Level 8

MATHEMATICS

Content Descriptors with Learning Goals / Indicators and Proficiencies

Level 8

All Content Strands

Introduction

  What is a Scope and Sequence?

  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

·         Teaching Primary Mathematics George Booker, Denise Bond, Len Sparrow, Paul Swan

·         What We Know About Mathematics Teaching and Learning- MCREL

·         WMR Numeracy Design Space 106126201

·         Acara Scope and Sequence Documents http://www.australiancurriculum.edu.au/Download

·         VCAA – resources http://www.vcaa.vic.edu.au/Pages/foundation10/curriculum/index.aspx

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 8 Number and Algebra

Number and Place Value

Achievement Standard:

By the end of Year 8, students recognise index laws and apply them to whole numbers. Students use efficient mental and written strategies to carry out the four operations with integers.

eBookbox: Working with Numbers

Level 8 Number and Algebra

Real Numbers and Financial Maths

Achievement Standard:

By the end of Level 8, students solve everyday problems involving rates, ratios and percentages. They describe rational and irrational numbers. Students solve problems involving profit and loss.

eBookbox Sets and Real Numbers

Level 8 Number and Algebra

Patterns and Algebra and Linear and Non-Linear Relationships

Achievement Standard:

By the end of Year 8, students make connections between expanding and factorising algebraic expressions. They simplify a variety of algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane.

eBookbox: Linear and Non-Linear Functions

Level 8 Measurement and Geometry

Units of Measurement

Achievement Standard:

By the end of Level 8, students convert between units of measurement for area and volume. They perform calculations to determine perimeter and area of parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles. Students solve problems relating to the volume of prisms. They make sense of time duration in real applications.

eBookbox:    Measurement: Circles and 3D objects

Level 8 Measurement and Geometry

Geometric Reasoning

Achievement Standard:

By the end of Year 8, students identify conditions for the congruence of triangles and deduce the properties of quadrilaterals.

eBookbox: Angles, Shapes and Transformations

Level 8 Statistics and Probability

Chance and Data Representations

Achievement Standard:

By the end of Year 8, students choose appropriate language to describe events and experiments. Students model authentic situations with two-way tables and Venn diagrams. They explain issues related to the collection of data and the effect of outliers on means and medians in that data.

eBookbox:        Sets and Real Numbers

                        Probability, inferences and Conjecture

                        Sets and Logic