# Level 1

MATHEMATICS

Content Descriptors with Learning Goals / Indicators and Proficiencies

Level 1

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.

Level 1 Sequence

Level 1 document learning goals and proficiencies are sequenced within each sub-strand by order of conceptual development. Sub-strands are not in difficulty order.

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.

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

All descriptors can be taught independently, the goals and proficiencies for each are in difficulty order.

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

Level 1

Number and Algebra

AusVELS Content Descriptors

Number and place value

· Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012)

· Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013)

· Count collections to 100 by partitioning numbers using place value (ACMNA014)

· Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015)

Fractions and decimals

· Recognise and describe one half as one of two equal parts of a whole. (ACMNA016)

Money and financial mathematics

· Recognise, describe and order Australian coins according to their value (ACMNA017)

Patterns and Algebra

· Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA018)

Learning Goals/ Intentions and Proficiencies

Essential Learning

Students will:

· Count forwards and backwards to and from 100 from any number (F)

· Count orally by 2’s, 5’s, 10’s to and beyond 100 starting at 0 (F)

· Understand and connect names, numerals and quantities

· Order Number sequences (U)

· Use number lines and number grids to count forwards, backwards and by patterns (F)

· Model counting using number lines (F)

· 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

· Bundle ones to create ten and tens to create 100 (F)

· Create, name and order teen numbers as 10 and some more (F)

· understanding partitioning of numbers and the importance of grouping in tens

· understanding two digit numbers as comprised of tens and ones/units

· model with materials, number lines and number grids addition and subtraction within and including 10 (F)

· Model with materials, number lines and number grids addition and subtractions within and including 20 (F)

· Discuss and compare strategies for addition and subtraction (R)

· develop a range of mental strategies for addition and subtraction problems (F)

· Real world (authentic) problems modelling addition and subtraction (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

· Model the partitioning of one whole into two equal parts (U)

· Model the partitioning of a group into two equal parts (U)

· Name equal parts as halves, one equal part as one half (R)

· sharing a collection of readily available materials into two equal portions (F)

· Show reasoning by splitting an object into two equal pieces and describing how the pieces are equal

· Recognise Australian coins according to their value (F)

· Order Australian coins according to their value (F)

· Describe and order Australian coins according to their value (R)

· showing that coins are different in other countries by comparing Asian coins to Australian coins (U)

· Understanding that the value of Australian coins is not related to size

· Show reasoning by describing the features of coins that make it possible to identify them

· Identify and say patterns 1’s forwards and backwards from any point to 100 (F)

· Identify and say patterns 2’s to 50, 5’s to 100 and 10’s to and beyond 100 (F)

· Identify and say patterns with explanation of the repeating elements (R)

· Investigate and model patterns on a number grid and a number line as ‘skip counting’ (PS)

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

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

Reason when explaining comparisons of quantities, creating patterns, and explain processes for indirect comparisons

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 describe number sequences resulting from skip counting by 2s, 5s and 10s. They identify representations of one half. 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. They recognise Australian coins according to their value.

Level 1

Measurement and Geometry

AusVELS Content Descriptors

Using units of measurement

· Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019)

· Tell time to the half hour (ACMMG020)

· Describe duration using months, weeks, days and hours (ACMMG021)

Shape

· Recognise and classify familiar two dimensional shapes and three dimensional objects using obvious features (ACMMG022)

Location and transformation

· Give and follow directions to familiar locations (ACMMG023)

Learning Goals/ Intentions and Proficiencies

Essential Learning

Students will:

· Use uniform informal units to compare longer, shorter, same and explain reasoning (R)

· Use uniform informal units to compare heavier, lighter, same and explain reasoning (R)

· Use uniform informal units to compare which holds more, less or same and explain reasoning (R)

· Understand that in order to compare objects, the unit of measurement must be the same size (U)

· Be Fluent in comparing objects directly (F)

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

· To know and use the language of time (F)

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

· read time on analogue and digital clocks and observing the characteristics of half hour times (F)

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

· Reason by explaining comparisons of time (R)

· Connect months, weeks and days to familiar events and actions (U)

· Describe durations using months, weeks, days and hours (U)

· Understand connections between days, weeks and months

· Understand and order relative size of months, weeks, days and hours

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

· Connect shape names to everyday objects (F)

· Explore geometric features and describe shapes and objects using everyday words such as 'corners', 'edges' and 'faces' (R)

· Show Understanding by connecting names with objects

· Problem Solve through sorting, describe and classify objects by corners, edges and faces

· Reason by comparing and naming the shapes and attributes of objects

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

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

· Understand the language of location and direction (U)

· Understand that people need to give and follow directions to and from a place, and that this involves turns, direction and distance (U)

Understand the meaning and importance of words such as ‘clockwise’, ‘anticlockwise’, ‘forward’ and ‘under’ when giving and following directions interpreting and following directions around familiar locations (U)

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 recognise Australian coins according to their value. Students explain time durations. They describe two dimensional shapes and three dimensional 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.

Level 1

Statistics and Probability

AusVELS Content Descriptors

Chance

· Identify outcomes of familiar events involving chance anddescribe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024)

Data representation and interpretation

· Choose simple questions and gather responses (ACMSP262)

· Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays (ACMSP263)

Learning Goals/ Intentions and Proficiencies

Essential Learning

Students will:

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

· identify outcomes of familiar events involving chance, describing them using everyday language (R)

· represent responses to questions using simple displays such as a probability line (F)

· 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)

· use data displays to answer simple questions, developing the language of least, most, same amount (U)

· Use tally marks to record (F)

· determinine which questions will gather appropriate responses for a simple investigation (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)

· Understand that one object or drawing represents on data value (U)

· Explain the display and what it tells us about the data (U)

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?

Compares categories using language such as greatest or least (R

Achievement Standard: Students describe data displays. Students classify outcomes of simple familiar events. They collect data by asking questions and draw simple data displays.