Level 10 /10A

 

Mathematics

Content Descriptors with Learning Goals / Indicators and Proficiencies

Level 10 and 10A

All Content Strands 

Introduction

 

  What is a Scope and Sequence?

 

scope

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.

 

sequence

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 10 Number and Algebra

Money and Financial Mathematics                         

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

Money and Financial Maths

 

·         Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229)

 

 

 

 

 

 

 

 

 

 

 

 

 

Students will:

 

·         Solve equations using substitution (F)

·         Define compound interest using examples (U)

·         Understand the difference between compound interest and simple interest and the context in which each may be used (U)

·         Understand the connection between compound interest and simple interest (U)

·         Calculate compound interest using a formula (F)

·         Transpose equations as required to perform calculations (U)

·         Use digital technologies to calculate compound interest (F)

·         Decide whether compound interest or simple interest applies to a situation (R)

·         Solve authentic problems that involve calculations of compound interest (F, U, R, PS)

 

 

 

Achievement Standard: By the end of Level 10, students recognise the connection between simple and compound interest.

 

 

Level 10 Number and Algebra

Patterns and Algebra

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

 

·         Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230)

 

 

 

 

 

 

 

 

 

 

·         Simplify algebraic products and quotients using index laws (ACMNA231)

 

 

 

 

 

 

·         Apply the four operations to simple algebraic fractions with numerical denominators (ACMNA232)

 

 

 

 

 

·         Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

·         Substitute values into formulas to determine an unknown (ACMNA234)

 

 

 

Students will:

·         Determine factors of numbers and algebraic terms (U)

·         Determine common factors in a group of numbers or algebraic terms (F, U)

·         Recognise the highest common factor in a group of numbers or algebraic terms (F)

·         Recognise the highest common factor in algebraic expressions (U)

·         Factorise an algebraic expression by recognising the highest common factor (number or algebraic term or expression) and dividing each term by this factor (R)

 

·         Simplify number sentences and algebraic expressions using a range of index laws (F)

·         Represent large numbers and small numbers using scientific notation (F)

·         Explain why index notation is used (U)

·         Explain, using indices, the meaning of a negative index (U)

·         Simplify algebraic expressions involving positive and negative indices and applying a range of index laws (U) (R)

 

·         Simplify fractions using highest common factors (U)

·         Add fractions using common denominators (F)

·         Solve a range of linear equations (not fractions) using the four operations (U) (R)

·         Solve linear equations, including those with numerical denominators (U) (R) (PS)

·         Check solutions to linear equations using substitution (R)

 

·         Multiply algebraic terms (U)

·         Expand binomial products (U)

·         Simplify expressions resulting from expansion of binomial products (U)

·         Factorise monic quadratic equations e.g. x2 + 7x + 12 using a variety of strategies (R) (PS)

·         Identify common factors including binomial terms in algebraic expressions (U)

·         Factorise algebraic expressions with four terms by using grouping in pairs (U) (R)

·         Recognise patterns for special binomial products e.g. (a+b)(a-b) and (a+b)2 to expand the products (F) (U)

·         Recognise patterns to factorise special cases of quadratic equations e.g. a2 – b2  (F) (U)

·         Use the area model to factorise quadratic expressions  such as ax2 + bx + c where a = + 1 (U)

·         Factorise quadratic expressions using the method of completing the square (U) (R)

 

·         Write linear equations to represent word problems (U) (R) (PS)

·         Solve word problems using linear equations (R) (PS) (U)

 

Achievement Standard: Students expand binomial expressions and factorise monic quadratic expressions. They find unknown values after substitution into formulas. They perform the four operations with simple algebraic fractions.

 

 

eBookbox: Linear Functions and Modeling, Introducing Quadratic Functions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 10 Number and Algebra

Linear and Non-Linear Relationships

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

Linear and Non-Linear Relationships

 

·         Solve problems involving linear equations, including those derived from formulas (ACMNA235)

 

 

 

 

·         Solve linear inequalities and graph their solutions on a number line (ACMNA236)

 

 

 

 

 

 

 

 

 

·         Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology (ACMNA237)

 

 

 

 

 

 

·         Solve problems involving parallel and perpendicular lines (ACMNA238)

 

 

 

 

 

 

 

 

 

·         Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate (ACMNA239)

 

 

 

 

 

 

 

·         Solve linear equations involving simple algebraic fractions (ACMNA240)

 

 

 

 

 

·         Solve simple quadratic equations using a range of strategies (ACMNA241)

 

 

 

 

Students will:

 

·         Transpose equations (mathematical and other) in order to solve for a particular unknown

 

·         use substitution as a checking strategy (R) (U)

 

 

·         solve linear inequalities (F)

·         graph linear inequalities and their solutions (U)

·         identify word problems that can be represented with simple linear inequalities (U)

·         represent word problems using simple linear inequalities (R)

·         solve word problems through the use of linear inequalities (PS)

 

 

·         solve linear equations (F)

·         solve pairs of simultaneous equations using a variety of techniques e.g. elimination, graphing, substitution (R) (F)

·         identify the pairs of equations in worded problems (U)

·         solve worded problems involving simultaneous equations (R) (PS)


·         recognise parallel and perpendicular lines from their graphical representation (F)

·         identify parallel lines and perpendicular lines using their algebraic representations (F) (U)

·         use geometric software to investigate parallel and perpendicular lines (F)


 

 

 

·         Identify graphical representations of parabolas, exponential functions and circles (F)

·         Match algebraic representations of parabolas, exponential functions and circles to their graphs (U)

·         Describe the effect of changing an algebraic expression on its corresponding graph (U)

·         Identify intercepts, turning points and transformations from an algebraic expression and a graph (F)

·         Sketch graphs of parabolas, exponential functions and circles from their algebraic representation (U)

 

 

 

·         Solve a wide range of linear equations including those with simple algebraic fractions (F) (U)

·         Check solutions to equations using substitution (F)

·         Represent word problems using linear equations (R)

·         Solve word problems using linear equations (PS) (R)

 

 

 

·         Identify non-linear relationships from their algebraic or graphical representations (F)

·         Connect real-life situations to linear and non–linear relationships (U)

·         Solve quadratic equations using a variety of strategies (U)

·         Factorise quadratic expressions using a variety of strategies including completing the square (U)

·         Represent quadratic equations graphically by first solving and/ or factorising (U) (R)

 

 

 

Achievement Standard: Students make the connections between algebraic and graphical representations of relations. They solve simple quadratic equations and pairs of simultaneous equations. They recognise the relationships between parallel and perpendicular lines.

 

 

 

eBookboxes:     Linear Functions and Modeling, Introducing Quadratic Functions

 

 

 

 

 

 

 

 

 

 

 

 

Level 10 Measurement and Geometry 

Using units of measurement

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

 

  • Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (ACMMG242)

 

 

 

 

 

Students will:

 

l  Explain the difference between surface area and volume including the use of square and cubic units(U)

l  Use a variety of strategies to calculate surface area and volume of prisms, cylinders, cones, pyramids, spheres and composite solids (R) (F) (U)

l  Solve worded problems involving surface area and/or volume calculations and/or comparisons using a variety of strategies (F) (U) (R) (PS)

 

 

 

 

Achievement Standard

Students solve surface area and volume problems relating to composite solids.

 

 

eBookbox: In development

 

 

 

 

Level 10 Measurement and Geometry

Geometric Reasoning

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

 

·         Formulate proofs involving congruent triangles and angle properties (ACMMG243)

 

 

 

 

 

·         Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes (ACMMG244)

 

 

Students will:

 

·         Identify a shape by its properties (U)

·         Identify congruent triangles (U)

·         Use congruent triangles and angle properties to prove that a quadrilateral with equal length diagonals bisecting at right angles is a square (R)

 

 

·         present formal geometric arguments to develop skills in mathematical reasoning and present reasoned arguments (proofs) (R) (U)

 

·         use mathematical language and notation, based on congruence and similarity (U)

 

·         apply an understanding of relationships to deduce properties of geometric figures (for example the base angles of an isosceles triangle are equal) (R) (PS) (U)

 

·         distinguish between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent) (U) (R)

 

 

Achievement Standard: Students apply deductive reasoning to proofs and numerical exercises involving plane shapes. They use triangle and angle properties to prove congruence and similarity.

 

 

eBookbox: Transformation, Location and Angle Properties (in development), Describing, constructing and transforming shapes and 3D objects

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 10 Measurement and Geometry 

Pythagoras and Trigonometry                                                                                                                                                                                                                                                                                                                                                                                                                                   

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

 

·         Solve right­angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245)

 

 

 

 

 

Students will:

 

·         Identify a right angled triangle (F)

·         Recall Pythagoras’s Theorem (F)

·         Calculate the lengths of sides of triangles using Pythagoras’s Theorem (F) (U)

·         Apply Pythagoras’s Theorem to worded problems and real life situations to solve problems (PS) (R) (U)

·         Label sides of a triangle according to their location in relation to an angle (e.g. opposite, adjacent ) (F)

·         Recall trigonometric relationships (F)

·         Use trigonometric relationships to calculate lengths of sides and sizes of angles (F)

·         Represent real life situations diagrammatically in order to apply trigonometry to solve a problem (R)

·         Apply trigonometric relationships to real life situations to solve problems (PS) (R)

·         Solve problems involving angles of elevation and depression using Pythagoras’s Theorem and Trigonometry (R) (PS)

 

 

Achievement Standard: Students use trigonometry to calculate unknown angles in right­angled triangles.

eBookboxes: Trigonometric Ratios and Pythagoras Theorem

 

Level 10 Statistics and Probability

Chance

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

·         Describe the results of two­ and three­step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence (ACMSP246)

 

 

 

 

 

 

 

 

·         Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language (ACMSP247)

 

 

Students will:

·         Recognise chance events that are dependent on previous results

·         Recognise chance events that are independent of each other

·         Determine possible outcomes for chance events of two or three steps

·         Determine the probability of an event including those involving two or three steps with and without replacement

·         Recognise that for independent events P(A) x P(B) = P(A and B)

 

·         Use an understanding of statistics and probability to critically analyse, evaluate and explain data presented in a wide range of contexts (e.g. media reports)

 

 

 

Achievement Standard: Students list outcomes for multi­step chance experiments and assign probabilities for these experiments.

 

eBookbox: Probability   

 

 

Level 10 Statistics and Probability

Data representation and Interpretation

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

·         Determine quartiles and interquartile range (ACMSP248)

 

 

 

 

 

 

 

 

 

 

·         Construct and interpret box plots and use them to compare data sets (ACMSP249)

 

 

 

 

 

 

 

 

 

·         Compare shapes of box plots to corresponding histograms and dot plots (ACMSP250)

 

 

 

·         Use scatter plots to investigate and comment on relationships between two continuous variables (ACMSP251)

 

 

 

 

 

·         Investigate and describe bivariate numerical data where the independent variable is time (ACMSP252)

 

 

 

 

 

 

·        
Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (ACMSP253)

 

Students will:

·         determine the minimum and maximum values in a set of data (F)

·         determine the range in a set of data (F)

·         determine the median in a set of data (F)

·         determine the upper and lower quartiles in a set of data (F)

·         determine the interquartile range in a set of data (F)

·         compare data sets numerically (U) (R)

 

 

·         represent data by constructing a box plot (F)

·         compare data sets visually using box plots (U) (R) e.g. the distribution of Aboriginal and Torres Strait Islander people by age with that of the Australian population as a whole

 

·         understanding that box plots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets

 

·         represent the same set of data visually in various ways such as box plots, histograms and dot plots(U)

·         compare the various visual representations of a set of data and explain their features (U)



·         represent data sets as scatter plots (F)

·         use authentic data to construct scatter plots, make comparisons and draw conclusions (R)

 

·         comment on relationships between continuous variables using their scatter plots

·         investigate and describe relationships between variables (F) (U)

·         construct and interpret data displays representing bivariate data over time (F) (U) (R)

·         investigate and describe bivariate data where the independent variable is time (F) (U)


 

·         Use real life data to explain and evaluate statistical reports presented in the media (F) (U) (R)

 

 

·         Investigate data in different ways to make comparisons and draw conclusions (R) (PS) (U) (F)

 

Achievement Standard:

Students compare data sets by referring to the shapes of the various data displays. They describe bivariate data where the independent variable is time. Students describe statistical relationships between two continuous variables. They evaluate statistical reports. They calculate quartiles and inter­quartile ranges.

 

eBookbox: Data (in development)

 

 

 

 

 

 

Level 10A

Year 10A content descriptors indicate optional additional content suitable for development of  student mathematical background in preparation for further study of functions, algebra, and calculus; as well as other additional content related to statistics and trigonometry. Teachers can incorporate a selection of this and other additional content in Year 10 mathematics courses, as applicable for extension and enrichment purposes, and  to prepare students for subsequent study.

 

Level 10A Number and Algebra

Real Numbers

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

·         Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264)

 

 

 

 

 

 

 

 

 

 

·         Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265)

 

Students will:

·         define a rational number (U)

·         define an irrational number (U)

·         simplify expressions involving surds including rationalizing denonminators(U)

·         perform operations (addition, subtraction and multiplication) with surds (F)

·         represent surds with fractional indices (U)

·         perform operations with fractional indices (F)

·         evaluate numeric expressions using index laws (U)

·         simplify algebraic expressions using index laws (U)


·         define a logarithm

·         understand the application of logarithms in real-life situations (U)

·         understand the relationship between exponential and logarithmic expressions (U)

·         understand the logarithmic scale and its use (U)

·         use the laws of logarithms to simplify expressions (R)

 

 

 

Level 10A Number and Algebra

Patterns and Algebra

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

·         Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266)

 

Students will:

 

  • Identify a polynomial expression (F)
  • Perform long division using numerals (F) (U)
  • Perform divisions of polynomials using factors and remainders (F) (U)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 10A Number and Algebra

Linear and Non-Linear Relationships

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

·         Solve simple exponential equations (ACMNA270)

                 

 

 

 

 

 

·         Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations (ACMNA267)

 

 

·         Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation (ACMNA268)

 

 

 

 

 

 

 

 

 

 

·         Factorise monic and non­monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts (ACMNA269)

 

Students will:

 

·         Understand that exponential equations can describe real life data such as population growth (U)

·         Solve exponential equations (R) (U)

·         Solve problems involving multiplying by a constant term (including negative terms) using a range of strategies (PS) (R)

 

 

·         Represent parabolas graphically given their algebraic representation (F)

·         Represent hyperbolas graphically given their algebraic representation (F)

·         Represent circles graphically given their algebraic representation (F)

·         Represent exponential functions graphically given their algebraic representation (F)

·         Transform graphs as a result of changes to their algebraic representations (U)

·         Sketch polynomials efficiently given their algebraic representation (U)

·         Describe the features of a polynomial given its algebraic representation (U)

·         investigate the features of graphs of polynomials using digital technology (F)

 

 

·         apply factorisation of a range of quadratic expressions to solve word problems (PS) (U) (R)

·         apply the solving of quadratic equations using a variety of strategies to solve word problems (PS) (U) (R)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 10A Measurement and Geometry

Using Units of Measurement

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

·         Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271)

 

 

 

 

Students will:

  • Use length, area and volume relationaships to solve problems (F) (R)
  • Calculate simple surface areas and volumes using a variety of strategies (F)
  • Solve problems involving surface area of right pyramids (R) (PS) (U) (F)
  • Solve problems involving surface area of right cones (R) (PS) (U) (F)
  • Solve problems involving surface area of spheres (R) (PS) (U) (F)
  • Solve problems involving surface area of composite solids (R) (PS) (U) (F)
  • Solve problems involving volume of right pyramids (R) (PS) (U) (F)
  • Solve problems involving volume of right cones (R) (PS) (U) (F)
  • Solve problems involving volume of spheres (R) (PS) (U) (F)
  • Solve problems involving volume of composite solids (R) (PS) (U) (F)

 

 

 

 

 

 

 

Level 10A Measurement and Geometry

Geometric Reasoning

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

 

·         Prove and apply angle and chord properties of circles (ACMMG272)

 

 

 

 

Students will:

 

·         Describe a variety of parts of circles (U)

·         Calculate arc lengths (F)

·         Calculate angles and chord lengths using circle theorems (R)

·         Prove angle and chord properties of circles (R)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Level 10A Measurement and Geometry

Pythagoras and Trigonometry

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

·         Establish the sine, cosine and area rules for any triangle and solve related problems (ACMMG273)

 

 

·         Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies (ACMMG274)

 

 

 

 

 

·         Solve simple trigonometric equations (ACMMG275)

 

 

·         Apply Pythagoras’ theorem and trigonometry to solving three­ dimensional problems in right­angled triangles (ACMMG276)

 

 

 

 

Students will:

 

·         apply knowledge of sine, cosine and area rules to authentic problems such as those involving surveying and design (PS) (R) (U) (F)

 

·         understand the relationship of the unit circle to trigonometric functions for angles of any magnitude (U)

·         graph trigonometric functions with and without digital technologies (U)

·         understand the graphs of trigonometric functions (U)

 

·         solve simple trigonometric equations (F)


·         solve problems related to trigonometric functions as periodic e.g. those describing motion (PS) (R)

·         represent real-life problems using right angled triangles where appropriate in three dimensions (R) (U)

·         Solve authentic problems using Pythagoras’s Theorem and Trigonometry (PS) (R) (U) (F)

 

 

 

 

Level 10A Statistics and Probability

Chance

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

 

·         Investigate reports of studies in digital media and elsewhere for information on the planning and implementation of such studies, and the reporting of variability (ACMSP277)

           

 

 

Students will:

 

·         Evaluate media reports that refer to data from a range of contexts (R)

 

·         Evaluate the visual representation of data in media reports (R)

 

·         Evaluate the size and type of samples used for data collection in a variety of contexts (R)

 

·         Discuss appropriate methods of sampling for data collection (U)

·         Generate data by posing appropriate questions and making decisions about sampling a population (U)(R)

 

 

 

 

 

 

 

 

 

 

 

 

Level 10A Statistics and Probability

Data Representation and Interpretation

AusVELS Content Descriptors

Learning Goals/ Intentions and Proficiencies

Essential Learning

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?

 

 

 

·         Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)

                        

 

 

 

 

·         Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation (ACMSP279)

 

 

Students will:

 

·         Calculate the mean for a data set (F)

·         Calculate the standard deviation for a data set (F)

·         Compare data sets using their standard deviations and mean values (R) (U)

·         Discuss data sets by interpreting their mean and standard deviations (R) (U)

 

 

·         Represent bivariate numerical data sets graphically using digital technologies (F)

·         Use straight lines (line of best fit) to represent scatter plots and to describe the relationships between variables (F) (U)

 

 

 

 

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