## YEAR-Reception (FOUNDATION)

Mathematics at Garden College provides students with essential mathematical skills and knowledge in Number and Algebra, Measurement and Geometry, and Statistics and Probability. It develops the numeracy capabilities that all students need in their personal, work and civic life, and provides the fundamentals on which mathematical specialties and professional applications of mathematics are built.

### Overview

The Mathematics curriculum at Garden College aims to ensure that all students benefit from access to the power of mathematical reasoning and learn to apply mathematical understandings creatively and efficiently. Skills are developed through a range of open ended and interactive activities using concrete materials. This includes games, hands on activities, formal procedures and problem solving tasks. Lower Primary classes use the ‘Early Years Numeracy Program’ in which each individual student’s strengths and weaknesses are assessed and built upon. All areas of Mathematics are covered each term, throughout the year.

### Lesson Structure

During Mathematics sessions, the classroom is set up with enough floor space to allow interactive and engaging tuning in sessions to introduce new topics. The tables are set up in groups to allow flexibility to work both individually and in mixed ability groups, depending on what is required for that lesson. In a typical lesson, students are introduced to the Mathematical concept, actively take part in an opening activity are exposed to focus words for that concept and complete an individual or group task to consolidate the Mathematical skills and understanding relevant to that lesson.

### Assessment

Assessment includes:

- Teacher observations – ongoing
- Anecdotal notes – ongoing
- Topical Tests and the Early Years Numeracy Test – 1st and 3rd Term

### Resources

Mathematics resources referenced regularly include:

- iMaths
- Interactive Australian Curriculum aligned websites such as Scootle and Studyladder

### Benchmarks and Recommendations

Numeracy Week is a celebration of our mathematical skills in the real world. Each year, different activities are planned for different year levels and are often tied in with current affairs, such as the Olympics. This provides an enjoyable and valuable learning foundation for the whole school community. To ensure that students develop Mathematics concepts with confidence, the following skills are taught and emphasized very early in the year:

- Counting from 1-20 verbally and recognising and writing 1-10
- Recognising shapes & colours
- Identifying Heavy/light/long/short
- Adding and subtracting a collection of simple objects
- Using position language to identify location

### Foundation/Reception Year Achievement Standard

By the end of the Foundation year, students make connections between number names, numerals and quantities up to 10. They compare objects using mass, length and capacity. Students connect events and the days of the week. They explain the order and duration of events. They use appropriate language to describe location.

Students count to and from 20 and order small collections. They group objects based on common characteristics and sort shapes and objects. Students answer simple questions to collect information.

# Australian Curriculum Achievement Levels

** **

## Year 1

The Mathematics curriculum at Garden College aims to ensure that all students benefit from access to the power of mathematical reasoning and learn to apply mathematical understandings creatively and efficiently. Skills are developed through a range of open ended and interactive activities using concrete materials. This includes games, hands on activities, formal procedures and problem solving tasks. Lower Primary classes use the ‘Early Years Numeracy Program’ in which each individual student’s strengths and weaknesses are assessed and built upon.

### Lesson Structure

During Mathematics sessions, the classroom is set up with enough floor space to allow interactive and engaging tuning in sessions to introduce new topics. The tables are set up in groups to allow flexibility to work both individually and in mixed ability groups, depending on what is required for that lesson. In a typical lesson, students are introduced to the Mathematical concept, actively take part in an opening activity are exposed to focus words for that concept and complete an individual or group task to consolidate the Mathematical skills and understanding relevant to that lesson.

### Scope and Sequences

*In year 1, there is a focus on developing the following abilities throughout the year:*

Understanding |
Fluency |
Problem Solving |
Reasoning |

includes connecting names, numerals and quantities, and partitioning numbers in various ways | Includes counting numbers in sequences readily forward and backwards, locating numbers on a line, and naming the days of the week | includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, and using familiar counting sequences to solve unfamiliar problems and discussing the reasonableness of the answer | includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of data, and explaining patterns that have been created |

### Assessment

Assessment includes:

- Teacher observations – ongoing
- Anecdotal notes – ongoing
- Topical Tests and the Early Years Numeracy Test – 1
^{st}and 3^{rd}Term

### Resources

Mathematics resources referenced regularly include:

- iMaths
- Interactive Australian Curriculum aligned websites such as Scootle and Studyladder

### Benchmarks and Recommendations

By the end of Year 1, it is recommended that students describe number sequences resulting from skip counting by 2s, 5s and 10s. They identify representations of one half. They recognise Australian coins according to their value. Students explain time durations. They describe two-dimensional shapes and three-dimensional objects. Students describe data displays.

Students count to and from 100 and locate numbers on a number line. They carry out simple additions and subtractions using counting strategies. They partition numbers using place value. They continue simple patterns involving numbers and objects. Students order objects based on lengths and capacities using informal units. They tell time to the half hour. They use the language of direction to move from place to place. Students classify outcomes of simple familiar events. They collect data by asking questions and draw simple data displays.

### Year 1 Achievement Standard

By the end of Year 1, students describe number sequences resulting from skip counting by 2s, 5s and 10s. They identify representations of one half. They recognise Australian coins according to their value. Students explain time durations. They describe two-dimensional shapes and three-dimensional objects. Students describe data displays.

Students count to and from 100 and locate numbers on a number line. They carry out simple additions and subtractions using counting strategies. They partition numbers using place value. They continue simple patterns involving numbers and objects. Students order objects based on lengths and capacities using informal units. They tell time to the half hour. They use the language of direction to move from place to place. Students classify outcomes of simple familiar events. They collect data by asking questions and draw simple data displays.

** **

## Year 2

Mathematics at Garden College provides students with essential mathematical skills and knowledge in *Number and Algebra*, *Measurement and Geometry*, and *Statistics and Probability*. It develops the numeracy capabilities that all students need in their personal, work and civic life, and provides the fundamentals on which mathematical specialties and professional applications of mathematics are built.

### Overview

The Mathematics curriculum at Garden College aims to ensure that all students benefit from access to the power of mathematical reasoning and learn to apply mathematical understandings creatively and efficiently. Skills are developed through a range of open ended and interactive activities using concrete materials. This includes games, hands on activities, formal procedures and problem solving tasks. Lower Primary classes use the ‘Early Years Numeracy Program’ in which each individual student’s strengths and weaknesses are assessed and built upon.

### Lesson Structure

During Mathematics sessions, the classroom is set up with enough floor space to allow interactive and engaging tuning in sessions to introduce new topics. The tables are set up in groups to allow flexibility to work both individually and in mixed ability groups, depending on what is required for that lesson. In a typical lesson, students are introduced to the Mathematical concept, actively take part in an opening activity are exposed to focus words for that concept and complete an individual or group task to consolidate the Mathematical skills and understanding relevant to that lesson.

### Scope and Sequences

*In Year 2, there is a focus on developing the following abilities throughout the year:*

Understanding |
Fluency |
Problem Solving |
Reasoning |

includes connecting number calculations with counting sequences, partitioning and combining numbers flexibly, identifying and describing the relationship between addition and subtraction and between multiplication and division | includes counting numbers in sequences readily, 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 | includes formulating problems from authentic situations, making models and using number sentences that represent problem situations, and matching transformations with their original shape | 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 |

### Assessment

Assessment includes:

- Teacher observations – ongoing
- Anecdotal notes – ongoing
- Topical Tests and the Early Years Numeracy Test – 1
^{st}and 3^{rd}Term

### Resources

Mathematics resources referenced regularly include:

- iMaths
- Interactive Australian Curriculum aligned websites such as Scootle and Studyladder

### Benchmarks and Recommendations

By the end of Year 2, it is recommended that students recognise increasing and decreasing number sequences involving 2s, 3s and 5s. They represent multiplication and division by grouping into sets. They associate collections of Australian coins with their value. Students identify the missing element in a number sequence. Students recognise the features of three-dimensional objects. They interpret simple maps of familiar locations. They explain the effects of one-step transformations. Students make sense of collected information.

Students count to and from 1000. They perform simple addition and subtraction calculations using a range of strategies. They divide collections and shapes into halves, quarters and eighths. Students order shapes and objects using informal units. They tell time to the quarter hour and use a calendar to identify the date and the months included in seasons. They draw two- dimensional shapes. They describe outcomes for everyday events. Students collect data from relevant questions to create lists, tables and picture graphs.

### Year 2 Achievement Standard

By the end of Year 2, students recognise increasing and decreasing number sequences involving 2s, 3s and 5s. They represent multiplication and division by grouping into sets. They associate collections of Australian coins with their value. Students identify the missing element in a number sequence. Students recognise the features of three-dimensional objects. They interpret simple maps of familiar locations. They explain the effects of one-step transformations. Students make sense of collected information.

Students count to and from 1000. They perform simple addition and subtraction calculations using a range of strategies. They divide collections and shapes into halves, quarters and eighths. Students order shapes and objects using informal units. They tell time to the quarter hour and use a calendar to identify the date and the months included in seasons. They draw two- dimensional shapes. They describe outcomes for everyday events. Students collect data from relevant questions to create lists, tables and picture graphs.

** **

** **

## Year 3

### Overview

The Mathematics curriculum at Garden College aims to ensure that all students benefit from access to the power of mathematical reasoning and learn to apply mathematical understandings creatively and efficiently. Skills are developed through a range of open ended and interactive activities using concrete materials. This includes games, hands on activities, formal procedures and problem solving tasks. Lower Primary classes use the ‘Early Years Numeracy Program’ in which each individual student’s strengths and weaknesses are assessed and built upon.

### Lesson Structure

### Scope and Sequences

In Year 3, there is a focus on developing the following abilities throughout the year:

Understanding |
Fluency |
Problem Solving |
Reasoning |

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

### Assessment

Assessment includes:

- NAPLAN
- Teacher observations – ongoing
- Anecdotal notes – ongoing
- Topical Tests and Nelson Numeracy Assessments

### Resources

Mathematics resources referenced regularly include:

- iMaths
- Interactive Australian Curriculum aligned websites such as Scootle and Studyladder

### Benchmarks and Recommendations

By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays.

Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical

### Year 3 Achievement Standard

By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real situations. They interpret and compare data displays.

Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables.

## Year 4

### Overview

### Lesson Structure

### Scope and Sequences

In year 4, there is a focus on developing the following abilities throughout the year:

Understanding |
Fluency |
Problem Solving |
Reasoning |

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 | 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 | 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 | 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 |

### Assessment

Assessment includes:

- Teacher observations – ongoing
- Anecdotal notes – ongoing
- Topical Tests and Nelson Numeracy Assessments

### Resources

Mathematics resources referenced regularly include:

- iMaths
- Interactive Australian Curriculum aligned websites such as Scootle and Studyladder

### Benchmarks and Recommendations

By the end of Year 4, students should be able to choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.

Students need to be able to recall multiplication facts to 10 x 10 and related division facts. Students are expected to locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.

### Year 4 Achievement Standard

By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.

Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.

## Year 5

### Overview

### Lesson Structure

During Mathematics sessions, the classroom is set up with enough floor space to allow interactive and engaging tuning in sessions to introduce new topics. In a typical lesson, students are introduced to the Mathematical concept, actively take part in an opening activity are exposed to focus words for that concept and complete an individual or group task to consolidate the Mathematical skills and understanding relevant to that lesson.

### Scope and Sequences

In Year 5, there is a focus on developing the following abilities throughout the year:

Understanding |
Fluency |
Problem Solving |
Reasoning |

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 | 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 | includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans | 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 |

### Assessment

Assessment includes:

- NAPLAN
- Teacher observations – ongoing
- Anecdotal notes – ongoing
- Topical Tests and Nelson Numeracy Assessments

### Resources

Mathematics resources referenced regularly include:

- iMaths
- Interactive Australian Curriculum aligned websites such as Scootle and Studyladder

### Benchmarks and Recommendations

By the end of Year 5, students are expected to be able to solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. Students order decimals and unit fractions and locate them on number lines. They compute with fractions and decimals. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time and use a grid reference system to locate landmarks. They measure and construct different angles.

### Year 5 Achievement Standard

By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets.

Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data.

## Year 6

### Overview

### Lesson Structure

### Scope and Sequences

In year 6, there is a focus on developing the following abilities throughout the year:

Understanding |
Fluency |
Problem Solving |
Reasoning |

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 | 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 | includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays, and finding the size of unknown angles | includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformations of one shape into another, explaining why the actual results of chance experiments may differ from expected results |

### Assessment

Assessment includes:

- Teacher observations – ongoing
- Anecdotal notes – ongoing
- Topical Tests and Nelson Numeracy Assessments

### Resources

Mathematics resources referenced regularly include:

- iMaths
- Interactive Australian Curriculum aligned websites such as Scootle and Studyladder

### Benchmarks and Recommendations

By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number and compute with them. Students make connections between the powers of 10 and the multiplication and division of decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation.

Students are also expected to be able to calculate a simple fraction of a quantity add, subtract and multiply decimals and divide decimals where the result is rational. Students should also be able to locate an ordered pair in any one of the four quadrants on the Cartesian plane.

### Year 6 Achievement Standard

By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They evaluate secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate probabilities using simple fractions, decimals and percentages.