# Level 3

MATHEMATICS

Content Descriptors with Learning Goals / Indicators and Proficiencies

Level 3

All Content Strands

Introduction

What is a Scope and Sequence?

scope

sequence

The breadth and depth of content to be covered in a curriculum at any one time (e.g. week, term, year, over a student’s school life.) All that you do in a given period.

The order in which content is presented to learners over time. The order in which you do it.

Together a scope and sequence of learning bring order to the delivery of content, supporting the maximising of student learning and offering sustained opportunities for learning. Without a considered scope and sequence there is the risk of ad hoc content delivery and the missing of significant learning.

http://activated.act.edu.au/ectl/design/scope_and_sequence.htm

Why does a school need a scope and sequence?

An agreed Scope and Sequence for a Learning Area, provides a sound basis for a school being able to offer a guaranteed and viable curriculum by addressing gaps in students’ leaning and eliminating unnecessary repetition. A shared Scope and Sequence within a school enables teachers to have clarity about the knowledge, skills and dispositions that students will acquire in their learning and what they need to learn next. A Scope and Sequence supports teachers with effective unit and lesson planning and enables teachers to maintain a developmental focus on student learning as students progress through the school.

The Mathematics Scope and Sequence developed by WMR

This document has been developed to support schools with the transition to AusVELS Mathematics for 2013. While it provides examples of yearly overviews and learning sequences based on the content descriptors in the Australian Curriculum, it is not a complete curriculum. Each individual school can use the documents as a basis for developing a guaranteed and viable curriculum that caters for the needs of their school community.

Levels Foundation to 10A each include a set of learning goals/ intentions for each content sub-strand intended to provide a user friendly guide to the essential learnings around which teachers and teams could base their unit and lesson development.

Proficiency strands are listed next to each learning goal / intention as a guide only and teachers / teams are encouraged to consider all proficiencies equally whilst planning units and lessons. Where a particular proficiency is not listed for a content sub-strand teachers and teams should endeavour to contextualise the learning goals to address these proficiencies. Please note the following:

Sequence of teaching

The learning goals/intentions are listed adjacent to the content descriptions to assist teachers when developing a teaching program. They are not necessarily in the order to be taught – teachers /teams will make their own decisions regarding this. The third column has been included to assist teams to develop ideas for unit planning.

A sample Scope and Sequence Overview is also provided for each of the year levels from F to 10A. The number of weeks given to each unit in the overview acts as a guide and the total number of weeks allows for the many interruptions in a typical school year.

Links between the Learning Goals/Intentions and the proficiency strands

(a) The Learning Goals/Intentions have been identified to relate most closely to one of the four proficiency strands (shown in 3 below). This identification is shown in brackets at the end of each Learning Goal/Intention:

· Understanding is identified by (U)

· Fluency is identified by (F)

· Problem Solving is identified by (PS)

· Reasoning is identified by (R)

(b) In this document there are less Problem Solving and Reasoning proficiency strands identified than those for Understanding and Fluency. Should teachers wish to include more of these proficiencies in their curriculum, they are encouraged to emphasise them when teaching, and to develop appropriate learning tasks.

Proficiency strands

The proficiency strands describe the actions in which students can engage when learning and using the content. While not all proficiency strands apply to every content description, they indicate the breadth of mathematical actions that teachers can emphasise. The proficiencies listed next to each learning goal / intention are examples of how students might achieve the goal or what they have demonstrated by achieving the goal but are dependent on the context in which the learning takes place.

Understanding

Students build a robust knowledge of adaptable and transferable mathematical concepts. They make connections between related concepts and progressively apply the familiar to develop new ideas. They develop an understanding of the relationship between the ‘why’ and the ‘how’ of mathematics. Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and when they interpret mathematical information.

Fluency

Students develop skills in choosing appropriate procedures, carrying out procedures flexibly, accurately, efficiently and appropriately, and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognise robust ways of answering questions, when they choose appropriate methods and approximations, when they recall definitions and regularly use facts, and when they can manipulate expressions and equations to find solutions.

Problem Solving

Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.

Reasoning

Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false and when they compare and contrast related ideas and explain their choices.

Useful references for teams and teachers to use when planning units of work and lessons include the following:

· Ultranet Design Space – DEECD Big Ideas in Number Maps - 128428217

· Ultranet design Space – Mathematics eBookboxes - 66512121

· Teaching Mathematics Foundations to Middle Years

Dianne Siemon, Kim Beswick, Kathy Brady, Julie Clark, Rhonda Faragher and Elizabeth Warren

· Mathematics Domain Page DEECD

· Building Numeracy – George Booker

# · What We Know About Mathematics Teaching and Learning- MCREL

Please note: Teachers will be required to join each Ultranet design space before being able to access the resource. The number associated with each space should be entered into the search box in ‘available design spaces’ in order to find the space.

Level 3

All Content Strands and Sub-strands

AusVELS Content Descriptors

Number and Algebra

Number and place value

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

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

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

Learning Goals/ Intentions and Proficiencies

Essential Learning

Students will:

Unit Development Ideas

How is the essential learning developed into units of work? How do students make connections between the learning goals and those included in other content strands or sub-strands? How do we ensure students become proficient in fluency, understanding, reasoning and problem solving?

· Explain if and why a number is odd or even. (U)

· Read, write and order numbers to 10 000. (F)

· Rename larger numbers using place value and using other non place value partitions. (F)

· Partition larger numbers into place value parts to use to assist calculations (Partial sums, Partial products). (R,F)

· Recognise and explain the connection between addition and subtraction

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

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

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

· Understand subtraction is the inverse of addition (U)

· Be able to write addition and subtraction fact family number sentences for a set of numbers. (F)

· Know addition facts and strategies such as compliments to ten, doubles and near doubles and counting by tens and ones forwards and backwards. (F)

· Apply a range of mental and written strategies to solve the result of addition and subtraction calculations such as partial sums and compensation. (U,F)

· Know multiplication facts for 2’s, 3’s, 5’s and 10’s. (F)

· Relate skip counting to multiplication to division. (U)

· Use a range of strategies for multiplication such as the area model and the partitioning of numbers.(U,F)

Fractions and decimals

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

Money and financial mathematics

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

Patterns and algebra

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

Measurement and Geometry

Using units of measurement

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

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

Shape

· Understand and model unit fractions. Find and relate unit fractions of a group through sharing (such as shared between (÷) 3 is 1/3)

· Count by ½’s, 1/3’s and 1`/4’s to 1. (F)

· Partition money amounts using place value denominations ($100’s, $10’s, $1’s) and also with other denomination partitions.(F)

· Calculate change using strategies such as counting up. (F)

· Solve addition and subtraction problems using money as a context using strategies such as counting on for addition and counting up for subtraction. (F)

· Understand and apply skip counting number patterns in solving problems involving repeated addition and repeated subtraction (U,F)

Students will:

· Recognise the importance of using common units of measurement. (R)

· Recognise and use centimetres and metres, grams and kilograms, and millilitres and litres. (F)

· Tell and write time to the minute. (F)

· Understand, use and order units of time. (U,F)

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

Location and transformation

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

· Identify symmetry in the environment (ACMMG066)

Geometric reasoning

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

Statistics and Probability

Chance

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

Data representation and interpretation

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

· 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)

· Interpret and compare data displays (ACMSP070)

· Use nets to make three-dimensional objects and identify faces, edges and vertices. (P)

· Create simple maps. (P)

· Use simple maps such as theme park or zoo maps. (U)

· Identify symmetrical patterns, pictures and shapes. (P)

· Identify comparative sizes of angles in everyday situations including the hands on a clock. (R)

Students will:

· Conduct repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials. (F,R)

· Collect and record categorical data to answer an identified question. (R)

· Identify efficient ways to record data, and representing and reporting the results of investigations including using digital technologies. (P)

· Compare and contrast between displays of data and make appropriate conclusions. (U)

Achievement Standard: By the end of Level 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.