Year 10/10a unit overview � Australian Curriculum: Mathematics - DOC

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					Year 10/10a unit overview — Australian Curriculum: Mathematics                                                                                         DRAFT
School name                               Unit title                                                                           Duration of unit
Our School                                Mathematics and sport                                                                10 weeks

Unit outline
Students develop an understanding of the mathematics that can be applied in sports, including: statistics and probability, measurement and geometry, and ratio
and proportion. Students apply mathematical reasoning and problem solving to claims that are made about sport. They analyse scenarios in sports such as
orienteering, archery, basketball, netball and darts.
The big ideas of the unit include:
 real-world problems can be analysed through statistics, algebraic processes and modelling
 the application of mathematics can generate an accurate assessment of a situation that is often counter to our initial intuition.
Inquiry questions for the unit include:
 A feature of sports commentary is frequent reference to data and statistics. Do the commentators make mathematically valid claims?
 When testing a claim using data and mathematical techniques, how can data and probability be applied?
 How can models be used to assist in solving problems?
 What elements of trigonometry and geometry could be helpful in a sporting context, e.g. planning tactics in orienteering?
 How can we decide who the most valuable player (MVP) in a team is in different sports? Why is identifying this person tactically important?

                                                                                                                     Queensland Studies Authority February 2012 DRAFT   |   1
        Identify curriculum
        Content descriptions to be taught                                                                                                General capabilities and
        Number and Algebra                  Measurement and Geometry                   Statistics and Probability                        cross-curriculum priorities

        Patterns and algebra                Geometric reasoning                        Chance
        Substitute values into              Apply logical reasoning, including the     Describe the results of two- and three-step
                                                                                                                                          Create print, visual and digital
        formulas to determine an            use of congruence and similarity, to       chance experiments, both with and without
        unknown                             proofs and numerical exercises             replacements, assign probabilities to outcomes
        Linear and non-linear               involving plane shapes                     and determine probabilities of events.             Write reports, including evaluation
        relationships                       Pythagoras and trigonometry                Investigate the concept of independence             and conclusion.

        Solve problems involving            Solve right-angled triangle problems       Use the language of ‘if...then, ‘given’, ‘of’,     Communicate using mathematical
        linear equations, including         including those involving direction and    ‘knowing that’ to investigate conditional           terminology.
        those derived from formulas         angles of elevation and depression         statements and identify common mistakes in
                                                                                       interpreting such language                             Numeracy
        Real numbers (10a)                  Pythagoras and trigonometry (10a)
                                                                                       Data representation and interpretation             Understand data in real-world
        Define rational and irrational      Establish the sine, cosine and area                                                            applications.
        numbers and perform                 rules for any triangle and solve related   Use scatter plots to investigate and comment
        operations with surds and           problems                                   on relationships between two continuous
                                                                                                                                              ICT competence
        fractional indices                                                             variables
                                            Use the unit circle to define                                                                 Use spreadsheets and graphing
                                            trigonometric functions, and graph         Investigate and describe bivariate numerical
                                                                                                                                           software to model real-world data.
                                            them with and without the use of digital   data where the independent variable is time
                                            technologies                               Evaluate statistical reports in the media and      Use interactive manipulatives to
                                                                                       other places by linking claims to displays,         generate experimental data.
                                            Solve simple trigonometric equations
                                                                                       statistics and representative data                     Critical and creative thinking
                                            Apply Pythagoras’ theorem and
                                                                                       Chance (10a)
                                            trigonometry to solving three-                                                                Evaluate approaches to solving
                                            dimensional problems in right-angled       Investigate reports of studies in digital media     problems.
                                            triangles                                  and elsewhere for information on the planning
                                                                                                                                          Design an investigation.
                                                                                       and implementation of such studies, and the
                                                                                       reporting of variability                               Ethical behaviour
                                                                                       Data representation and interpretation (10a)
                                                                                                                                          Evaluate media reports that refer to
                                                                                       Use information technologies to investigate         data.
                                                                                       bivariate numerical data sets. Where
                                                                                       appropriate use a straight line to describe the
                                                                                       relationship allowing for variation

2   |    Year 10/10a unit overview   Australian Curriculum: Mathematics
Identify curriculum
In this unit:
Understanding includes describing patterns in uses of indices, applying the four operations to algebraic fractions,
finding unknowns in formulas after substitution, making the connection between algebraic and graphical representations
of relations, connecting simple and compound interest in financial contexts and determining probabilities of multiple
Fluency includes formulating proofs using congruent triangles and angle properties, factorising and expanding algebraic
expressions, using a range of strategies to solve equations and using calculations to investigate the shape of data sets
Problem Solving includes calculating the surface area and volume of a diverse range of prisms, finding unknown
lengths and angles using applications of trigonometry, using algebraic and graphical techniques to find solutions to
simultaneous equations and inequalities, and investigating independence of events and their probabilities
Reasoning includes formulating geometric proofs involving congruence and similarity, interpreting and evaluating media
statements and interpreting and comparing data sets

                                                                                                                       Queensland Studies Authority February 2012 DRAFT   |   3
        Relevant prior curriculum                                                           Curriculum working towards
        In the Australian Curriculum: Mathematics at Year 9                                 In the Mathematics A senior syllabus
        This unit builds upon students’ understanding of the basic concepts of               elements of applied geometry
        probability and data representation:
                                                                                             data collection and presentation
         linear and non-linear relationships                                               In the Mathematics B senior syllabus
         Pythagoras and trigonometry                                                        introduction to functions
         assigning probabilities                                                            periodic functions and applications
         collecting and displaying data.                                                    applied statistical analysis.
                                                                                            This unit develops students’ familiarity with the assessment required in senior
                                                                                             modelling and problem solving tasks
                                                                                             reports
                                                                                             supervised tests.
        Bridging content
        The Essential Learnings, by the end of Year 9, provide a good foundation to this unit. In Year 9, students have engaged with theoretical and experimental
        probability, and have gathered, displayed and analysed data. They have modelled, interpreted and evaluated algebraic relationships, and related linear and non-
        linear equations to real-world situations.
        The application of technology (such as spreadsheets) to create mathematical models will not necessarily be something students have experience with, and may
        require modelling.
        Achievement standard
        By the end of Year 10, students expand and factorise monic quadratic expressions and find unknown values after substitution into formulas. They represent
        relations on the Cartesian plane and solve linear and quadratic equations. They make connections between simple and compound interest. Students list
        outcomes, assign and determine probabilities for chance experiments and investigate independent events. They construct box-plots and compare data sets.
        Students investigate and describe statistical relationships and evaluate statistical reports. Students solve problems involving volume and surface area of a range
        of prisms and apply reasoning to proofs and numerical exercises. They apply trigonometry to solve right-angled triangle problems.

4   |    Year 10/10a unit overview   Australian Curriculum: Mathematics
Links to other learning areas
Links to Australian Curriculum: Science at Year 10:
Science understanding — Physical science
 The motion of objects can be described and predicted using the laws of physics
Science as a human endeavour — Use and influence of science
 People can use scientific knowledge to evaluate whether they should accept claims, explanations or predictions.

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        Assessment                                                                                                         Make judgments
        Describe the assessment                                                                          Assessment date   Attributes of student work that demonstrates
                                                                                                                           the achievement standard include:
        Report                                                                                           Week 4
                                                                                                                            describing patterns in uses of indices
        Students focus on the use of probability and statistics in real-world research. They gather
        primary data (in small groups) and analyse data and write a conclusion (individual). Students:                      making connections between algebraic
                                                                                                                             and graphical representations of relations
         conduct an investigation into “hot streaks” in sports such as in basketball and netball
                                                                                                                            identifing of outcomes for chance
         demonstrate an understanding of the difference between dependent and independent                                   experiments
                                                                                                                            using a range of strategies to solve
         collect primary data (small groups)                                                                                equations
         write a data analysis and conclusion (200–300 words — individual response)
                                                                                                                            applying trigonometry to find unknown
         peer- and self-assess their data analysis and conclusion.                                                          lengths and angles
        Extended modelling and problem-solving task                                                      Week 7             investigating independent events and
                                                                                                                             their probabilities
        Students respond to a specific sporting scenario by modelling it using mathematics. Students
        have the opportunity to apply mathematics to real-world applications, and provide significant                       interpreting and evaluating media
        evidence towards problem solving and reasoning.                                                                      statements using statistical argument
         Year 10 students model two scenarios in a chosen sport mathematically,                                            interpreting and comparing data sets.
          e.g. find perceived displacement between goalposts from various positions on a football
          field; find the quickest route to take in orienteering.
         Year 10a students model one of the above scenarios and also look at the probabilities of
          hitting the various scoring areas of a dart board. They consider the areas of the sample
          space, from 1 to triple 20, in their analysis.
        Students complete a report containing diagrams, calculations and a discussion (200–300
        words for each scenario).
        Supervised test                                                                                  End of term
        The test includes:
         a short-response items that focus on Understanding and Fluency
         an extended-response with a focus on Problem solving
         a response to stimulus (unseen) that focuses on Reasoning
         an individual response under supervised conditions.

6   |    Year 10/10a unit overview   Australian Curriculum: Mathematics
Teaching and learning                                                                        Supportive learning environment
Teaching strategies and learning experiences                                                 Adjustments for needs of learners        Resources
Probability, statistics and algebra                                                          Section 6 of the Disability Standards     Relevant textbook
                                                                                             for Education (The Standards for
Students learn about and explore the concepts of dependent and independent events                                                      Worksheets
through practical exercises and problems. They evaluate statistical reports in the           Curriculum Development,
                                                                                             Accreditation and Delivery) state that    Optional: interactive
media. In particular, students explore cases where a misunderstanding of statistics is
                                                                                             education providers, including class       whiteboard with access to
                                                                                             teachers, must take reasonable             mathematics programs and
Use relevant questions from textbooks, worksheets and other stimulus, as                     steps to ensure a course/program is        websites/images
appropriate.                                                                                 designed to allow any student to          Coordination of primary data
 Introduce students to independent events by discussing the following statement:            participate and experience success         collection for report will require
  “I’ve just tossed 5 heads in a row. Surely the next toss is more likely to be a tail!”     in learning.                               coordination with HPE
 Discuss the importance of appropriate sample sizes for chance experiments.                 The Disability Standards for               department for access to
                                                                                             Education 2005 (Cwlth) is available        basketball and netball courts
 Construct a glossary of relevant terms, including: experimental probability,               from: <> select               and equipment (or other
  theoretical probability, trial, favourable outcome, event, relative frequency,                                                        sports)
                                                                                             Human rights and anti-discrimination
  expected frequency, replacement, independence, scatter plot, sample space,
                                                                                             > Disability standards for education.     Computer access required for
  bivariate, tree diagram.
                                                                                                                                        data analysis
 Plan and conduct chance experiments.                                                                                                  (spreadsheet) and report
 Tabulate results.                                                                                                                     writing (word processing)
 Substitute values into formulas.
 Use sample spaces including using tables and tree diagrams to determine the
  probability of compound events.
 Transfer word problems into probability notation, including n(event), P(event).
 Discuss and investigate how commentators in various sports cite statistics. How
  accurate is their interpretation of the data? What is the significance of the statistics
  they cite?
 Investigate the myth of Australian batters getting out on 87 (the unlucky number)
  in cricket.
 Research and compare the sporting achievements of three or more champion
  athletes and decide who is the greatest based on their statistics
 Begin research on the “hot streak”. (This investigation requires scaffolding and
  monitoring of student understanding.)

                                                                                                                       Queensland Studies Authority February 2012 DRAFT      |   7
        Teaching and learning                                                                 Supportive learning environment
        Teaching strategies and learning experiences                                          Adjustments for needs of learners   Resources
         Research the “clustering myth”, including a class discussion of the concepts
          involved in evaluating a “hot streak” mathematically.
        Measurement, geometry and algebra
        Students develop their understanding of the logical reasoning involved in solving
        geometric problems and right angles.
        Students use algebra to model real-world situations, and extend their understanding
        of trigonometry. Students apply this learning to exploring the physical aspects of
        Use relevant questions from textbooks, worksheets and other stimulus, as
         Explore the congruence and similarity of plane shapes using scale drawings.
         Investigate Thales’ use of similar triangles to find the height the Pyramids.
         Review trigonometry and Pythagoras from Year 9, e.g. the terms opposite,
          adjacent, hypotenuse, and the trigonometric ratios.
         Solve problems involving bearings (direction) and elevation.
         Solve linear equations using graph paper and technology (graphing calculators/
          spread sheet).
         Use technology to determine the acceleration of an object falling freely using a
          linear regression (can be done theoretically or using primary data from ticker
          timers/strobe light/high speed camera).
        Implement Extended modelling and problem solving task
        Revise for supervised test

8   |    Year 10/10a unit overview   Australian Curriculum: Mathematics
Use feedback
Ways to monitor learning      Teachers collaboratively plan the teaching, learning and assessment to meet the needs of all learners.
and assessment                Teachers mark student responses individually, then select samples representative of the A–E qualities for moderation. Teachers
                              moderate samples to ensure consistency of judgments.
Feedback to students          Teachers plan opportunities through the teaching strategies and learning experiences of the unit. Teachers provide ongoing
                              feedback and encouragement to students on their strengths and areas for improvement. Through particular learning experiences
                              students can reflect on and discuss with their teachers and peers what they are able to do well and what they need to do to
                              improve, e.g. transfer word problems into probability notation, including n(event), P(event).
Reflection on the unit plan   At the conclusion of the unit, all teachers involved in the planning, teaching, learning and assessment come together to reflect on
                              the successes and challenges of the unit. They prepare, share and discuss their personal reflections through answers to the
                              following questions:
                               What worked well in this unit?
                               What was a stumbling block?
                               How would you refine it?
                               What trends and gaps in learning have you identified?
                               How will you build on these learning experiences next term and beyond?

                                                                                                                  Queensland Studies Authority February 2012 DRAFT   |   9

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