# 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

#### 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)

### 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

#### 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)

### 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

#### 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)

### 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

#### 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)

### 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

#### 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)

### 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...

### Level 9 Content Descriptions

#### Measurement and Geometry

##### Using units of measurement
1. Calculate the areas of composite shapes (VCMMG312)
2. Calculate the surface area and volume of cylinders and solve related problems (VCMMG313)
3. Solve problems involving the surface area and volume of right prisms (VCMMG314)
4. Investigate very small and very large time scales and intervals (VCMMG315)
##### Geometric reasoning
1. Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (VCMMG316)
2. Solve problems using ratio and scale factors in similar figures (VCMMG317)
##### Pythagoras and trigonometry
1. Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (VCMMG318)
2. Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (VCMMG319)
3. Apply trigonometry to solve right-angled triangle problems (VCMMG320)

### 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

#### Measurement and Geometry

##### Using units of measurement
1. Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (VCMMG343)
##### Geometric reasoning
1. Formulate proofs involving congruent triangles and angle properties (VCMMG344)
2. Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (VCMMG345)
##### Pythagoras and trigonometry
1. Solve right-angled triangle problems including those involving direction and angles of elevation and depression (VCMMG346)

### 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...