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
· Building Numeracy – George Booker
· 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
· Investigate and use the properties of odd and even numbers (ACMNA071)
· Recognise, represent and order numbers to at least tens of thousands (ACMNA072)
· Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)
· Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)
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?
· Explain why a number is odd or even. (U)
· Relate the properties of odd or even to authentic contexts. (R)
· Read, write and order numbers to 10 000’s. (F)
· Rename larger numbers using place value and using other non-place value partitions. (F)
· Partition larger numbers into place value parts to use to assist calculations (Partial sums, Partial products). (R,F)
· Apply a range of mental strategies to solve and/or estimate the result of calculations. (F)
· Understand the number patterns for the multiples of 3 - 9 and use in assisting with determining multiplication facts. (U)
· Know multiplication facts to 10x10. (F)
· Be able to relate all four fact family number facts for multiplication and division to any multiplication or division number sentence. (U)
· Use a range of techniques for multiplication such as the area model and the partitioning of numbers.(F)
Fractions and decimals
· Investigate equivalent fractions used in contexts(ACMNA077)
· Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)
· Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation(ACMNA079)
Money and financial mathematics
· Understand the relationship between ½, 2/4 and 4/8 in authentic contexts and other equivalent fractions. (U)
· Count by ½’s, 1/3’s and 1`/4’s with and without a number line. (F)
· Understand the place value system into the hundredths using real life contexts such as money. (U,R)
· Relate fractions as another way of representing division.
· Relate fractions to decimals through fractions of 100 (1 metre, $1.00, 100 piece block of chocolate). (R)
· Solve addition and subtraction problems using money as a context using strategies such as counting on for addition and counting up for subtraction. (F)
Patterns and algebra
· Explore and describe number patterns resulting from performing multiplication (ACMNA081)
· Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)
· Use equivalent number sentences involving addition and subtraction to find unknown quantities(ACMNA083)
· Understand and apply the multiplication (skip counting) number patterns in solving multiplication and resulting products. (U,F)
· Apply a variety of strategies for multiplication and division including mental strategies for problem solving. (F)
· Rearrange subtraction number sentences into addition and vise versa to solve for unknown quantities. (F)
Measurement and Geometry
Using units of measurement
· Use scaled instruments to measure and compare lengths, masses, capacities and temperatures(ACMMG084)
· Compare objects using familiar metric units of area and volume (ACMMG290)
· Convert between units of time (ACMMG085)
· Use am and pm notation and solve simple time problems (ACMMG086)
· Compare the areas of regular and irregular shapes by informal means (ACMMG087)
· Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies(ACMMG088)
Location and transformation
· Read and interpreting scales on a range of measuring instruments. (U)
· Comparing areas using centimeter grid paper and volume using centicubes and litres in authentic contexts. (R)
· Convert between units of time including hours to minutes and weeks to days and vise versa. (F)
· Apply am and pm appropriately. (R)
· Calculate elapsed time problems using counting on strategies. (F)
· Comparing areas using informal means such as centimeter grid paper or tiles. (R)
· Identifying common two-dimensional shapes that are part of a composite shape by re-creating it from these shapes. (R)
· Use simple scales, legends and directions to interpret information contained in basic maps(ACMMG090)
· Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)
· Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)
Statistics and Probability
· Describe possible everyday events and order their chances of occurring (ACMSP092)
· Identify everyday events where one cannot happen if the other happens (ACMSP093)
· Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)
Data representation and interpretation
· Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)
· Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096)
· Evaluate the effectiveness of different displays in illustrating data features including variability(ACMSP097)
· Understand and use scales and directions in maps. (U)
· Create symmetrical patterns, pictures and shapes. (P)
· Apply Acute, Right and Obtuse correctly to angles in everyday situations. (F)
· Discuss and apply probabilities to everyday situations ranging from Impossible (0) to Certain(1). (R)
· Apply an understanding of mutually exclusive events such as tossing a coin once, which can result in either heads or tails, but not both. (R)
· Apply an understanding of independent events such as the outcome in rolling a die cannot affect the outcome in tossing a coin. (R)
· Choose an effective way to collect and record data for a given investigation. (P)
· Choose appropriate representations for different types of data for interpretation, especially using digital technologies. (P)
· Compare and contrast different displays of data and make appropriate conclusions. (U)
Achievement Standard: By the end of Level 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems. They identify unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.
Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities of everyday events. They construct data displays from given or collected data.