## 1. Patterns & Algebra

### 1.1. Foundations

1.1.1. Content Descriptors

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

1.1.1.1.1. Declarative & Procedural Progression

1.1.2. Proficiency Strands in Year Level Descriptors

1.1.2.1. Understanding

1.1.2.1.1. Includes connecting names, numerals and quantities

1.1.2.2. Fluency

1.1.2.2.1. Includes readily counting numbers in sequences, continuing patterns and comparing the lengths of objects

1.1.2.3. Problem Solving

1.1.2.3.1. Includes using materials to model authentic problems, sorting objects, using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer

1.1.2.4. Reasoning

1.1.2.4.1. Includes explaining comparisons of quantities, creating patterns and explaining processes for indirect comparison of length.

### 1.2. Year 1

1.2.1. Content Descriptors

1.2.1.1. 1. Investigate and describe number patterns formed by skip-counting and patterns with objects (ACMNA018)

1.2.1.1.1. Declarative & Procedural Progression

1.2.2. Proficiency Strands in Year Level Descriptors

1.2.2.1. Understanding

1.2.2.1.1. Includes connecting names, numerals and quantities, and partitioning numbers in various ways

1.2.2.2. Fluency

1.2.2.2.1. Includes readily counting number in sequences forwards and backwards, locating numbers on a line and naming the days of the week

1.2.2.3. Problem Solving

1.2.2.3.1. Includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer

1.2.2.4. Reasoning

1.2.2.4.1. Includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data and explaining patterns that have been created.

### 1.3. Year 2

1.3.1. Content Descriptors

1.3.1.1. 1. Describe patterns with numbers and identify missing elements (ACMNA035) 2. Solve problems by using number sentences for addition or subtraction (ACMNA036)

1.3.1.1.1. Declarative & Procedural Progression

1.3.2. Proficiency Strands in Year Level Descriptors

1.3.2.1. Understanding

1.3.2.1.1. Includes connecting number calculations with counting sequences, partitioning and combining numbers flexibly and identifying and describing the relationship between addition and subtraction and between multiplication and division

1.3.2.2. Fluency

1.3.2.2.1. Includes readily counting numbers in sequences, using informal units iteratively to compare measurements, using the language of chance to describe outcomes of familiar chance events and describing and comparing time durations

1.3.2.3. Problem Solving

1.3.2.3.1. Includes formulating problems from authentic situations, making models and using number sentences that represent problem situations, and matching transformations with their original shape

1.3.2.4. Reasoning

1.3.2.4.1. Includes using known facts to derive strategies for unfamiliar calculations, comparing and contrasting related models of operations and creating and interpreting simple representations of data.

### 1.4. Year 3

1.4.1. Content Descriptors

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

1.4.1.1.1. Declarative & Procedural Progression

1.4.2. Proficiency Strands in Year Level Descriptors

1.4.2.1. Understanding

1.4.2.1.1. Includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry

1.4.2.2. Fluency

1.4.2.2.1. Includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and communicating positions

1.4.2.3. Problem Solving

1.4.2.3.1. Includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and using number properties to continue number patterns

1.4.2.4. Reasoning

1.4.2.4.1. Includes using generalising from number properties and results of calculations, comparing angles and creating and interpreting variations in the results of data collections and data displays.

### 1.5. Year 4

1.5.1. Content Descriptors

1.5.1.1. 1. Explore and describe number patterns resulting from performing multiplication (ACMNA081) 2. Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082) 3. Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction (ACMNA083)

1.5.1.1.1. Declarative & Procedural Progression

1.5.2. Proficiency Strands in Year Level Descriptors

1.5.2.1. Understanding

1.5.2.1.1. Includes making connections between representations of numbers, partitioning and combining numbers flexibly, extending place value to decimals, using appropriate language to communicate times and describing properties of symmetrical shapes

1.5.2.2. Fluency

1.5.2.2.1. Includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure accurately, creating patterns with shapes and their transformations and collecting and recording data

1.5.2.3. Problem Solving

1.5.2.3.1. Includes formulating, modelling and recording authentic situations involving operations, comparing large numbers with each other, comparing time durations and using properties of numbers to continue patterns

1.5.2.4. Reasoning

1.5.2.4.1. Includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the appropriateness of different displays.

### 1.6. Year 5

1.6.1. Content Descriptors

1.6.1.1. 1. Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107) 2. Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division (ACMNA121)

1.6.1.1.1. Declarative & Procedural Progression

1.6.2. Proficiency Strands in Year Level Descriptors

1.6.2.1. Understanding

1.6.2.1.1. Includes making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry

1.6.2.2. Fluency

1.6.2.2.1. Includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles

1.6.2.3. Problem Solving

1.6.2.3.1. Includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans

1.6.2.4. Reasoning

1.6.2.4.1. Includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data sets.

### 1.7. Year 6

1.7.1. Content Descriptors

1.7.1.1. 1. Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133) 2. Explore the use of brackets and order of operations to write number sentences (ACMNA134)

1.7.1.1.1. Declarative & Procedural Progression

1.7.2. Proficiency Strands in Year Level Descriptors

1.7.2.1. Understanding

1.7.2.1.1. Includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations

1.7.2.2. Fluency

1.7.2.2.1. Includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units and interpreting timetables

1.7.2.3. Problem Solving

1.7.2.3.1. Includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays and finding the size of unknown angles

1.7.2.4. Reasoning

1.7.2.4.1. Includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another and explaining why the actual results of chance experiments may differ from expected results.

### 1.8. Year 7

1.8.1. Content Descriptors

1.8.1.1. 1. Introduce the concept of variables as a way of representing numbers using letters (ACMNA175) 2. Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176) 3. Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)

1.8.1.1.1. Declarative & Procedural Progression

1.8.2. Proficiency Strands in Year Level Descriptors

1.8.2.1. Understanding

1.8.2.1.1. Includes describing patterns in uses of indices with whole numbers, recognising equivalences between fractions, decimals, percentages and ratios, plotting points on the Cartesian plane, identifying angles formed by a transversal crossing a pair of lines, and connecting the laws and properties of numbers to algebraic terms and expressions

1.8.2.2. Fluency

1.8.2.2.1. Includes calculating accurately with integers, representing fractions and decimals in various ways, investigating best buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms

1.8.2.3. Problem Solving

1.8.2.3.1. Includes formulating and solving authentic problems using numbers and measurements, working with transformations and identifying symmetry, calculating angles and interpreting sets of data collected through chance experiments

1.8.2.4. Reasoning

1.8.2.4.1. Includes applying the number laws to calculations, applying known geometric facts to draw conclusions about shapes, applying an understanding of ratio and interpreting data displays.

### 1.9. Year 8

1.9.1. Content Descriptors

1.9.1.1. 1. Extend and apply the distributive law to the expansion of algebraic expressions (ACMNA190) 2. Factorise algebraic expressions by identifying numerical factors (ACMNA191) 3. Simplify algebraic expressions involving the four operations (ACMNA192)

1.9.1.1.1. Declarative & Procedural Progression

1.9.2. Proficiency Strands in Year Level Descriptors

1.9.2.1. Understanding

1.9.2.1.1. Includes describing patterns involving indices and recurring decimals, identifying commonalities between operations with algebra and arithmetic, connecting rules for linear relations with their graphs, explaining the purpose of statistical measures and explaining measurements of perimeter and area

1.9.2.2. Fluency

1.9.2.2.1. Includes calculating accurately with simple decimals, indices and integers; recognising equivalence of common decimals and fractions including recurring decimals; factorising and simplifying basic algebraic expressions and evaluating perimeters and areas of common shapes and volumes of three-dimensional objects

1.9.2.3. Problem Solving

1.9.2.3.1. Includes formulating and modelling practical situations involving ratios, profit and loss, areas and perimeters of common shapes and using two-way tables and Venn diagrams to calculate probabilities

1.9.2.4. Reasoning

1.9.2.4.1. Includes justifying the result of a calculation or estimation as reasonable, deriving probability from its complement, using congruence to deduce properties of triangles, finding estimates of means and proportions of populations.

### 1.10. Year 9

1.10.1. Content Descriptors

1.10.1.1. 1. Extend and apply the index laws to variables, using positive integer indices and the zero index (ACMNA212) 2. Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate (ACMNA213)

1.10.1.1.1. Declarative & Procedural Progression

1.10.2. Proficiency Strands in Year Level Descriptors

1.10.2.1. Understanding

1.10.2.1.1. Includes describing the relationship between graphs and equations, simplifying a range of algebraic expressions and explaining the use of relative frequencies to estimate probabilities and of the trigonometric ratios for right-angle triangles

1.10.2.2. Fluency

1.10.2.2.1. Includes applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing outcomes for experiments, developing familiarity with calculations involving the Cartesian plane and calculating areas of shapes and surface areas of prisms

1.10.2.3. Problem Solving

1.10.2.3.1. Includes formulating and modelling practical situations involving surface areas and volumes of right prisms, applying ratio and scale factors to similar figures, solving problems involving right-angle trigonometry and collecting data from secondary sources to investigate an issue

1.10.2.4. Reasoning

1.10.2.4.1. Includes following mathematical arguments, evaluating media reports and using statistical knowledge to clarify situations, developing strategies in investigating similarity and sketching linear graphs.