# Foundation

MATHEMATICS

Content Descriptors with Learning Goals / Indicators and Proficiencies

Foundation Level

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

· 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.

Foundation Sequence

Foundation document Learning goals and proficiencies are sequenced for each content descriptor.

Number and Algebra – Number and Place value descriptors are in sequence for teaching and learning.

Patterns and Algebra descriptor learning goals and proficiencies need to be integrated and developed consistently within Number and linked to Geometry.

Geometry and Measurement – Sorting shape will relate to the pattern and algebra concepts and be ongoing for students throughout the year.

Measurement descriptors and related goals are sequenced by difficulty.

Statistics and Probability – Is not a unit of work, rather the descriptor should be introduced and revisited frequently throughout each term, related to other curriculum areas and other content within mathematics.

Foundation Level

Number and Algebra

AusVELS Content Descriptors

Number and place value

· Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point(ACMNA001)

· Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002)

· Subitise small collections of objects (ACMNA003)

· Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289)

· Represent practical situations to model addition and sharing (ACMNA004)

Patterns and Algebra

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

Learning Goals/ Intentions and Proficiencies

Essential Learning

Students will:

· Know the names of the numbers (F)

· Count orally forwards and backwards (initially to and from 20) (F)

· Counting from any starting point to and beyond 20 (F)

· Understand and connect names, numerals and quantities (U)

· Match the names to the numbers and quantities (F)

· Understand and connecting names, numerals and quantities (U)

· Subitise up to 10 (F)

· Understand and connecting names, numerals and quantities (U)

· Compare larger and smaller of two numbers (R)

· Order 3 or more numbers with explanation (R)

· Fluent in counting numbers in sequences readily, continuing patterns, and comparing objects directly

· Reason by explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparisons

· Real world (authentic) problems modelling addition and sharing (U)

· Represent the problem using pictures, numbers or words (F)

· Convert between pictures, numbers and words (story problems) (PS)

· Problem Solve using materials to model authentic problems, sort objects, use familiar counting

sequences to solve unfamiliar problems, and discussing the reasonableness of the answer

Students will:

· Sort and classify objects with justification of the classification (U)

· Copy patterns with explanation of the repeating elements (F)

· Continue patterns with explanation of the repeating elements (F)

· Create patterns with explanation of the repeating elements (R)

· Be Fluent when counting numbers in sequences readily, continuing patterns, and comparing objects directly (F)

· Reason when explaining comparisons of quantities, creating patterns, and explain processes for indirect comparisons (R)

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?

Achievement Standard

Students make connections between number names, numerals and quantities up to 10. Students count to and from 20 and order small collections.

Foundation Level

Measurement and Geometry

AusVELS Content Descriptors

Using units of measurement

· Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006)

· Compare and order the duration of events using the everyday language of time (ACMMG007

· Connect days of the week to familiar events and actions (ACMMG008)

Shape

· Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment (ACMMG009)

Location and Transformation

· Describe position and movement (ACMMG010)

Learning Goals/ Intentions and Proficiencies

Essential Learning

Students will:

· Compare longer, shorter, same and explain reasoning (R)

· Compare heavier, lighter, same and explain reasoning (R)

· Compare which holds more, less or same and explain reasoning (R)

· Be Fluent in comparing objects directly (F)

· Reason by explaining comparisons of quantities and explaining processes for indirect comparison of measurement (R)

· Know and use the language of time (F)

· Compare and order the duration of events using the language of time (F)

· Be Fluent in sequencing and comparing the duration of events (F)

· Reason by explaining comparisons of time (R)

· Connect days of the week to familiar events and actions (U)

· Understand connections between days of the week and familiar events (U)

Students will:

· Sort and describe squares, circles, triangles, rectangles, spheres and cubes (U)

· Show Understanding by connecting names with objects (U)

· Problem Solve through sorting, describe and classify objects (PS)

· Reason by comparing and naming the shapes and attributes of objects (R)

Students will:

· Know the everyday language of location and direction (F)

· Understand and use the language of location and direction (U)

· Follow and give simple directions using the language of location and direction (PS)

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?

Achievement Standard: 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. They group objects based on common characteristics and sort shapes and objects.

Foundation Level

Statistics and Probability

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

Students will:

· pose questions about themselves and familiar objects and events (U)

· represent responses to questions using simple displays (PS)

· use data displays to answer simple questions (R)

· Problem Solve through modelling authentic problems, using familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer (PS)

Reason by explaining comparisons of quantities (R)

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?

Achievement Standard: Students answer simple questions to collect information.