)
2. Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations (VCMNA209)
3. Investigate everyday situations that use integers. Locate and represent these numbers on a number line (VCMNA210)
##### Fractions and decimals
1. Compare fractions with related denominators and locate and represent them on a number line (VCMNA211)
2. Solve problems involving addition and subtraction of fractions with the same or related denominators (VCMNA212)
3. Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (VCMNA213)
4. Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (VCMNA214)
5. Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (VCMNA215)
6. Multiply and divide decimals by powers of 10 (VCMNA216)
7. Make connections between equivalent fractions, decimals and percentages (VCMNA217)
##### Money and financial mathematics
1. Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (VCMNA218)
##### Patterns and algebra
1. Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (VCMNA219)
2. Explore the use of brackets and order of operations to write number sentences (VCMNA220)
3. Design algorithms involving branching and iteration to solve specific classes of mathematical problems (VCMNA221)

#### Measurement and Geometry

##### Using units of measurement
1. Connect decimal representations to the metric system (VCMMG222)
2. Convert between common metric units of length, mass and capacity (VCMMG223)
3. Solve problems involving the comparison of lengths and areas using appropriate units (VCMMG224)
4. Connect volume and capacity and their units of measurement (VCMMG225)
5. Interpret and use timetables (VCMMG226)
6. Measure, calculate and compare elapsed time (VCMMG227)
##### Shape
1. Construct simple prisms and pyramids (VCMMG228)
##### Location and transformation
1. Investigate the effect of combinations of transformations on simple and composite shapes, including creating tessellations, with and without the use of digital technologies (VCMMG229)
2. Introduce the Cartesian coordinate system using all four quadrants (VCMMG230)
##### Geometric reasoning
1. Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (VCMMG231)

#### 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

#### Number and Algebra

##### Number and place value
1. Investigate index notation and represent whole numbers as products of powers of prime numbers (VCMNA238)
2. Investigate and use square roots of perfect square numbers (VCMNA239)
3. Apply the associative, commutative and distributive laws to aid mental and written computation and make estimates for these computations (VCMNA240)
4. Compare, order, add and subtract integers (VCMNA241)
##### Real numbers
1. Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line (VCMNA242)
2. Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (VCMNA243)
3. Multiply and divide fractions and decimals using efficient written strategies and digital technologies (VCMNA244)
4. Express one quantity as a fraction of another, with and without the use of digital technologies (VCMNA245)
5. Round decimals to a specified number of decimal places (VCMNA246)
6. Connect fractions, decimals and percentages and carry out simple conversions (VCMNA247)
7. Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (VCMNA248)
8. Recognise and solve problems involving simple ratios (VCMNA249)
##### Money and financial mathematics
1. Investigate and calculate 'best buys', with and without digital technologies (VCMNA250)
##### Patterns and algebra
1. Introduce the concept of variables as a way of representing numbers using letters (VCMNA251)
2. Create algebraic expressions and evaluate them by substituting a given value for each variable (VCMNA252)
3. Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (VCMNA253)
4. Design and implement mathematical algorithms using a simple general purpose programming language (VCMNA254)
##### Linear and non-linear relationships
1. Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (VCMNA255)
2. Solve simple linear equations (VCMNA256)
3. Investigate, interpret and analyse graphs from real life data, including consideration of domain and range (VCMNA257)

#### Measurement and Geometry

##### Using units of measurement
1. Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (VCMMG258)
2. Calculate volumes of rectangular prisms (VCMMG259)
##### Shape
1. Draw different views of prisms and solids formed from combinations of prisms (VCMMG260)
##### Location and transformation
1. Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (VCMMG261)
##### Geometric reasoning
1. Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (VCMMG264)
2. Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (VCMMG265)
3. Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (VCMMG263)
4. Classify triangles according to their side and angle properties and describe quadrilaterals (VCMMG262)

#### 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

#### Number and Algebra

##### Number and place value
1. Use index notation with numbers to establish the index laws with positive integral indices and the zero index (VCMNA272)
2. Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies and make estimates for these computations (VCMNA273)
##### Real numbers
1. Investigate terminating and recurring decimals (VCMNA274)
2. Investigate the concept of irrational numbers, including π (VCMNA275)
3. Solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital technologies (VCMNA276)
4. Solve a range of problems involving rates and ratios, including distance-time problems for travel at a constant speed, with and without digital technologies (VCMNA277)
##### Money and financial mathematics
1. Solve problems involving profit and loss, with and without digital technologies (VCMNA278)
##### Patterns and algebra
1. Extend and apply the distributive law to the expansion of algebraic expressions (VCMNA279)
2. Factorise algebraic expressions by identifying numerical factors (VCMNA280)
3. Simplify algebraic expressions involving the four operations (VCMNA281)
4. Use algorithms and related testing procedures to identify and correct errors (VCMNA282)
##### Linear and non-linear relationships
1. Plot linear relationships on the Cartesian plane with and without the use of digital technologies (VCMNA283)
2. Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (VCMNA284)
3. Plot graphs of non-linear real life data with and without the use of digital technologies, and interpret and analyse these graphs (VCMNA285)

#### Measurement and Geometry

##### Using units of measurement
1. Choose appropriate units of measurement for area and volume and convert from one unit to another (VCMMG286)
2. Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites (VCMMG287)
3. Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving determining radius, diameter, circumference and area from each other (VCMMG288)
4. Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume (VCMMG289)
5. Solve problems involving duration, including using 12- and 24-hour time within a single time zone (VCMMG290)
##### Geometric reasoning
1. Define congruence of plane shapes using transformations and use transformations of congruent shapes to produce regular patterns in the plane including tessellations with and without the use of digital technology (VCMMG291)
2. Develop the conditions for congruence of triangles (VCMMG292)
3. Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (VCMMG293)

#### 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...