Content Descriptors with Learning Goals / Indicators and Proficiencies
All Content Strands
What is a Scope and 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.
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.
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.
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.
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.
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.
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
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.
All Content Strands and Sub-strands
AusVELS Content Descriptors
Number and Algebra
Number and place value
· Identify and describe factors and multiples of whole numbers and use them to solve problems(ACMNA098)
· Use estimation and rounding to check the reasonableness of answers to calculations(ACMNA099)
· Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)
· Solve problems involving division by a one digit number, including those that result in a remainder(ACMNA101)
· Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)
Fractions and decimals
· Compare and order common unit fractions and locate and represent them on a number line(ACMNA102)
· Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)
· Recognise that the place value system can be extended beyond hundredths (ACMNA104)
· Compare, order and represent decimals(ACMNA105)
Money and financial mathematics
Create simple financial plans (ACMNA106)
Patterns and algebra
· Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)
· Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121)
Measurement and Geometry
Using units of measurement
· Choose appropriate units of measurement for length, area, volume, capacity and mass(ACMMG108)
· Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109)
· Compare 12- and 24-hour time systems and convert between them (ACMMG110)
· Connect three-dimensional objects with their nets and other two-dimensional representations(ACMMG111)
Location and transformation
· Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)
· Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries
· Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original(ACMMG115)
· Estimate, measure and compare angles using degrees. Construct angles using a protractor(ACMMG112)
Statistics and Probability
· List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)
· Recognise that probabilities range from 0 to 1(ACMSP117)
Data representation and interpretation
· Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)
· Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies(ACMSP119)
· Describe and interpret different data sets in context (ACMSP120)
Learning Goals/ Intentions and Proficiencies
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 factors and multiples of whole numbers. (F)
· Know the difference between factors and multiples. (U)
· Identify the patterns involved in identifying factors and multiples. (R)
· Apply a range of mental strategies to estimate the result of calculations and know the usefulness of this. (F)
· Use a range of techniques for multiplication such as the area model and the partitioning of numbers.(F)
· Apply the distributive law and represent arrays to model multiplication. (F,R)
· Solve real life division problems that result in a remainder. (F)
· Use a range of written and mental calculation strategies to solve division problems. (F)
· Interpret the resulting remainder in real contexts. (R)
· Understand, model and order unit fractions. (U)
· Model and therefore add and subtract fractions with similar denominators, such as using the area model for adding and subtracting fractions. (U,R,F)
· Understand the place value system into the thousandths and smaller, including in real life situations such as mass and volume. (R)
· Know how to represent decimals in different ways, such as words, numbers, fractions and models and compare relative sizes of decimals. ((U)
· Develop financial plans for suitable relevant real life situations. (P)
· Find, continue and create number patterns using fractions, decimals and whole numbers. (R)
· Make relevant fact family number sentences for multiplication and division with known and unknown multipliers and quotients. (F)
· Use a variety of strategies in calculating the area and perimeter of rectangles. (F,R)
· Compare 12- and 24-hour time systems and convert between them. (F)
· Make and use nets of a variety of 3D shapes. (R)
· Use 2D representations of 3D shapes. ®
· Understand and use common grids in everyday situations such as maps. (U)
· Describe routes using the language of direction. (U)
· identify and describe the lines and rotational symmetries of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies. (P)
· identify the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies. (R)
· Enlarge 2D figures using manual and digital technologies. (F)
· Identify and measure the angles in a figure. (F)
· Estimate and compare angles in a figure. (R)
· Understand the likelihood of winning simple games of chance by considering the number of possible outcomes. (U)
· Represent the likelihood of winning simple games of chance in fractional form. (F)
· Discuss and apply probabilities to everyday situations ranging from 0 to 1. (R)
· Pose questions regarding and collect and interpret both numerical and categorical data. (R,P)
· Choose appropriate representations for different types of data for interpretation, especially using digital technologies. (R)
· Compare and contrast different sets of data and make appropriate conclusions. (U)
Achievement Standard: By the end of Level 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets.
Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data.