## 1. Number and Algebra

### 1.1. Number and place value (F-8)

1.1.1. Primary

1.1.1.1. Foundation

1.1.1.1.1. Represent practical situations to model addition and sharing (ACMNA004)

1.1.1.1.2. Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)

1.1.1.1.3. Subitise small collections of objects (ACMNA003)

1.1.1.1.4. Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)

1.1.1.1.5. Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001)

1.1.1.2. Year 1

1.1.1.2.1. Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012)

1.1.1.2.2. Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)

1.1.1.2.3. Count collections to 100 by partitioning numbers using place value (ACMNA014)

1.1.1.2.4. Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015)

1.1.1.3. Year 2

1.1.1.3.1. Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. (ACMNA026)

1.1.1.3.2. Recognise, model, represent and order numbers to at least 1000 (ACMNA027)

1.1.1.3.3. Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)

1.1.1.3.4. Explore the connection between addition and subtraction (ACMNA029)

1.1.1.3.5. Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030)

1.1.1.3.6. Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031)

1.1.1.3.7. Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032)

1.1.1.4. Year 3

1.1.1.4.1. Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)

1.1.1.4.2. Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)

1.1.1.4.3. Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

1.1.1.4.4. Recognise and explain the connection between addition and subtraction (ACMNA054)

1.1.1.4.5. Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

1.1.1.4.6. Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

1.1.1.4.7. Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

1.1.1.5. Year 4

1.1.1.5.1. Investigate and use the properties of odd and even numbers (ACMNA071)

1.1.1.5.2. Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

1.1.1.5.3. Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

1.1.1.5.4. Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

1.1.1.5.5. Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075)

1.1.1.5.6. Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

1.1.1.6. Year 5

1.1.1.6.1. Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

1.1.1.6.2. Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

1.1.1.6.3. Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

1.1.1.6.4. Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)

1.1.1.6.5. Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

1.1.1.7. Year 6

1.1.1.7.1. Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)

1.1.1.7.2. Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123), including negative numbers?

1.1.1.7.3. Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)

1.1.2. Secondary

1.1.2.1. Year 7

1.1.2.1.1. Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149)

1.1.2.1.2. Investigate and use square roots of perfect square numbers (ACMNA150)

1.1.2.1.3. Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)

1.1.2.1.4. Compare, order, add and subtract integers (ACMNA280)

1.1.2.2. Year 8

1.1.2.2.1. Use index notation with numbers to establish the index laws with positive integral indices and the zero index (ACMNA182)

1.1.2.2.2. Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183)

### 1.2. Patterns and algebra (F-10A)

1.2.1. Primary

1.2.1.1. Year 6

1.2.1.1.1. Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)

1.2.1.1.2. Explore the use of brackets and order of operations to write number sentences (ACMNA134)

1.2.1.2. Year 5

1.2.1.2.1. Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)

1.2.1.2.2. Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)

1.2.1.2.3. Recognise that the place value system can be extended beyond hundredths (ACMNA104)

1.2.1.2.4. Compare, order and represent decimals (ACMNA105)

1.2.1.3. Year 4

1.2.1.3.1. Explore and describe number patterns resulting from performing multiplication (ACMNA081)

1.2.1.3.2. Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

1.2.1.3.3. Use equivalent number sentences involving addition and subtraction to find unknown quantities (ACMNA083)

1.2.1.4. Year 3

1.2.1.4.1. Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060)

1.2.1.5. Year 2

1.2.1.5.1. Describe patterns with numbers and identify missing elements (ACMNA035)

1.2.1.5.2. Solve problems by using number sentences for addition or subtraction (ACMNA036)

1.2.1.6. Year 1

1.2.1.6.1. Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA018)

1.2.1.7. Foundation

1.2.1.7.1. Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings (ACMNA005)

1.2.2. Secondary

1.2.2.1. Year 7

1.2.2.1.1. Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)

1.2.2.1.2. Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176)

1.2.2.1.3. Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)

1.2.2.2. Year 8

1.2.2.2.1. Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA190)

1.2.2.2.2. Factorise algebraic expressions by identifying numerical factors (ACMNA191)

1.2.2.2.3. Simplify algebraic expressions involving the four operations (ACMNA192)

1.2.2.3. Year 9

1.2.2.3.1. Extend and apply the index laws to variables, using positive integer indices and the zero index (ACMNA212)

1.2.2.3.2. Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213)

1.2.2.4. Year 10

1.2.2.4.1. Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230)

1.2.2.4.2. Simplify algebraic products and quotients using index laws (ACMNA231)

1.2.2.4.3. Apply the four operations to simple algebraic fractions with numerical denominators (ACMNA232)

1.2.2.4.4. Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233)

1.2.2.4.5. Substitute values into formulas to determine an unknown (ACMNA234)

1.2.2.5. Year 10A

1.2.2.5.1. Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266)

### 1.3. Fractions and Decimals (1-6)

1.3.1. Primary

1.3.1.1. Year 1

1.3.1.1.1. Recognise and describe one-half as one of two equal parts of a whole. (ACMNA016)

1.3.1.2. Year 2

1.3.1.2.1. Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033)

1.3.1.3. Year 3

1.3.1.3.1. Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058)

1.3.1.4. Year 4

1.3.1.4.1. Investigate equivalent fractions used in contexts (ACMNA077)

1.3.1.4.2. Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)

1.3.1.4.3. Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

1.3.1.5. Year 5

1.3.1.5.1. Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)

1.3.1.5.2. Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121)

1.3.1.6. Year 6

1.3.1.6.1. Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)

1.3.1.6.2. Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)

1.3.1.6.3. Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)

1.3.1.6.4. Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

1.3.1.6.5. Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129)

1.3.1.6.6. Multiply and divide decimals by powers of 10 (ACMNA130)

1.3.1.6.7. Make connections between equivalent fractions, decimals and percentages (ACMNA131)

1.3.2. Secondary

1.3.2.1. Real Numbers (7-10A)

1.3.2.1.1. Year 7

1.3.2.1.2. Year 8

1.3.2.1.3. Year 9

1.3.2.1.4. Year 10A

### 1.4. Money and Financial Mathematics (1-10)

1.4.1. Primary

1.4.1.1. Year 1

1.4.1.1.1. Recognise, describe and order Australian coins according to their value (ACMNA017)

1.4.1.2. Year 2

1.4.1.2.1. Count and order small collections of Australian coins and notes according to their value (ACMNA034)

1.4.1.3. Year 3

1.4.1.3.1. Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)

1.4.1.4. Year 4

1.4.1.4.1. Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

1.4.1.5. Year 5

1.4.1.5.1. Create simple financial plans (ACMNA106)

1.4.1.6. Year 6

1.4.1.6.1. Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

1.4.2. Secondary

1.4.2.1. Year 7

1.4.2.1.1. Investigate and calculate 'best buys', with and without digital technologies (ACMNA174)

1.4.2.2. Year 8

1.4.2.2.1. Solve problems involving profit and loss, with and without digital technologies (ACMNA189)

1.4.2.3. Year 9

1.4.2.3.1. Solve problems involving simple interest (ACMNA211)

1.4.2.4. Year 10

1.4.2.4.1. Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229)

### 1.5. Linear and non-linear relationships (7-10A)

1.5.1. Secondary

1.5.1.1. Year 7

1.5.1.1.1. Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)

1.5.1.1.2. Solve simple linear equations (ACMNA179)

1.5.1.1.3. Investigate, interpret and analyse graphs from authentic data (ACMNA180)

1.5.1.2. Year 8

1.5.1.2.1. Plot linear relationships on the Cartesian plane with and without the use of digital technologies (ACMNA193)

1.5.1.2.2. Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution (ACMNA194)

1.5.1.3. Year 9

1.5.1.3.1. Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software (ACMNA214)

1.5.1.3.2. Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software (ACMNA294)

1.5.1.3.3. Sketch linear graphs using the coordinates of two points and solve linear equations (ACMNA215)

1.5.1.3.4. Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations (ACMNA296)

1.5.1.4. Year 10

1.5.1.4.1. Solve problems involving linear equations, including those derived from formulas (ACMNA235)

1.5.1.4.2. Solve linear inequalities and graph their solutions on a number line (ACMNA236)

1.5.1.4.3. Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology (ACMNA237)

1.5.1.4.4. Solve problems involving parallel and perpendicular lines (ACMNA238)

1.5.1.4.5. Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate (ACMNA239)

1.5.1.4.6. Solve linear equations involving simple algebraic fractions (ACMNA240)

1.5.1.4.7. Solve simple quadratic equations using a range of strategies (ACMNA241)

1.5.1.5. Year 10A

1.5.1.5.1. Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)

1.5.1.5.2. Solve simple exponential equations (ACMNA270)

1.5.1.5.3. Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268)

1.5.1.5.4. Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts (ACMNA269)

## 2. Measurement and Geometry

### 2.1. Using units of measurement (F-10A)

2.1.1. Primary

2.1.1.1. Foundation

2.1.1.1.1. Connect days of the week to familiar events and actions (ACMMG008)

2.1.1.1.2. Compare and order the duration of events using the everyday language of time (ACMMG007)

2.1.1.1.3. Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006)

2.1.1.2. Year 1

2.1.1.2.1. Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019)

2.1.1.2.2. Tell time to the half-hour (ACMMG020)

2.1.1.2.3. Describe duration using months, weeks, days and hours (ACMMG021)

2.1.1.3. Year 2

2.1.1.3.1. Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037)

2.1.1.3.2. Compare masses of objects using balance scales (ACMMG038)

2.1.1.3.3. Tell time to the quarter-hour, using the language of 'past' and 'to' (ACMMG039)

2.1.1.3.4. Name and order months and seasons (ACMMG040)

2.1.1.3.5. Use a calendar to identify the date and determine the number of days in each month (ACMMG041)

2.1.1.4. Year 3

2.1.1.4.1. Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

2.1.1.4.2. Tell time to the minute and investigate the relationship between units of time (ACMMG062)

2.1.1.5. Year 4

2.1.1.5.1. Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)

2.1.1.5.2. Compare objects using familiar metric units of area and volume (ACMMG290)

2.1.1.5.3. Convert between units of time (ACMMG085)

2.1.1.5.4. Use am and pm notation and solve simple time problems (ACMMG086)

2.1.1.6. Year 5

2.1.1.6.1. Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

2.1.1.6.2. Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)

2.1.1.6.3. Compare 12- and 24-hour time systems and convert between them (ACMMG110)

2.1.1.7. Year 6

2.1.1.7.1. Connect decimal representations to the metric system (ACMMG135)

2.1.1.7.2. Convert between common metric units of length, mass and capacity (ACMMG136)

2.1.1.7.3. Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137)

2.1.1.7.4. Connect volume and capacity and their units of measurement (ACMMG138)

2.1.1.7.5. Interpret and use timetables (ACMMG139)

2.1.2. Secondary

2.1.2.1. Year 7

2.1.2.1.1. Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (ACMMG159)

2.1.2.1.2. Calculate volumes of rectangular prisms (ACMMG160)

2.1.2.2. Year 8

2.1.2.2.1. Choose appropriate units of measurement for area and volume and convert from one unit to another (ACMMG195)

2.1.2.2.2. Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites (ACMMG196)

2.1.2.2.3. Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving circumference and area (ACMMG197)

2.1.2.2.4. Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume (ACMMG198)

2.1.2.2.5. Solve problems involving duration, including using 12- and 24-hour time within a single time zone (ACMMG199)

2.1.2.3. Year 9

2.1.2.3.1. Calculate the areas of composite shapes (ACMMG216)

2.1.2.3.2. Calculate the surface area and volume of cylinders and solve related problems (ACMMG217)

2.1.2.3.3. Solve problems involving the surface area and volume of right prisms (ACMMG218)

2.1.2.3.4. Investigate very small and very large time scales and intervals (ACMMG219)

2.1.2.4. Year 10

2.1.2.4.1. Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (ACMMG242)

2.1.2.5. Year 10A

2.1.2.5.1. Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271)

### 2.2. Shape (F-7)

2.2.1. Primary

2.2.1.1. Foundation

2.2.1.1.1. Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment (ACMMG009)

2.2.1.2. Year 1

2.2.1.2.1. Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features (ACMMG022)

2.2.1.3. Year 2

2.2.1.3.1. Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042)

2.2.1.3.2. Describe the features of three-dimensional objects (ACMMG043)

2.2.1.4. Year 3

2.2.1.4.1. Make models of three-dimensional objects and describe key features (ACMMG063)

2.2.1.5. Year 4

2.2.1.5.1. Compare the areas of regular and irregular shapes by informal means (ACMMG087)

2.2.1.5.2. Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)

2.2.1.6. Year 5

2.2.1.6.1. Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)

2.2.1.7. Year 6

2.2.1.7.1. Construct simple prisms and pyramids (ACMMG140)

2.2.2. Secondary

2.2.2.1. Year 7

2.2.2.1.1. Draw different views of prisms and solids formed from combinations of prisms (ACMMG161)

### 2.3. Location and transformation (F-7

2.3.1. Primary

2.3.1.1. Foundation

2.3.1.1.1. Describe position and movement (ACMMG010)

2.3.1.2. Year 1

2.3.1.2.1. Give and follow directions to familiar locations (ACMMG023)

2.3.1.3. Year 2

2.3.1.3.1. Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044)

2.3.1.3.2. Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045)

2.3.1.3.3. Identify and describe half and quarter turns (ACMMG046)

2.3.1.4. Year 3

2.3.1.4.1. Create and interpret simple grid maps to show position and pathways (ACMMG065)

2.3.1.4.2. Identify symmetry in the environment (ACMMG066)

2.3.1.5. Year 4

2.3.1.5.1. Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)

2.3.1.5.2. Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)

2.3.1.6. Year 5

2.3.1.6.1. Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)

2.3.1.6.2. Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114)

2.3.1.6.3. Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)

2.3.1.7. Year 6

2.3.1.7.1. Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)

2.3.1.7.2. Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

2.3.2. Secondary

2.3.2.1. Year 7

2.3.2.1.1. Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (ACMMG181)

### 2.4. Geometric Reasoning (3-10A)

2.4.1. Primary

2.4.1.1. Year 3

2.4.1.1.1. Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)

2.4.1.2. Year 4

2.4.1.2.1. Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)

2.4.1.3. Year 5

2.4.1.3.1. Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112)

2.4.1.4. Year 6

2.4.1.4.1. 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 (ACMMG141)

2.4.2. Secondary

2.4.2.1. Year 7

2.4.2.1.1. Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)

2.4.2.1.2. Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166)

2.4.2.1.3. Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal (ACMMG163)

2.4.2.1.4. Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164)

2.4.2.2. Year 8

2.4.2.2.1. Define congruence of plane shapes using transformations (ACMMG200)

2.4.2.2.2. Develop the conditions for congruence of triangles (ACMMG201)

2.4.2.2.3. Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning (ACMMG202)

2.4.2.3. Year 9

2.4.2.3.1. Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar (ACMMG220)

2.4.2.3.2. Solve problems using ratio and scale factors in similar figures (ACMMG221)

2.4.2.4. Year 10

2.4.2.4.1. Formulate proofs involving congruent triangles and angle properties (ACMMG243)

2.4.2.4.2. Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244)

2.4.2.5. Year 10A

2.4.2.5.1. Prove and apply angle and chord properties of circles (ACMMG272)

### 2.5. Pythagoras and Trigonometry (9-10A)

2.5.1. Secondary

2.5.1.1. Year 9

2.5.1.1.1. Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles (ACMMG222)

2.5.1.1.2. Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles (ACMMG223)

2.5.1.1.3. Apply trigonometry to solve right-angled triangle problems (ACMMG224)

2.5.1.2. Year 10

2.5.1.2.1. Solve right-angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245)

2.5.1.3. Year 10A

2.5.1.3.1. Establish the sine, cosine and area rules for any triangle and solve related problems (ACMMG273)

2.5.1.3.2. Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies (ACMMG274)

2.5.1.3.3. Solve simple trigonometric equations (ACMMG275)

2.5.1.3.4. Pythagoras' theorem and trigonometry to solving three-dimensional problems in right-angled triangles (ACMMG276)

## 3. Statistics and Probability

### 3.1. Data representation and interpretation (F-10A)

3.1.1. Primary

3.1.1.1. Year 6

3.1.1.1.1. Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

3.1.1.1.2. Interpret secondary data presented in digital media and elsewhere (ACMSP148)

3.1.1.2. Year 5

3.1.1.2.1. Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

3.1.1.2.2. Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

3.1.1.2.3. Describe and interpret different data sets in context (ACMSP120)

3.1.1.3. Year 4

3.1.1.3.1. Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)

3.1.1.3.2. 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 (ACMSP096)

3.1.1.3.3. Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

3.1.1.4. Year 3

3.1.1.4.1. Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

3.1.1.4.2. 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 (ACMSP069)

3.1.1.4.3. Interpret and compare data displays (ACMSP070)

3.1.1.5. Year 2

3.1.1.5.1. Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048)

3.1.1.5.2. Collect, check and classify data (ACMSP049)

3.1.1.5.3. Create displays of data using lists, table and picture graphs and interpret them (ACMSP050)

3.1.1.6. Year 1

3.1.1.6.1. Choose simple questions and gather responses (ACMSP262)

3.1.1.6.2. Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays (ACMSP263)

3.1.1.7. Foundation

3.1.1.7.1. Answer yes/no questions to collect information (ACMSP011)

3.1.2. Secondary

3.1.2.1. Year 7

3.1.2.1.1. Describe and interpret data displays using median, mean and range (ACMSP172)

3.1.2.1.2. Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171)

3.1.2.1.3. Construct and compare a range of data displays including stem-and-leaf plots and dot plots (ACMSP170)

3.1.2.1.4. Identify and investigate issues involving numerical data collected from primary and secondary sources (ACMSP169)

3.1.2.2. Year 8

3.1.2.2.1. Investigate techniques for collecting data, including census, sampling and observation (ACMSP284)

3.1.2.2.2. Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (ACMSP206)

3.1.2.2.3. Explore the variation of means and proportions of random samples drawn from the same population (ACMSP293)

3.1.2.2.4. Investigate the effect of individual data values , including outliers, on the mean and median (ACMSP207)

3.1.2.3. Year 9

3.1.2.3.1. Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources (ACMSP228)

3.1.2.3.2. Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (ACMSP282)

3.1.2.3.3. Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread (ACMSP283)

3.1.2.4. Year 10

3.1.2.4.1. Determine quartiles and interquartile range (ACMSP248)

3.1.2.4.2. Construct and interpret box plots and use them to compare data sets (ACMSP249)

3.1.2.4.3. Compare shapes of box plots to corresponding histograms and dot plots (ACMSP250)

3.1.2.4.4. Use scatter plots to investigate and comment on relationships between two numerical variables (ACMSP251)

3.1.2.4.5. Investigate and describe bivariate numerical data where the independent variable is time (ACMSP252)

3.1.2.4.6. Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (ACMSP253)

3.1.2.5. Year 10A

3.1.2.5.1. Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)

3.1.2.5.2. Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation (ACMSP279)

### 3.2. Chance (1-10A)

3.2.1. Primary

3.2.1.1. Year 6

3.2.1.1.1. Describe probabilities using fractions, decimals and percentages (ACMSP144)

3.2.1.1.2. Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

3.2.1.1.3. Compare observed frequencies across experiments with expected frequencies (ACMSP146)

3.2.1.2. Year 5

3.2.1.2.1. List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

3.2.1.2.2. Recognise that probabilities range from 0 to 1 (ACMSP117)

3.2.1.3. Year 4

3.2.1.3.1. Describe possible everyday events and order their chances of occurring (ACMSP092)

3.2.1.3.2. Identify everyday events where one cannot happen if the other happens (ACMSP093)

3.2.1.3.3. Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

3.2.1.4. Year 3

3.2.1.4.1. Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

3.2.1.5. Year 2

3.2.1.5.1. Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047)

3.2.1.6. Year 1

3.2.1.6.1. Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024)

3.2.2. Secondary

3.2.2.1. Year 7

3.2.2.1.1. Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167)

3.2.2.1.2. Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)

3.2.2.2. Year 8

3.2.2.2.1. Identify complementary events and use the sum of probabilities to solve problems (ACMSP204)

3.2.2.2.2. Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and'. (ACMSP205)

3.2.2.2.3. Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292)

3.2.2.3. Year 9

3.2.2.3.1. 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 (ACMSP225)

3.2.2.3.2. Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226)

3.2.2.3.3. Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians (ACMSP227)

3.2.2.4. Year 10

3.2.2.4.1. 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 (ACMSP246)

3.2.2.4.2. Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language (ACMSP247)

3.2.2.5. Year 10A

3.2.2.5.1. Investigate reports of studies in digital media and elsewhere for information on their planning and implementation (ACMSP277)