# Level 6

Mathematics

Content Descriptors with Learning Goals / Indicators and Proficiencies

Level 6

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 6

All Content Strands and Sub-strands

AusVELS Content Descriptors

Number and Algebra

Number and place value

1.

· Apply efficient Identify and describe properties of prime, composite, square and triangular numbers(ACMNA122)

· Select and mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

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

Fractions and decimals

1.

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

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

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

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

· 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)

· Multiply and divide decimals by powers of 10(ACMNA130)

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

Money and financial mathematics

1.

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

2.

Patterns and algebra

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

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

Measurement and Geometry

Using units of measurement

· Connect decimal representations to the metric system (ACMMG135)

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

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

· Connect volume and capacity and their units of measurement (ACMMG138)

· Interpret and use timetables (ACMMG139)

Shape

1.

Construct simple prisms and pyramids (ACMMG140)

Location and transformation

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

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

Geometric reasoning

· 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)

Statistics and Probability

Chance

· Describe probabilities using fractions, decimals and percentages (ACMSP144)

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

· Compare observed frequencies across experiments with expected frequencies(ACMSP146)

·

Data representation and interpretation

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

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

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?

· Identify and describe properties of prime, composite, square and triangular numbers. (F)

· Use these properties to create patterns and solve problems. (R)

· Select between and use a variety of written, mental and digital calculation strategies involving the four operations to solve a variety of everyday problems. (F)

· Become familiar with and use the range of integers. (F)

· Use a number line to solve addition and subtraction problems using positive and negative integers. (F)

· Apply integers in everyday situations. (F)

· Understand, model and order fractions with related denominators. (U)

· Model and therefore add and subtract fractions with related denominators, such as using the area model for adding and subtracting fractions. (U,F)

· Find fractional quantities where a group is the whole. (F)

· Apply a variety of strategies to add and subtract decimals. (F)

· Estimate the solution to addition and subtraction problems involving decimals. (R)

· Understand and use as variety of strategies to multiply and divide problems involving decimals in everyday situations (U,F)

· Understand how multiplying and dividing decimals by powers of ten affects the initial decimal. (U)

· Know how to represent decimals in different ways, such as words, numbers, fractions and models and compare relative sizes of decimals. (R)

· Use the understanding of percentages to calculate the sale price of items in everyday situations. (U,F)

· Find, continue and create number patterns using fractions, decimals and whole numbers. (R)

· Find and describe the rule used to create a pattern. (R)

· Understand and apply the rules for completing multiple operations within the same number sentence including brackets (BODMAS,BOMDAS,PEMDAS,etc.) (F)

Students will:

· Understand the connection between the Base 10 System of numbers and the Decimal system of measurement. (U)

· Convert between different decimal units. (F)

· Be able to use different units of measurement in appropriate contexts to solve everyday problems involving length and area. (P)

· Use volume and capacity in everyday situations. (F)

· Use common timetables such as public transport. (F)

· Use a variety of materials to construct and deconstruct prisms and pyramids. (P)

· identify the effects of a combination of transformations by flipping, sliding and turning two-dimensional shapes. (R)

· Use and relate the Cartesian Plane to everyday situations. (U)

· Identify the four quadrants of a Cartesian plane and plot points into all four quadrants. (F)

· Identify, define and measure right, acute, obtuse, straight and reflex angles. (F)

· Identify vertically opposite angles and use to determine unknown angles such as intersecting roads. (U,R)

Students will:

· Understand use and convert between probabilities using fractions, decimals and percentages. (U,F)

· conduct trials of chance and identify the variation between trials. (U,F)

· understand why larger numbers of trials result in more accurate probabilities. (U)

· compare observed and expected probabilities. (R)

· select and use a range of appropriate data representations for comparison between sets of similar data. (U,F)

· discuss and interpret data found in everyday situations. (R)

Achievement Standard: By the end of Level 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.