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ASSESSMENT TASK: 2

EDSE11006 Middle Phase PedagogyUnit of work and justification

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Contents1. Student Profiles.........................................................................................................................5

2. Unit of Work.............................................................................................................................7

3. Evaluation................................................................................................................................46

4. Appendix – Attitudes, Perceptions and Habits of Mind strategies.............................................49

4.1. Appendix 4.1: Lesson 1 - DOL 1 & 5.................................................................................49

4.2. Appendix 4.2: Lesson 2 – DOL 1 & 5.................................................................................50








4.10. Appendix 4.10: Lesson 10 – DOL 1 & 5.........................................................................58






5. Appendix – Learning Materials.................................................................................................64

5.1. Appendix 5.1: Why learn Mathematics............................................................................64

5.2. Appendix 5.2: Advantages of learning about money and financial mathematics............65

5.3. Appendix 5.3: Characteristics of financial mathematics (concept map)..........................66

5.4. Appendix 5.4: KWHL table...............................................................................................67

5.5. Appendix 5.5: Money and financial mathematics vocabulary..........................................68

5.6. Appendix 5.6: Financial mathematics terminology and word walls.................................69

5.7. Appendix 5.7: Simple interest formula sheet...................................................................71

5.8. Appendix 5.8 Trigonometric concepts.............................................................................71

5.9. Appendix 5.9 Tips to solve word problems efficiently.....................................................71

5.10. Appendix 5.10: Advantages of using graphic organisers..............................................72

5.11. Appendix 5.11: Advantages of note-taking for academic success and beyond............73

5.12. Appendix 5.12: Do’s and Don’ts for effective Note-taking...........................................74

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5.13. Appendix 5.13: How can someone become richer than Bill Gates?.............................75

5.14. Appendix 5.14: Benefits of learning Trigonometry......................................................76

5.15. Appendix 5.15: Benefits of learning Statistics..............................................................78

6. Appendix – Instructional Design and Teaching Strategies.........................................................79

6.1. Appendix 6.1: Four Resource Model................................................................................79

6.2. Appendix 6.2: Newman’s 5 prompts................................................................................80

6.3. Appendix 6.3: T.H.I.E.V.E.S pre-reading strategy.............................................................80

6.4. Appendix 6.4: Promoting literacy proficiency in ADHD and Autism students..................81

6.5. Appendix 6.5: Promoting numeracy proficiency in ADHD and Autism students..............82

6.6. Appendix 6.6: Encouraging literacy in boys.....................................................................83

6.7. Appendix 6.7: Building Reading Comprehension skills.....................................................84

6.8. Appendix 6.8: Problem-based learning strategy..............................................................85

6.9. Appendix 6.9: Jigsaw........................................................................................................86

6.10. Appendix 6.10: Problem Solving strategy (DOL 4)........................................................87

6.11. Appendix 6.11: Decision Making strategy (DOL 4).......................................................89

6.12. Appendix 6.12: Cooperative learning 2-4-8 strategy....................................................91

6.13. Appendix 6.13: Cooperative learning Formulate, Listen, Share, Create.......................92

6.14. Appendix 6.14: Skill developed through Cooperative learning....................................92

6.15. Appendix 6.15: Role-Play strategy...............................................................................92

6.16. Appendix 6.16: Bloom’s Taxonomy sequence of questions.........................................93

6.17. Appendix 6.17: Encouraging all the students to answer questions in the classroom...97

6.18. Appendix 6.18: Provide support and challenge students for higher achievement.......98

6.19. Appendix 6.19: Encouraging achievement in girls........................................................99

6.20. Appendix 6.20: Helps boys to “be Masculine” in a positive way................................100

6.21. Appendix 6.21: Building study skills...........................................................................101

6.22. Appendix 6.22: Enhancing the intellectual development of middle school students.102

6.23. Appendix 6.23: Building positive communication with young adolescents...............103

6.24. Appendix 6.24: Model and establish inclusive learning environment........................104

6.25. Appendix 6.25: Supporting ADHD students...............................................................105

6.26. Appendix 6.26: Supporting Autism students..............................................................106

6.27. Appendix 6.27: Strategies for gaining acceptance from your teachers and peers.....107

6.28. Appendix 6.28: Step-by-step process for building self-confidence in young adolescents108

6.29. Appendix 6.29: Benefits of developing resilience......................................................109

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6.30. Appendix 6.30: Promoting productive interests in young adolescents......................110

6.31. Appendix 6.31: Preparing young adolescents to become independent persons.......111

7. Appendix – Student reflection strategies................................................................................112

7.1. Appendix 7.1: Metacognitive questions.........................................................................112

7.2. Appendix 7.2: Venn diagram..........................................................................................113

7.3. Appendix 7.3: 3-2-1 strategy..........................................................................................113

7.4. Appendix 7.4: Traffic light..............................................................................................114

7.5. Appendix 7.5: Plus Minus Interesting (PMI)...................................................................114

7.6. Appendix 7.6: Muddy points..........................................................................................115

7.7. Appendix 7.7: Head Heart Hand strategy.......................................................................115

7.8. Appendix 7.8: Triangle...................................................................................................115

7.9. Appendix 7.9: Concept Circle.........................................................................................116

7.10. Appendix 7.10: Group reflective activity....................................................................116

7.11. Appendix 7.11: Sharing Circle....................................................................................116

7.12. Appendix 7.12: DEAL model.......................................................................................117

7.13. Appendix 7.13: Reflection log or journal....................................................................118

8. Appendix – Practice activities.................................................................................................119

8.1. Appendix 8.1: Activity 1.................................................................................................119







9. Appendix – Assessment..........................................................................................................126

9.1. Appendix 9.1: Diagnostic Assessment............................................................................126

9.2. Appendix 9.2: Formative Assessment............................................................................130

9.3. Appendix 9.3: Summative Assessment..........................................................................142

9.4. Appendix 9.4: Formative Assessment - Grade record sheet..........................................146

9.5. Appendix 9.5: Teacher observation check chart for year 9 class...................................147

10. Appendix – Feedback.............................................................................................................148

10.1. Appendix 10.1: Methods of providing effective feedback.........................................148

10.2. Appendix 10.2: Levels of feedback.............................................................................149

References.....................................................................................................................................150

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1. Student ProfilesThe unit of work is designed for a year 9 cohort. The class comprises of students with varied abilities, learning needs, medical conditions and cultural backgrounds. Most of the students are keen to use ICT in the learning environment. They become disengaged when the learning activities are not fun and exciting for them. There are few At Risk learners in the class. The mentor teacher has confirmed that these students are from low socio-economic background and has alcoholic parents. The school records show that some of these students have been mentally abused by their parents. They lack positive role models, resilient skills and motivation to try for academic excellence.

The cohort comprises of students with special learning needs. One student is diagnosed with the Attention Deficit Hyperactive Disorder (ADHD) and another student has mild Autism. The student with Autism looks very tired in the class. It gives an impression that he is not sleeping and eating well. Both these students are below average in studies. The three other students come from Non-English speaking background. These three ESL students have difficulty reading and interpreting mathematical word problems. They speak their first language at home. They often refer the dictionary and pocket thesaurus to understand the meanings. Few other students tease and make fun of these ESL students about their frequent use of dictionary.

Some students are rude, arrogant and exhibit rebelliousness towards authority. They become extremely defensive when the teacher corrects them by pointing out their mistakes. These students always have excuses for not completing the tasks. They demand independence but often shun the responsibilities. On a positive note, they respond well to hands-on learning where they learn by doing. When they are bored, they try to disturb other students and deliberately irritate teacher in the class. Some students seem to be utterly self-absorbed and self-centered. It looks like they are concerned about their personal identity and physical appearance. Quite a few students have difficulty controlling their feelings and emotions. Sarcastic backtalk, tremendous temper tantrum, emotional outburst of tears and mood swings is common in few learners. The class has a good mix of number of boys and girls. They seem to pursue their learning journey very differently.

Some students show the fear of failure and therefore do not even try to complete tasks on their own. They mask their fear by saying that they do not need strong mathematical knowledge as they will not go to university for the tertiary education. These students have the capability to learn but lack self-confidence and academic guidance to thrive. They struggle to apply the knowledge in new learning situations. Student-teacher believes that these students will do well if they are taught to ‘learn how to learn’ by embracing effective study skills.

Few students are keen to learn but are carried away by distractions caused by the influences of their peers. Some students are ‘attention seekers’, who constantly seek attention from the teacher or peers and wants to be in the ‘lime light’. Student-teacher believes that these students will develop strong leadership qualities if the opportunities are given. Few students always look dull and upset. They say that they are not happy with their life. This is indeed

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affecting their personal and academic growth and prosperity. They need guidance to develop gratitude, appreciate their life and be happy. One student always talks negative who has nothing positive to say. Most of the students respond well to humour and praise, and wants to be liked by their peers and teachers.

Few girls in the class are below average in studies. Few boys are struggling to master basic literacy skills. Some boys constantly exhibit destructive behaviour in the process of trying to be masculine. Some students claimed that they have no special interests. They look lost and do not respond to questions posed at class.

School Priorities

Beliefs: Every child can learn Every child can be a high achiever You cannot learn without feedback Quality teaching impacts on student outcomes Building relationships enable success

Values: Respect Responsibility Learning Excellence

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2. Unit of Work

School name Unit title Year level Duration of unit

North Rockhampton High School

Exploring Financial Mathematics and Trigonometry 9 5 Weeks

Unit outline

Focus Questions:How students will

1. Solve financial mathematical problems using the concept of simple interest model?2. Apply theory of trigonometry to solve the right-angled triangle problems?3. Appreciate Australia’s engagement with Asia using statistics?

Financial security is a major concern in the contemporary realm. This is due to the ongoing economic uncertainty, high cost of living and low income potentials as the growth in salaries is not keeping up with the increase in the living expenses. This clearly indicates that students need to understand the value of money and how to invest it wisely for capital growth and keep up with the inflation. They also need to understand how much interest they will be paying for their home loans, car loans etc.

Once the students acquire the knowledge of financial mathematics, they will not have the need to visit financial planners to get advice on how to save and grow the savings by prudent investments. Students will develop an understanding of the advantages of products that various financial institutions offer. This will allow them to identify the best product suited for their goals and budgets. Moreover, financial knowledge will assist students to check and reconcile their bank accounts successfully. Finally, students will realise that financial decisions can be supported by mathematical concepts and calculations. This unit will help the students gain the knowledge and understanding of the financial systems so that they will have an edge in the contemporary uncertain economy.

The statistics is used to carryout research, read journals and make logical decisions. Students develop high quality critical and analytical thinking skills and become informed consumers by exploring statistical data analysis (StatsR4us, n.d.; Cornell University Learning Strategies Center, n.d.).

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Unit outline

Students will be involved in collecting statistical data from the Asia-pacific region. Students will identify everyday enquiries and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources.

The knowledge of trigonometry is essential to understand how to build structures economically and effectively. With trigonometry, it is easy to identify the weak spot where things are most likely to break and how thick structural parts must be to carry the loads safely. Trigonometry is very useful to make demarcations for workspaces in buildings. Trigonometry is also used to understand radio waves and waves on water etc. The knowledge of trigonometry is useful in developing computer music, modern architecture, digital imaging, measuring the heights of mountains, aircraft designing and navigation, geography, medical scanning, astronomy and predicting stock market and financial cycles (QFAk, n.d.; Clark University, n.d.; Malini math blog, n.d.; Math Work Sheet Center, n.d; Yu, 2011).

Students will also have an opportunity to apply the theory of trigonometry to solve right-angled triangle problems. Students will learn to select and apply an accurate trigonometric ratio to determine the unknown sides and angles in right-angled triangles. Students can apply Pythagoras theorem in real life situations such as identifying the shortest path (hypotenuse is always the shortest) for morning walk. In this unit, students learn systematic problem solving techniques, build confidence on their ability to solve mathematical problems and realise their full potential and contribute towards individual’s success. This further leads to nation’s social and economic development.

Furthermore, students will have the opportunity to read questions, interpret word problems, convert texts into mathematical symbols, solve the problems and derive the solutions methodically. Students will enhance their reading and comprehension skills. Students will learn to construct the meaning logically without memorising the facts. Students will develop complex analysis, logical reasoning, critical thinking, creative thinking, higher-order thinking and problem-solving skills while dealing with the real-world situations. Students will have the opportunity to appreciate the importance of developing positive attitudes and perceptions in order to accomplish their career and personal life aspirations. The essential critical thinking, creative thinking, self-regulated thinking and productive habits of mind strategies are entrenched in the learning journey to equip students to build resilience and self-confidence and therefore enrich their capacities to learn in any circumstances and acquire the characteristics of lifelong learning and succeed in the competitive global village.

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Student’s prior knowledge Understanding basic algebra and solve quadratic equations Solving problems involving profit and loss Converting from one unit to another Solving mathematical word problems using analysis and logical reasoning Investigating techniques for collecting statistical data Understanding Pythagoras Theorem Application of sine, cosine and tangent ratios to solve simple trigonometric problems Using scientific calculator to calculate trigonometric functions

(Observation, conversation with the teacher and syllabus document)

The Declarative and Procedural knowledge’sIn this unit plan students will acquire the following declarative and procedure knowledge’s.

DK1: Know the theory of financial mathematics and its application in real-lifeDK2: Know the concept of Pythagoras theorem, trigonometric ratios and right-angled trianglesDK3: Familiarise with the statistical data

PK1: Comprehend the process of applying the financial mathematical models such as simple interest to formulate the investment decisions methodicallyPK2: Identify the appropriate tangent ratios to find the unknown sides of trianglesPK3: Apply the trigonometric paradigms to solve the right-angled triangle word problemsPK4: Appreciate the process of investigating, collecting, interpreting and representing the statistical data logically

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Identify curriculum

Content descriptions to be taughtGeneral capabilities and cross-curriculum prioritiesNumber and

AlgebraMeasurement and Geometry

Statistics and Probability

Solve problems involving simple interest (ACMNA211): Understanding that financial decisions can be assisted by mathematical calculations.

Apply trigonometry to solve right-angled triangle problems (ACMMG224): Understanding the terms 'adjacent' and 'opposite' sides in a right-angled triangle.Selecting and accurately using the correct trigonometric ratio to find unknown sides (adjacent, opposite and hypotenuse) and angles in right-angled triangles.

Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources (ACMSP228): Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources.

Literacy Students learn the vocabulary, concepts and processes associated with financial

mathematics, trigonometry, Pythagoras theorem, right-angled triangles and statistical information. The vocabulary students will learn is shown in Appendix 5.5. Students develop the capability to read and interpret case studies, word problems and instructions to learn the process of applying the mathematical paradigms. Students pose and answer questions, engage in mathematical (simple interests, right-angled triangles and statistics) problem solving, discuss the concepts with peers and teachers, and generate and explain solutions in meaningful sentences.

Numeracy Students apply the concept of Number and Algebra in solving financial mathematical

problems. Students have an opportunity to apply the trigonometry concepts to design right-angled triangles and solve problems methodically. Students develop in-depth analysis, processing and problem-solving skills while calculating simple interest and right-angled triangle real-world problems. Students learn to interpret data and make informed decisions and further develop skills to survive in the twenty-first century information era.

ICT capability Students use ICT for checking their knowledge, practising and mastering the

mathematical models using online interactive quizzes, games and multimedia technologies. Students watch online videos to understand the concepts of financial mathematics and trigonometry. Students use ICT to communicate with their peers and teachers to clarify and explain their knowledge and understandings. Students use World Wide Web to collect information and find worksheets for practising and

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Identify curriculum

mastering the mathematical problems. Students use spread sheets to record, manage, analyse, interpret data and draw graphs.

Critical and creative thinking Students engage in analysis, logical reasoning and higher order thinking while reading

and interpreting the statistical information and word problems. Students develop critical thinking skills when they self-critique their knowledge and the learning process. Students develop critical thinking skills when they justify their choice of an investigation strategy or a mathematical process. They develop creative thinking skills by identifying effective and alternative (innovative) ways of solving simple interest and right-angled triangle problems and analysing statistical data. Students use mnemonics, flow charts, graphic organisers and process diagrams to simplify the problem solving methodologies and derive the solutions accurately.

Personal and social capability Students work independently and collaboratively in acquiring and integrating the

knowledge of financial mathematics and statistics. Students will participate in activities that relate to their own lives and communities and understand these concepts in everyday contexts. These activities provide opportunities for students to take initiative, discuss with others, communicate their ideas, seek for more information and make responsible and intelligent decisions.

Intercultural understanding Students work in heterogeneous teams to develop intercultural understanding. They

appreciate and celebrate the similarities and differences in cultural perspectives, values and beliefs.

Asia and Australia’s engagement with Asia Students develop mathematical knowledge and understanding by collecting,

interpreting, comparing and analysing statistical data from the Asia-pacific region.

Proficiencies

Understanding includes describing the theory of financial mathematics, comprehending the process of solving simple interest problems and the use of trigonometric ratios for right-angle triangles.

Fluency includes developing the familiarity with financial mathematical and right-angled triangle problems. Applying the mathematical paradigms accurately for solving simple interest and right-angle triangle problems.

Problem Solving includes formulating, and modelling practical situations involving simple interest rate and right-angle trigonometry problems, and collecting data from secondary sources to investigate an issue.

Reasoning includes reading and interpreting mathematical scenarios or case studies, evaluating media reports and using statistical knowledge to clarify situations, assessing solutions, draw conclusions and make informed decisions.

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Achievement standard

Understanding dimension: By the end of Year 9, students solve problems involving simple interest. They interpret ratio and scale factors in similar figures. Students explain similarity of triangles. They recognise the connections between similarity and the trigonometric ratios. Students compare techniques for collecting data in primary and secondary sources. They make sense of the position of the mean and median in skewed, symmetric and bi-modal displays to describe and interpret data.Skills dimension: Students apply the index laws to numbers and express numbers in scientific notation. They expand binomial expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment. They sketch linear and non-linear relations. Students calculate areas of shapes and the volume and surface area of right prisms and cylinders. They use Pythagoras’ Theorem and trigonometry to find unknown sides of right-angled triangles. Students calculate relative frequencies to estimate probabilities, list outcomes for two-step experiments and assign probabilities for those outcomes. They construct histograms and back-to-back stem-and-leaf plots.

Relevant prior curriculum Curriculum working towards

Outline relevant previous curriculum content and standards (knowledge, skills and processes) that students need to succeed in this unit.Specify where this content occurs by identifying the curriculum document, year level and learning area.

In the Australian Curriculum: Year 8: MathematicsMoney and financial mathematics:Solve problems involving profit and loss, with and without digital technologies (ACMNA189):

Expressing profit and loss as a percentage of cost or selling price, comparing the difference

Investigating the methods used in retail stores to express discounts

Outline curriculum content (knowledge, skills and processes) that students are working towards. Specify where this content occurs by identifying the year level and learning area.

In the Australian Curriculum: Year 10: MathematicsMoney and financial mathematics:Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229)

Working with authentic information, data and interest rates to calculate compound interest and solve related problems

Pythagoras and trigonometrySolve right-angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245)

Applying Pythagoras' Theorem and trigonometry to problems in surveying and design

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Real numbers:Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies (ACMNA187)

Using percentages to solve problems, including those involving mark-ups, discounts and GST

Using percentages to calculate population increases and decreases

Geometric reasoning:Develop the conditions for congruence of triangles (ACMMG201)

Investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA and RHS)

Solving problems using the properties of congruent figures Constructing triangles using the conditions for congruence

Data representation and interpretation:Investigate techniques for collecting data, including census, sampling and observation (ACMSP284)

Identifying situations where data can be collected by census and those where a sample is appropriate1

Data representation and interpretation:Construct and interpret box plots and use them to compare data sets (ACMSP249)

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

Using parallel box plots to compare data about the age distribution of Aboriginal and Torres Strait Islander people with that of the Australian population as a whole

Bridging content

Identify bridging content (knowledge, skills and processes) needed to address gaps in student understandings.

The Australian Curriculum: Mathematics builds the knowledge on “Number and Algebra”, “Measurement and Geometry” and “Statistics and Probability” sequentially. Students develop high quality Literacy, Numeracy, ICT capability, Critical and creative thinking and Personal and social capability in the Australian curriculum. In Year 8 Essential Learning’s, students develop high quality Literacy, Numeracy, ICT and Indigenous

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Perspectives. The opportunity to develop high quality Critical and creative thinking and Personal and social capability is not particularly emphasised in year 8 Essential Learning’s.

Incorporate effective teaching strategies and learning activities that require critical and creative thinking and social skills. Provide adequate scaffolding and facilitate peer-assistance to address the gaps in student understandings.

Links to other learning areas

Explain how this unit links to other learning areas.Science:Processing and analysing data and information:Analyse patterns and trends in data, including describing relationships between variables and identifying inconsistencies (ACSIS169)

Evaluating:Critically analyse the validity of information in secondary sources and evaluate the approaches used to solve problems (ACSIS172)

English:Interpreting, analysing and evaluating:Use comprehension strategies to interpret and analyse texts, comparing and evaluating representations of an event, issue, situation or character in different texts (ACELY1744)

Creating texts:Create imaginative, informative and persuasive texts that present a point of view and advance or illustrate arguments, including texts that integrate visual, print and/or audio features (ACELY1746)

Geography:Collecting, recording, evaluating and representing:Collect, select, record and organise relevant geographical data and information, using ethical protocols, from a range of appropriate primary and secondary sources (ACHGS064)

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Assessment Make judgments

Describe the assessment Assessment date Diagnostic

assessment: Student’s knowledge,

understanding and application of trigonometric models.

Formative assessment:Learning outcomes assessed to provide regular feedback: Knowledge and

understanding of simple interest concepts and applying the financial mathematical theory in real-life situations

Knowledge and understanding of Trigonometry and applying the trigonometric models to solve right-angled triangle problems

Higher-order thinking and Problem-solving skills

Diagnostic assessment:The assessment task (see Appendix 9.1) is designed to assess student’s prior knowledge on trigonometric ratios. The assessment provides information about student’s needs, strengths and weaknesses. The teacher uses this information to prepare student-centred learning experiences appropriate for the cohort.

Formative assessment:The formative assessment task (see Appendix 9.2) is intended to provide an exciting learning opportunity for encouraging all the students to learn the concepts thoroughly and solve the problems systematically. The purpose of the assessment task is to facilitate students to develop critical and creative thinking, higher-order thinking, problem-solving skills and self-confidence and further develop the attributes of lifelong learning.

Length: No word limitResources required: Laptop, internet, scientific calculator, set textbook and learning materials provided by the teacher.

The formative assessment task is divided into 7 assessment techniques.

1. Student's self-assessment: Students are asked to assess their strengths, weaknesses, opportunities and threats by using the checklist provided by the teacher. This assessment type is supposed to empower students to take responsibility for their own learning (Appendix 9.2.1).

2. Peer-assessment: The assessment will be carried out by peers to provide an opportunity for

Week 2

Students work on formative assessment task from week 1 to week 5.

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students to internalise the characteristics of high quality work by evaluating each other’s work. This provides positive and energetic peer-pressure for students to set high expectations and thrive.

3. Teacher observation: The teacher observes students using the strategies articulated in Appendix 9.2.2 and records the observations systematically in the observation check chart (Appendix 9.5).

4. Quiz: Assess student’s knowledge, understanding and skills using an interactive quiz (Appendix 9.2.3).

5. Homework: Give homework to encourage and cater for students with mixed abilities and learning needs (Appendix 9.2.4). Give homework (O'Donnell, Dobozy, Bartlett, Bryer, Reeve, & Smith, 2011, p. 69)

o based on concepts taught in the classo based on alternative methodologies students need to research and exploreo that expands and extends beyond classroom learning (e.g. interesting and meaningful

real-world examples and case studies)

6. Forced-choice questions: Students are expected to complete Forced-choice questions (Appendix 9.2.5).

7. Short-answer questions: Students are asked to describe the step-by-step process of solving simple interest and right-angled triangle problems (Appendix 9.2.6). Students are expected to explain each question in simple English sentences and show the process of identifying the appropriate mathematical concepts, transforming questions (words) into mathematical formulas, applying the formulas systematically by substituting the given values and determine the final result (unknown values).

General Capabilities (Literacy, numeracy, critical and creative thinking, ICT capability and personal and social capability)

Cross-curriculum priorities: Evaluate student’s knowledge on Australia’s engagement with Asia

Students attitudes and perceptions towards school and learning tasks (DOL 1)

Students habits of mind towards continuous learning (DOL 5)

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Addressing the diverse needs and abilities of all the students for completing the formative assessment:

Students are allowed to take the help of peers in the classroom (without disturbing others) Students with special learning needs (e.g. ADHD, Autism and ESL) are given extra time to

complete the tasks. Assist them develop effective study skills. The teacher will scaffold students to categorise the tasks and break the tasks into smaller

chunks. Help students to progress from easy to more difficult, familiar to unfamiliar, routine to non-

routine tasks (QSA, 2012). Provide stimulating cues, prompts and directions for students to complete tasks efficiently

(QSA, 2012). Make students believe that “Success builds on success”.

Summative assessment: Modelling and problem-solving taskThe purpose of the assessment task (see Appendix 9.3) is to evaluate student’s learning on their abilities to apply their knowledge and understanding in solving financial mathematical questions, right-angled triangle problems and statistical data analysis and hence meet the year 9 achievement standards relevant to the unit of work. The assessment task requires students to demonstrate strong literacy, numeracy, ICT, critical and creative thinking and higher-order thinking, problem-solving and communication skills.

Students are expected to solve all the problems methodically by illustrating step-by-step instructions and explain the solutions in general terms. Students are encouraged to present a comprehensive algorithm that represents the process of solving each word problem. This task is supposed to be completed in student's own time.

Students submit summative assessment task in Week 9.

Summative assessmentUnderstanding and Fluency: Connection and

description of mathematical understandings involving simple interest, trigonometric ratios and exploring techniques for collecting data from different sources.

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Assessment type: Unsupervised Individual workFormat: The presentation format can be hand written, typed, video, wiki page (learning resource) or a web podcast. This should be supported by the appropriate use of graphics, diagrams, flowcharts, graphic organisers, algorithms and calculations.Length: No word limitResources required: Laptop, internet, scientific calculator, set textbook and learning materials provided by the teacher.

Addressing the diverse needs and abilities of all the students for completing the summative assessment task:

Incorporate the following five inclusive strategies to cater for varied needs and abilities of all the students.

Timing inclusive strategy: Students with special learning needs (e.g. ADHD, Autism and ESL) are allowed to take one week additional time to submit the assignment.

Scheduling inclusive strategy: Make adjustments to the order of sessions by allowing student’s (who lack confidence in solving mathematical problems or who has difficulty understanding mathematical problems) to start an assessment with a section that engages the student or the topic student finds it easier to complete. Make adjustments to the number of sessions to allow students to submit the assessment task in smaller chunks.

Setting inclusive strategy: Make adjustments to the location and placement for reducing distractions, minimise background noise and reduce anxiety of the student. Allow students (who lack confidence) to sit closer to the teacher when they are engaged in solving complex problems.

Presentation inclusive strategy: Make adjustments to the presentation of the assessment task

Recall and use of facts, definitions, technologies and procedures to solve simple interest problems, trigonometric ratios and interpreting and representing data involving at least one numerical and one categorical variable.

Use of mathematical language, conventions and symbols related to financial mathematics, trigonometry, Pythagoras’ Theorem and representation of statistical data.

Problem solving and Reasoning: Application of problem-

solving strategies to find unknown sides of right-angled triangles.

Mathematical modelling and representation of trigonometric paradigms.

Results and conclusions of

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by categorising and highlighting key words in meaningful colours. Response inclusive strategy: Allow students to submit assignments in hand written, typed,

video, wiki page or a web podcast to cater for all the students learning preferences.

Scaffolding and feedback: Provide opportunities for students to learn the targeted content, and review and consolidate

the content that students may not have engaged recently (QSA, 2012). The teacher will explain the assignment questions by rephrasing and summarising the sentences

to make it easier for all the students to understand the problems. Provide learning experiences that support the format of the assessment and modelling the

assessment technique where possible without rehearsal of the actual assessment (QSA, 2012). Students are allowed to submit the draft assignment to receive constructive feedback.

Learning communities of practice: The teacher will facilitate an assignment discussion forum for students to discuss with peers and

share their ideas.

investigations and inquiries related to everyday statistical questions.

Discussion of mathematical thinking, choices and strategies used to apply the concepts of trigonometry for solving right-angled triangle problems.

Seeking accuracy in checking answers and logical justification of the reasonableness of answers.

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Teaching and learning Supportive learning environment

ILO (link to

content descriptors)

Teaching strategies and learning experiences Links to Dimensions of Learning

Adjustments for needs of learners

Resources

ACMNA211

DK1

Week 1Lesson 1:Introduction:

Introduce the concept of financial mathematics Tell students the inspirational story (Appendix 12.1)

Communicate the purpose of the lesson / persuade curiosity and motivation: Tell students why they need to learn mathematics (Appendix 5.1) and the

benefits of learning financial mathematics (Appendix 5.2)Body:

Involve students in establishing the classroom rules and decisions and in discussing how the rules will be enforced

Students work individually: Handout KWHL matrix (Appendix 5.4) for students to record “What do I Know?”, “What do I Want to find out?” and “How will I learn?” on the financial mathematics topic

Whole class discussion – teacher models from board:o Brainstorm information about financial mathematicso Demonstrate the process of preparing a graphic organiser - a

concept map (Appendix 5.3) that depicts the physiognomies and applications of financial mathematical concepts in the real-world

o Discuss the advantages of using graphic organisers to organise the information efficiently (Appendix 5.10)

Students work in pairs (think-pair-share):o Students are asked to read the handout “Advantages of financial

DOL 1: Establish and communicate classroom rules and procedures(Appendix 4.1)

DOL 1: Help students understand that learning is influenced by attitudes and perceptions related to classroom tasks (Appendix 4.1)

DOL 5: Critical Thinking: Be clear and seek clarity(Appendix 4.1)

Maintain positive communication and relationship with middle phase of learners (Appendix 6.23)

Developing Literacy skills:Several studies show that boys underperform compared with girls in literacy (Coil, 2003).

Provided tips forencouraging literacy in boys (Appendix 6.6)

TextbookNote booksCalculatorsInteractive white boardComputers

Handouts:Why learn mathematics (Appendix 5.1)

Advantages of learning about money and financial mathematics (Appendix 5.2)

Financial Mathematics Concept Map (Appendix

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mathematical knowledge in real-life” (Appendix 5.2) alone, and then pair with the partner to discuss both of their understandings and finally share their ideas with the whole class.

Whole class discussion - Teacher models from boardo Help students using the link strategy for storing information

efficiently without memorising through repetitionConclusion:

Ask students if they have any questions Quickly revise the concepts covered in the lesson Emphasise the importance of constructing the meaning, organising the

information systematically and finally storing the information efficiently to acquire the new knowledge

Handout the Formative assessment task (Appendix 9.2) for students to complete in their own time

Reflect on students learning: Ask students to reflect on their learning by completing the last column

“What have I Learnt?” in the KWHL table (Appendix 5.4)

Homework: Remind students to complete the homework designated for day 1

(Appendix 9.2.4 – day 1)

Proficiencies targeted in this lesson:Understanding: Describing the theory of financial mathematics.

DOL 2: Construct Meaning – Present KWHL strategy

DOL 2: Organise – Use graphic organisers

DOL 2: Store – Use the link strategy with students

Provided tips for building Reading Comprehension skills(Appendix 6.7)

Encourage students to develop literacy skills through interactive quizzes and games (Appendix 15)

Selected the strategy “CRUSH” (Appendix 6.4) for promoting literacy in students diagnosed with ADHD and

5.3)

KWHL table (Appendix 5.4)

Advantages of using graphic organisers (Appendix 5.10)

Formative Assessment Task(Appendix 9.2)

Homework (Appendix 9.2.4)

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Lesson 2:Introduction:

Revise the concepts of financial mathematics and its benefits Introduce the terminology used in the financial mathematical domain Briefly explain the simple interest formula

Communicate the purpose of the lesson / persuade curiosity and motivation: Remind students the benefits of learning about money and financial

mathematics (Appendix 5.2) Tell students the inspirational story (Appendix 12.2)

Body Word walls (Shults, 2008): Post new words (Appendix 5.6) on walls for

learners to acquaint with the new terminology Teacher models from board:

o Explain the meaning of each word using the interesting and real-word examples (Appendix 5.5)

o Scaffold and assist students to take notes while explaining the definitions

o Explain the benefits of note-taking for academic success and beyond (Appendix 5.11)

o Discuss the Do’s and Don’ts in taking notes (Appendix 5.12) Peer-assessment: Students swap their academic notes with the partner

and evaluate each other’s method of note-taking Whole class discussion – Teacher models from board:

o Work with students to identify “mnemonics” (a meaningful word or

DOL 1: Establish a relationship with each student in the class (Appendix 4.2)

DOL 1: Teach students use positive self-talk (Appendix 4.2)

DOL 5: Habits of mind: Learning Continuously(Appendix 4.2)

DOL 2: Organise: Note-taking

DOL 2: Store – Provide mnemonics

Autism

Teaching ESL studentsRole-Play in ESL classes can provide interesting and challenging ways for students to use the new language.

Provide the players’ with cue cards on which you have indicated what they are required to do so all that students’ have to think about is the language.

Handouts:Word walls (Appendix 5.6)

Financial mathematic terminology (Appendix 5.5)

Benefits of Note-taking (Appendix 5.11)

Do’s and Don’ts in Note-taking (Appendix 5.12)

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phrase) for remembering the information they learnt Students work in a group of 4: Students identify “mnemonics” for all the

remaining words Teacher models from board:

o Explain the simple interest formula (Appendix 5.7)o Encourage students to take notes

Students work individually using the technology:o Students work on interactive quiz (Appendix 9.2.3 – Simple interest

quiz) to assess their knowledge on financial mathematicsConclusion

Ask students if they have any questions Quickly revise the concepts covered in the lesson Emphasise the importance of taking notes

Reflect on students learning: Ask students to reflect on their learning using the Metacognitive questions

(Appendix 7.1)



Proficiencies targeted in this lesson:Fluency: Developing the familiarity with financial mathematical terminology and problems.

(Kodotchigova, 2002)

Progress from this to the use of cue cards with minimal directions that encourage students to explore the possibilities of the role in a more spontaneous manner (Kaye, 2002)

Use Role-plays for helping students to develop their language skills including developing

(Appendix 5.7)

Quiz (Appendix 9.2.3)Students reflection (Appendix 7.1)

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Revise the financial mathematical vocabulary and simple interest formula Introduce the process of solving simple interest word problems Discuss with students how someone can become richer than Bill Gates

(Appendix 5.13) Tell students the inspirational story (Appendix 12.3)

Communicate the purpose of the lesson / persuade curiosity and motivation: Remind students the benefits of learning about money and financial

mathematics (Appendix 5.2)

Body Whole class discussion - Teacher models from board:

o Write question from Activity 1 (Appendix 8.1) on boardo Think-aloud process: Demonstrate the step-by-step process of

solving the problemo Show the process of writing the learning journal along with the

logical thought processes adopted in solving the problemo Provide tips to solve mathematical word problems (Appendix 5.9)

Whole class discussion/students work in pairs– Teacher models from board:

o Work with students to solve Activity 2 (Appendix 8.2) using the Four Resource model (Appendix 6.1)

Students work individually:

DOL 1: Recognise and provide for students individual differences (Appendix 4.3)

DOL 1: Use a variety of ways to engage students in classroom tasks(Appendix 4.3)

DOL 5: Critical thinking – Maintain an open mind(Appendix 4.3)

DOL 2: Construct: Use a think-aloud process to

vocabulary, understanding of grammar and communication (Killen, 2013)

Developing Numeracy skills:Incorporate the following four numeracy tools for developing numeracy skills in middle phase of students.

Numeracy tool 1: tablesBeing numerate beyond school will include reading and interpreting tabulated information. If

Handouts:Activity 1 (Appendix 8.1)

Tips to solve word problems (Appendix 5.9)

Activity 2 (Appendix 8.2)

Four Resource Model (Appendix 6.1)


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o Students work on Activity 3 (Appendix 8.3)o Encourage peer-teaching. Allow students who have completed the

task to help other students.Conclusion

Ask students if they have any questions Quickly revise the concepts covered in the lesson Emphasise the importance of writing learning journal with step-by-step

process of solving the mathematical paradigms

Reflect on students learning: Students work in a group of 3:

o Ask students to reflect on their learning (the information they know well, the information they are confused about and the information they don’t get yet) using the Venn Diagram (Appendix 7.2)

o Ask students to discuss how they will master the concepts they are confused about and the concepts they have not learned yet



Proficiencies targeted in this lesson:Understanding: Comprehending the process of solving simple interest problems.Fluency: Applying the mathematical paradigms accurately for solving simple interest problems.

demonstrate new skills/process

students encounter a variety of tables in their numeracy learning they will become familiar with the common features of tables and hone their interpretation skills, particularly in recognising the relationship between the values presented in the table.

Numeracy tool 2: flow chartsFlow charts are

Students reflection (Appendix 7.2)

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Revise the process of solving simple interest problems Tell students the inspirational story (Appendix 12.4)

Communicate the purpose of the lesson / persuade curiosity and motivation: Remind students the benefits of developing problem-solving skills by

working on simple interest problemsBody

Whole class discussion - Teacher models from board:o Write question from Activity 4 (Appendix 8.4) on boardo Think-aloud process: Demonstrate the step-by-step process of

solving the problem using the Newman 5 prompt’s (Appendix 6.2)o Facilitate the discussion about developing self-confidence and

resilience in the middle phase of learners (Appendix 6.28; Appendix 6.29; Appendix 18)

Numeracy development: Scaffold students to draw a flow chart that represents the process of solving the simple interest word problems

Students work in a group of 3:o Students work on short-answer questions 1-8 (Appendix 9.26)

Conclusion Ask students if they have any questions Quickly revise the concepts covered in the lesson

DOL 1: Engage in equitable and positive classroom behaviour (Appendix 4.4)

DOL 1: Establish a sense of academic trust (Appendix 4.4)

DOL 5: Creative thinking: Persevere (Appendix 4.4)

DOL 2: Construct: Use a think-aloud process to demonstrate new skills/process

a useful way of illustrating the various components of a complex situation. Designing flow charts develop student’s skills in logical thinking.

Numeracy tool 3: graphsThe ability to read and interpret graphical information is important aspect of being numerate.


Step-by-step process for building self-confidence in young adolescents (Appendix 6.28)

Benefits of developing resilience (Appendix 6.29)

Principles for resilience building (Appendix

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Encourage students to develop self-confidence and resilience for fulfilling their life aspirations

Reflect on students learning: Ask students to reflect on their learning using the traffic light (Appendix

7.4)Homework:

Remind students to complete the homework designated for day 4 (Appendix 9.2.4 – day 4)

Proficiencies targeted in this lesson:Problem solving: Formulating, and modelling practical situations involving simple interest rate problems.


Introduce Trigonometry and Pythagoras theorem Introduce the T.H.I.E.V.E.S pre-reading (Shults, 2008) strategy (Appendix

6.3) for emphasising the importance of using textbook to learn mathematical concepts thoroughly

Communicate the purpose of the lesson / persuade curiosity and motivation: Tell students the inspirational story (Appendix 12.5) Discuss with students how the knowledge of trigonometry will be useful in

real-world (Appendix 5.14)

DOL 1: Introduce the concept of bracketing(Appendix 4.5)

DOL 1: Provide appropriate feedback(Appendix 4.5)

Numeracy tool 4: diagramsDiagrams are useful for presenting information and showing relationships. Venn diagrams and mind maps are some examples of the types of diagrams that could be useful for numeracy learning. When students construct and use diagrams they are developing their logical and analytical thinking skills.

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Short answer questions 1-8 (Appendix 9.26)

Students reflection(Appendix 7.4)

Handouts:THIEVES pre-reading strategy (Appendix 6.3)

Benefits of trigonometry (Appendix

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Body Formative assessment - Diagnostic test:

o Students complete the diagnostic test (Appendix 9.1) to evaluate their prior knowledge on Trigonometry

Whole class discussion – teacher models from boardo Review the concepts of Pythagorean Theorem, Special Right Angled

Triangles and Trigonometric Functions.o Write question from Activity 5 (Appendix 8.5) and illustrate the

process of solving the right-angled triangle problem methodically Students work in a group of 3:

o Students work on forced-choice questions 1-5 (Appendix 9.2.5) using the DOL 4 Complex Reasoning Processes - Problem Solving approach (Appendix 6.10)

o Teach students to mentally rehearse the stepso Ask students to mentally rehearse the process they have employed

to solve the right-angle triangle problem, write in their notes and share with the whole class

Conclusion Ask students if they have any questions Quickly revise the concepts covered in the lesson Encourage students to master the “steps for solving the word problems”

(Appendix 5.9) to derive accurate solutions

DOL 5: Critical thinking: Be accurate and seek accuracy(Appendix 4.5)

DOL 4: Complex Reasoning Processes – Problem Solving(Appendix 6.10)

DOL 2: Teach to mentally rehearse steps

(Siemon et al., 2011)

Selected the strategy “SOLVE-IT” (Appendix 6.5) for promoting numeracy in students diagnosed with ADHD and Autism

Supporting mathematics anxious students:Made the following adjustments to overcome the students’ fear of mathematics.

5.14)Diagnostic text (Appendix 9.1)


Forced-choice questions 1-5 (Appendix 9.2.5)

DOL 4 Problem solving approach (Appendix 6.10)

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Reflect on students learning: Students work in a group of 4:

o Ask students to reflect on their learning using the strategy “Muddy Points” (Appendix 7.6)



Proficiencies targeted in this lesson:Understanding: Use of trigonometric ratios for right-angle triangles.


Review the concepts of Trigonometry, Pythagoras theorem and the steps used for solving the right-angled triangle problems (Appendix 5.8)

Communicate the purpose of the lesson / persuade curiosity and motivation: Tell students the inspirational story (Appendix 12.6) Remind students the benefits of trigonometry. Discuss how trigonometry is

used in predicting financial/business cycle (Appendix 5.14).Body

Ask students to use the dictionary for understanding the meanings of mathematical terminology (evaluate, determine, execute, derive, resolve, perform, implement, employ, etc.), the commonly used vocabulary in the word problems.

DOL 1: Respond positively to students incorrect responses or lack of responses (Appendix 4.6)

DOL 1: Create classroom tasks that relate to students interests and goals (Appendix 4.6)

*Providing effective scaffolding.

*Progressing learning from easy to more difficult, familiar to unfamiliar, and routine to non-routine (QSA, 2012).

*Breaking the tasks into manageable sections.

*Making students believe that they have the capabilities to complete tasks.

Student reflection (Appendix 7.6)



Trigonometry concepts (Appendix

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Whole class discussion – teacher models from boardo Write question from Activity 5 (Appendix 8.5) and illustrate the

process of solving the right-angled triangle problem methodically Numeracy development: Students work in a group of 3:

o Students work on forced-choice questions 1-5 (Appendix 9.2.5) using the model SOLVE-IT (Appendix 6.5)

o Ask students to mentally rehearse the process they have employed to solve the right-angle triangle problem, write in their notes and share with the whole class

Conclusion Ask students if they have any questions Quickly revise the concepts covered in the lesson Encourage students to use the dictionary to improve their literacy skills

Reflect on students learning: Students work individually:

o Ask students to reflect on their learning using the strategy “Reflection log our journal” (Appendix 7.13)



Proficiencies targeted in this lesson:Fluency: Developing the familiarity with trigonometry and right-angled triangle problems.

DOL 5: Self-Regulated thinking: Plan Appropriately (Appendix 4.6)

DOL 2: Teach to mentally rehearse steps

*Encouraging students to practise positive self-talk.

Encourage students to develop numeracy skills through interactive quizzes and games (Appendix 15)

Inspire students to master numeracy competencies through “Who wants to be a mathionaire?” (Appendix 16)

5.8)

Numeracy development SOLVE-IT (Appendix 6.5)


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Review the process of employing problem solving and decision making models (DOL 4)


used in astrology (Appendix 5.14)Body

Whole class discussion – teacher models from boardo Write question from Activity 6 (Appendix 8.6)o Introduce the Rereading strategy (Harmon, Wood & Stover, 2012).

Encourage students to reread the word problems until they understand the questions.

o Illustrate the step-by-step process of solving the right-angled triangle problem methodically

Cooperative learning: 2-4-8 strategy:o Facilitate students to work on short-answer questions 9-10

(Appendix 9.2.6) using the 2-4-8 strategy (Appendix 6.12) Students work individually

o Students work on forced-choice questions 6-10 (Appendix 9.2.5)o Encourage peer-assistance

DOL 1: Structure opportunities for students to work with peers(Appendix 4.7)

DOL 1: Help students recognise that they have the abilities to complete a particular task(Appendix 4.7)

DOL 5: Self-Regulated thinking: Identify and use necessary resources(Appendix 4.7)

Positive learning climate (developing sense of belonging):Provided students the strategies for gaining acceptance from peers and teachers (Appendix 6.27)

Establishing inclusive learning environment:The strategies incorporated are shown in Appendix 6.24


2-4-8 strategy (Appendix 6.12)

Short-answer questions 9-10 (Appendix 9.2.6)


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Numeracy development: Scaffold students to draw a flow chart or mind map that represents the process of solving the right-angled triangle word problems

Conclusion Ask students if they have any questions Quickly revise the concepts covered in the lesson Emphasise the benefits of Rereading mathematical word problems or case

studies

Reflect on students learning:o Ask students to reflect on their learning using the strategy “Head

Heart Hand” (Appendix 7.7)Homework:


Proficiencies targeted in this lesson:Fluency: Applying the mathematical paradigms accurately for solving right-angle triangle problems.


Review the process of solving the right-angled triangle paradigms

DOL 1: Help students understand that attitudes and perceptions related to classroom climate influence learning

Support students with ADHD: Incorporated various strategies to provide encouragement and support for ADHD students(Appendix 6.25)

Support students with Autism:Incorporated various strategies to provide encouragement and support for Autism students(Appendix 6.26)


Handouts:Short-answer questions 11-14 (Appendix 9.2.6)

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used in medical field (Appendix 5.14)Body

Whole class discussion – teacher models from boardo Book talks (Shults, 2008): Facilitate the discussion about book talks.

Remind students the importance of literacy skills in solving word problems and academic success. Inspire students to keep reading and enrich their literacy capabilities.

Cooperative learning: Formulate, Listen, Share, Create strategy:o Facilitate students to work on short-answer questions 11-12

(Appendix 9.2.6) using the strategy Formulate, Listen, Share, Create (Appendix 6.13)

Students work individuallyo Students work on short-answer questions 13-14 (Appendix 9.2.6)o Peer-assessment: Students exchange solutions with peers to check

their answers and provide constructive feedbackConclusion

Ask students if they have any questions Quickly revise the concepts covered in the lesson Encourage students to keep reading books

Reflect on students learning:o Ask students to reflect on their learning using the strategy “3-2-1”

DOL 1: Provide students with clarity about the knowledge that task addresses

DOL 5: Self-Regulated thinking: Monitor your own thinking

Encouraging achievement in girlsIn middle phase of schooling, girls lose interest in academic life (Braggett, 1997). The chosen strategies for encouraging achievement in girls are shown in Appendix 6.19.

Encouraging achievement in boysThe chosen strategies for helping boys to “be Masculine”

Formulate, Listen, Share, Create (Appendix 6.13)


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(Appendix 7.3)Homework:


Proficiencies targeted in this lesson:Problem Solving: Formulating, and modelling practical situations involving right-angle trigonometry problems.


Facilitate students to discuss their opinion about solving trigonometric problems related to real-life situation


used in modern architecture (Appendix 5.14)Body

Whole class discussion – teacher models from boardo Write question 15 from short-answer questions (Appendix 9.2.6)o Think-aloud process: Demonstrate the step-by-step process of

solving the question systematically Cooperative learning: Problem-based Learning:

o Facilitate students to work on short-answer questions 16-17

DOL 1: Provide Opportunities for students to get know and accept each other (Appendix 4.9)

DOL 1: Help students understand that believing in their abilities to complete a task include being that they have the ability to get help and the resources needed(Appendix 4.9)

in a positive way are shown in Appendix 6.20.

Study skills:Many middle school students do not know how to learn on their own (Kiddey & Robson, 2004).

Provided study skills for students to learn “how to learn”(Appendix 6.21)

Handouts:Short-answer questions (Appendix 9.2.6)

Problem-based Learning (Appendix 6.8)

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(Appendix 9.2.6) using the strategy Problem-based Learning (Appendix 6.8)

Students work individuallyo Students work on short-answer questions 18-20 (Appendix 9.2.6)


Reflect on students learning:o Ask students to reflect on their learning using the strategy “Group

reflective activity” (Appendix 7.10)Homework:


Proficiencies targeted in this lesson:Reasoning: Reading and interpreting right angled triangle word problems related to real-world situations.


Revise the concepts of Trigonometric ratios in solving the right-angled triangle word problems

DOL 5: Creative thinking: Generate new ways of viewing a situation that are outside the boundaries of standard conventions:(Appendix 4.9)

DOL 2: Use athink-aloud process

DOL 1: Monitor and attend your own attitudes(Appendix 4.10)

Provide support and challenge students for higher achievement:The incorporated strategies are shown in Appendix 6.18.

Intellectual development:The strategies incorporated for enhancing the intellectual development of middle school students are shown in Appendix 6.22.


Handouts:Activity 7 (Appendix

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used in digital imaging (Appendix 5.14)Body

Whole class discussion – teacher models from boardo Write question from Activity 7 (Appendix 8.7) on board and

demonstrate the systematic process of solving the problem Whole class discussion – summative assessment task (Appendix 9.3)

supporto Go through the assessment task details and criteriao Encourage students to ask questions they may have on summative

assessment task and provide stimulating answers Online interactive Quizzes – students work individually:

o Students use quizzes to practice and assess their knowledge and skills on trigonometry and right-angled triangle problems (Appendix 9.2.3)


Reflect on students learning:o Ask students to reflect on their learning using the strategy

“Concept circle” (Appendix 7.9)

DOL 1: Provide students with clear expectations of performance levels for tasks:(Appendix 4.10)

DOL 5: Creative thinking: Push the limit of their knowledge and abilities:(Appendix 4.10)

Adjustments made while asking questions:Incorporated various strategies to encourage all the students to answer questions in the classroom (Appendix 6.17)

Building student’s confidence:Provided step-by-step process for building self-confidence in young adolescents (Appendix 6.28)

8.7)

Quizzes URL's (Appendix 9.2.3)


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Proficiencies targeted in this lesson:Problem Solving: Formulating, and modelling practical situations involving right-angle trigonometry problems.


Introduce the concept of statistics and representing the statistical data

Communicate the purpose of the lesson / persuade curiosity and motivation: Tell students the inspirational story (Appendix 12.11) Advise students the benefits of statistics in the real-world (Appendix 5.15)

Body Whole class discussion – teacher models from board

o Summarising texts (Munro, n.d.): Scaffold students to use the strategy of summarising texts to learn efficiently and improve their literacy skills

Cooperative learning – Jigsaw - students work in a group of 6 – teacher facilitates the session

o Write question (Appendix 9.2.4 – Question 12) on boardo Scaffold students to collect the categorical and numerical data

using the internet

DOL 1: Beware of malicious teasing or threats inside or outside of the classroom, and take steps to stop such behaviour (Appendix 4.11)

DOL 1: Help students understand how specific knowledge is valuable(Appendix 4.11)

Building Resilience:Provided the benefits of developing Resilience (Appendix 6.29)

Promoting productive interests:Provided some suggestions to help students discover interests (Appendix 6.30)

Preparing young adolescents to become independent persons:The strategies incorporated

Handouts:Benefits of statistics in the real-world (Appendix 5.15)

Question (Appendix 9.2.4 – Question 12)

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o Show how to enter the data into excel spread sheeto Students solve the Jigsaw puzzle (Appendix 6.9)


Reflect on students learning:o Ask students to reflect on their learning using the strategy “Plus

Minus Interesting (PMI)” (Appendix 7.5)Homework:


Proficiencies targeted in this lesson:Reasoning: Reading and interpreting scenarios or case studies, evaluating media reports and using statistical knowledge to clarify situations.


Revise the process of collecting categorical and numerical data

Communicate the purpose of the lesson / persuade curiosity and motivation: Tell students the inspirational story (Appendix 12.12) Advise students the benefits of statistics in medical research (Appendix

5.15)

DOL 5: Creative thinking: Generate, trust, and maintain your own standards of evaluation(Appendix 4.11)

DOL 1: Have students identify their own standards for comfort and order(Appendix 4.12)

are shown in Appendix 6.31.

Operational Health & Safety (OHS) standards:Make sure that all the learners

*Can clearly see the board

*Sit on comfortable chairs and keep their desks tidy

*Keep their bags away from the walking area

*Teacher: Write clearly on the

(Appendix 6.9)


Handouts:Question (Appendix 9.2.4 – Question 13)

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Body Whole class discussion – teacher models from board Numeracy development:

o Demonstrate the process of drawing graphs and charts in excelo Teach students the ability to read and interpret graphical

information Small group work – students work in a group of 3 – teacher facilitates the

sessiono Write question (Appendix 9.2.4 – Question 13) on boardo Students collect the data and enter into excelo Teacher provides hints to represent the data and draw conclusions


Reflect on students learning:o Ask students to reflect on their learning using the strategy

“Triangle” (Appendix 7.8)Homework:


Proficiencies targeted in this lesson: Reasoning: Using statistical knowledge to clarify situations, assessing solutions, and draw conclusions and make informed decisions.

DOL 1: Help students be clear about the directions and demands of the task and ensure clarity(Appendix 4.12)

DOL 5: Habits of Mind: Responding with wonderment and Awe(Appendix 4.12)

board for all the students to be able to see the demonstrations. (Ewing, Lowrie & Higgs, 2010, p. 86)

Make learning maths fun:Present technology driven interactive learning tools for inducing curiosity and enthusiasm in young adolescents (Appendix 14)

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Revise the process of representing the statistical data

Communicate the purpose of the lesson / persuade curiosity and motivation: Tell students the inspirational story (Appendix 12.13) Advise students the benefits of statistics in manufacturing companies

(Appendix 5.15)Body

Complex Reasoning Process - Decision Making (Appendix 6.11) – students work in a group of 6 - teacher facilitates the session

o Write question (Appendix 9.2.4 – Question 14) on boardo Students represent the data in excel spread sheets in various forms

including tabular format and chartso Presentation to the whole class: Each group will give a 3 minute

presentation on their findings to the whole classConclusion

Ask students if they have any questions Quickly revise the concepts covered in the lesson

Reflect on students learning:o Ask students to reflect on their learning using the strategy “Sharing

Circle” (Appendix 7.11)

DOL 1: Frequently and systematically use activities that involve physical movement(Appendix 4.13)

DOL 1: Providing inspiring feedback(Appendix 4.13)

DOL 5: Critical thinking: Respond appropriately to other’s feelings and level of knowledge(Appendix 4.13)

Establish effective group activities with the features articulated in Appendix 17.

Handouts:Question (Appendix 9.2.4 – Question 14)

DOL 4 Decision Making model (Appendix 6.11)


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Proficiencies targeted in this lesson:Problem Solving: Collecting data from secondary sources to investigate an issue.


Revise the process of decision making for interpreting and representing the statistical data

Communicate the purpose of the lesson / persuade curiosity and motivation: Tell students the inspirational story (Appendix 12.14) Advise students the benefits of statistics in the banking industry and also in

the daily life of everyone to be informed consumers (Appendix 5.15)Body

Whole class discussion – summative assessment task supporto Go through the assessment task details and criteria - “Statistics and

data” sectiono Encourage students to ask questions they may have on this task

and provide stimulating hints for students to develop creativity and innovation for addressing the task

Role-Play (Appendix 6.15)o Ask students to work on the real-world problem (Appendix 9.2.4 –

DOL 4: Complex Reasoning Processes – Decision Making(Appendix 6.11)

DOL 1: Help students develop their ability to use their own strategies for gaining acceptance from their teachers and peers(Appendix 4.14)

DOL 1: Teach students use positive self-talk(Appendix 4.14)

Handouts:Students reflection (Appendix 7.12)

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Question 14) Whole class discussion – teacher models from board

o Revise the concepts of financial mathematics and the process of solving simple interest problems


Reflect on students learning:o Ask students to reflect on their learning using the strategy “DEAL

model” (Appendix 7.12)Homework:


Proficiencies targeted in this lesson:Problem Solving: Collecting data from secondary sources to investigate an issue.Reasoning: Reading, interpreting, evaluating, and draw conclusions and make informed decisions.


Revise the concepts of trigonometric ratios

DOL 5: Habits of mind: Finding Humour(Appendix 4.14)

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Communicate the purpose of the lesson / persuade curiosity and motivation: Tell students the inspirational story (Appendix 12.15) Remind students the benefits of learning trigonometry (Appendix 5.14)

Body Students work in a group of 4 – teacher facilitates the activity

o Implement the Bloom’s Taxonomy sequence of questions (Appendix 6.16)

o Pose questions to each groupo Provide stimulating hints with a goal to promote higher-order

thinking in studentsConclusion

Ask students if they have any questions Quickly revise the concepts covered in the lesson

Reflect on students learning:o Ask students to reflect on their learning using the strategy “Self-

assessment checklist” (Appendix 9.2.1)Homework:


Proficiencies targeted in this lesson:Acquiring and evaluating knowledge and skills in financial mathematics, right-angled triangles and statistical data analysis and representation.

DOL 1: Vary the positive reinforcement offered when students give correct response(Appendix 4.15)

DOL 1: Help students recognise that they have the abilities to complete a particular task(Appendix 4.15)

DOL 5: Habits of mind: Questioning and posing problems(Appendix 4.15)

Handouts:Bloom’s Taxonomy sequence of questions (Appendix 6.16)

Self-assessment check list (Appendix 9.2.1)

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Use feedback

Ways to monitor learning and assessment

Use the assessment techniques articulated in the formative and summative assessment tasks (Appendix 9.2 and Appendix 9.3).

Used the proficiency standards and content descriptors to formulate the judgement measures as shown in the assessment section. Use the judgement measures to monitor students learning and assessment.

Feedback to students– strategy or tool/How will it be used on the learning journey?

Informal feedback: Provide timely feedback to offer guidance for improvement and tap deep knowledge Point out student’s strengths, but also suggest where work can be improved Avoid comparisons with other students Show the benefit of learning from one’s mistakes Praise persistence and effort rather than ability and intelligence Separate actions and behaviour from the student’s self-worth

(Coil, 2003)

Formal feedback: Provide formal feedback at the end of the unit using the “Formative Assessment - Grade record sheet”

(Appendix 9.4) and the summative assessment task rubric.

Feedback Mechanism:The teacher will

Embrace the feedback philosophies presented in Appendix 10.1. Provide feedback on four different aspects described in Appendix 10.2.

Reflection on the unit plan Identify what worked well during and at the end of the unit, including: activities that worked well and why activities that could be improved and how assessment that worked well and why assessment that could be improved and how

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Use feedback

common student misconceptions that need, or needed, to be clarified.

The four dimensions of productive pedagogies, intellectual quality, connectedness, supportive classroom environment and working with and valuing difference were employed to assist with reviewing and evaluating the unit design and teacher's practices (Appendix 13).

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3. Evaluation

The Backward Design process (Wiggins & McTighe, 2005) that correlates with the Dimensions of Teaching and Learning Framework (Education Queensland, 2011) is employed for designing the unit plan. This practice is corroborated by the “10-point cycle” (Mcleod & Reynolds, 2007, as cited in Ewing et al., 2010, p. 83) and “the effective teachers planning” (Killen, 2009) models. The unit plan is designed to teach Financial Mathematics, Right-angled triangles and Statistical data representations from the year 9 Australian curriculum. The unit encompasses the General Capabilities of Literacy, Numeracy, ICT capability, Critical and creative thinking, Personal and social capability and intercultural understanding. The unit covers Asia and Australia’s engagement with Asia from the Cross-curriculum priorities.

In the middle years of schooling, school mathematics, and thus the development of numeracy, is challenged by students’ disposition towards the study of mathematics (Dole, 2005). This challenge has been addressed in the unit plan by adopting Dimensions of learning 1 & 5 and 16 Habits of Mind strategies coupled with effective scaffolding. Progressing learning from easy to more difficult, familiar to unfamiliar, routine to non-routine (QSA, 2012), breaking the tasks into manageable sections, making students believe that they have the capabilities to complete tasks and encouraging students to practise positive self-talk is likely to overcome student's fear of mathematics.

Promoting literacy is a high priority task to ensure students are prepared for successful academic life in the middle phase and beyond (Kiddey & Robson, 2004). The Four Resource Model and Newman’s 5 prompts instructional strategies are embedded in the lesson plans. These models deeply encompass all the aspects of literacy competencies essential to master complex mathematical models in the middle phase of schooling (Newman, 1977, Luke & Freebody, 1999). Research shows that writing plays a key role in learning (Meiers, 2007). The Note-taking, writing learning journal and short-answer assessment techniques (Marzano & Pickering, 2007; Hiemstra, 2001) are implanted in the lessons. The unit design evolved around developing ICT, Critical and creative thinking, Social and Cross-curriculum capabilities through effective instructional philosophies.

Higher-order thinking is one of the main objectives of middle years’ pedagogy as it leads to both personal and social-economic prospects (Dinham & Rowe, 2008). Mayer (2004) declared that cognitive activities i.e. learning by thinking promote deep learning. This view is corroborated by neuroscience research and constructivist perspective (Sousa, 2010; Willis, 2006; Stahl, 1997, as cited in Killen, 2013, p. 229). The repertoire of higher-order thinking strategies are incorporated into the learning journey. In the unit of work, students develop higher order thinking skills by engaging in Bloom’s Taxonomy sequence of questions (O’Donnell et al., 2011, p. 49) and mastering mathematical paradigms through complex reasoning processes such as Problem Solving and Decision Making (Marzano & Pickering, 1997). The chosen assessment tasks give students the opportunity to develop multifaceted higher order thinking through researching, analysing, and exploring creative ways to derive accurate solutions, and further synthesising and justifying solutions for the real-world scenarios.

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Goals for middle school learning is more oriented towards using their minds to think critically and less about mastering basic skills (Braggett, 1997). Metacognitive reflection (Hinett, n.d) and mental rehearsal strategies (Marzano & Pickering, 1997) are employed to help students understand the concepts rather than memorising the facts. Learning is enhanced by challenge and inhibited by threat (Caine & Caine, 1991). Students are given an opportunity to master the complex mathematical paradigms in a challenging, exciting and cooperative learning platform. The teaching strategies 2-4-8 (Fogarty, 1990), Think-Pair-Share (Ibe, 2009) are selected to provide fruitful learning experience for young adolescents. Furthermore, these strategies contribute to the requirements of increased intellectual demand on middle school students.

Interest and motivation is essential to promote energy within the middle phase of students (Howard & Fogarty, 2004, p. 148). Inspirational stories and purpose of the lessons are provided to nurture student’s interest in learning. Intriguing questions and interesting tasks are included in the instruction for inviting young adolescents into the curriculum. Excellent mathematics teachers arouse curiosity, challenge student’s thinking and actively engage them in learning mathematics (Australian Association of Mathematics Teachers, 2002). The unit plan encompasses wide variety of stimulating activities such as online interactive quizzes, role-plays and Jigsaw puzzle. These activities are intended to ignite the spark of creativity and kindle student’s enthusiasm.

Constructing meaning from mathematics involves discovering how mathematics can be applied to realistic problems (Stowell et al., 1996, p. 37). Great emphasis has been placed on helping students to understand the relationships between what they are studying and the real-world. The real-life mathematical questions are included in the curriculum and assessment to make it meaningful for young adolescents. When the learning has personal relevance, knowledge is constructed more easily, and creative ideas are generated and deep understanding results (Fogarty, 1997, as cited in Howard & Fogarty, 2004, p. 149). The in-depth learning has the potential to engage students’ imaginations and emotions in learning and build their confidence and pride and inspire students to keep learning and develop lifelong learning skills (IERG, n.d.). The development of deep understanding and capabilities for life-long learning are the fundamental philosophies of middle phase reform (Jackson & Davis, 2000).

Adolescent brains differ from adult brains, neurochemically and anatomically, and in terms of activity levels (Wolfe, 2010). Middle school students often exhibit poor cognitive performance (Pendergast & Bahr, 2010, pp. 245-246). Fuller (1998) suggested that problem-based learning aid students to form complex neural connections through higher order thinking processes and assist brain's development. Hence, this learning strategy is enacted in the unit plan. Young adolescents often exhibit disruptive behaviour and rebelliousness towards control (Coil, 2003, p. 38). One strategy that can be used to manage this problem is to involve students in making the rules and in discussing how they will be enforced (Spear, 2010). The approaches outlined in the unit plan are certainly not definitive. It is imperative for teachers to continuously review the practices and select the appropriate techniques for managing the behaviour of middle school students.

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Small group activities are embedded in all the lessons. The use of small group work in the classroom is a way to manage middle phase students learning as this offers greater intimacy and involvement, mutual respect and can help students to achieve their potential (Reid et al, 2002, as cited in Dargusch, 2013). In the cooperative learning situation, students develop cognitive skills, social and personal competencies (Appendix 6.14) through equitable participation (Barry & King, 1993, as cited in Dargusch, 2013). These are the developmental milestones of middle school learners as advocated by Zembar and Blume (2009). Research revealed that middle phase students possess inadequate listening skills (Braggett, 1997, p. 74). “Formulate, listen, share, create” (Johnson, Johnson & Holubec, 1998 p. 114) strategy is specially implemented to improve student’s listening skills.

Teens may suffer dips in their self-esteem and have tremendous anxiety over their looks, schoolwork and friendships, etc. (King, 2002). Early adolescence is a time when positive interventions can make a difference (Stowell et al., 1996, p. 14). Inclusiveness, student-centred philosophy that focuses on the whole student (personal, social and academic) and positive school culture are fundamental to maximising appropriate behaviours and achieving learning outcomes (de Jong, 2005, pp. 226-241). This principle is entrenched in the learning journey by selecting appropriate strategies to meet the learning needs of all the students including gender differences, ESL, ADHD and Autism students. Feeling successful and popular is one of the most important needs for young adolescents (Coil, 2003, p. 19). Resilience is considered as a comprehensive therapy and social engineering to promote self-esteem, confidence and autonomy (Richardson, 1998). Dinham and Scott (2000) advocate that building resilience through middle schooling is essential for solving a range of academic, personal and social problems. Developing resilience in students is informed in the unit.

Positive humour is encouraged in the lessons. Laughter has positive affect on psychological functions and helps to liberate creativity and provoke higher level thinking skills in finding novel relationships, making analogies and learn to laugh at negative experiences (Arthur & Kallick, n.d.). This strategy is extremely beneficial for adolescents as they love fun in learning (Knipe, 2007). One of the main objectives of adolescence is to go from dependence to independence (Coil, 2003, p. 105). Many middle school students do not know how to learn on their own (Kiddey & Robson, 2004). The teacher plans to give young adolescents the latitude as well as the structure to learn successfully. Opportunities are provided for students to build self-confidence, intrapersonal intelligence, decision-making and emotional intelligence (Appendices 6.28-6.31) to be able to survive in the 21st century.

The unit plan encompasses an extensive repertoire of educational practices that are claimed by researchers and experienced teachers to work well in the middle years of schooling. Interestingly these philosophies align with Bhagvad Gita, referred to as "spiritual dictionary" by Mahatma Gandhi (Yandamoori, 2008).

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