Vidhya_Radhakrishan_EDME394_Unit_and_Lesson_Sequence_Assignment 1

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EDME394 Vidhya Radhakrishan 220210439 Unit Code: EDME394 Assignment 1 University of New England

EDME394 EDME394 Assignment 1 Unit Plan Topic: General Mathematics Unit 1, Topic 1 - Consumer Arithmetic Description Financial literacy is a vital life skill that enables the students to have financial knowledge, skill and attitude to make wise financial decisions. Through the various learning activities in this unit, students will be connected to real-life scenarios, acquiring the knowledge to earn money in different ways and understand related issues like taxation and solving income-related problems. No lessons 7 lessons, each 60 minutes 3 lessons per week Unit learning outcomes By the end of this unit, students: • understand the concepts and techniques introduced in consumer arithmetic, algebra and matrices, and shape and measurement • apply reasoning skills and solve practical problems arising in consumer arithmetic, algebra and matrices, and shape and measurement • communicate their arguments and strategies when solving problems, using appropriate mathematical language • interpret mathematical information, and ascertain the reasonableness of their solutions to problems • choose and use Technology appropriately and efficiently.

EDME394 Unit Sequencing Component Title Estimated number of lessons Principle concepts and learning activities Earning an Income • Salary and wages Lesson 1 Key Concepts • Calculate weekly or monthly wage from an annual salary, wages from an hourly rate including situations involving overtime and other allowances and earnings based on commission or piecework (ACMGM002) Learning Activities • Students work in small groups to explore Fair work ombudsman's website and find different ways of earning Income , summarizing their findings in a table (Appendix 1.1). (Constructivist Theory). • Demonstrate how to calculate weekly, fortnightly, monthly, and yearly earnings. (Worked Examples) Example 1: (Powers,2018) Wendy earns $27.80 per hour. She works an 8-hour day • How much does Wendy earn for a 5-day week? • Wendy works for 48 weeks in one year. What is her annual wage? • Explain time conversion facts used to calculate earnings. (Appendix 1.2)

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EDME394 • Demonstrate how to use a spreadsheet to calculate wages/salary (Integrated Technology) . (Appendix 2.1) Student Activity: • Students complete the spreadsheet to calculate earnings. (Appendix 2.1) • Students solve the problem and swap their solutions to mark each other's work and suggest what was done well, clarify the misconception and suggest the next step. (Appendix 1.6) (A programmer is paid an annual salary of $56 230. Calculate the equivalent hourly, weekly, fortnightly, and monthly pay if an average week is 42 hours of work.) • Provide answer key and observe students ,clarifying any gaps in understanding. • Students practice more problems for homework from Cambridge Mathematics Book- Exercise 2A × (1,5,9.11,12,14,15,17,18,20)( Powers,2018 )

EDME394 Earning Income • Overtime and Special Allowance Lesson 2 Key Concepts • Calculate overtime and other allowances (ACMGM002) Learning activities • Discuss terms overtime and allowances and provide examples. (Constructivist Theory) • Watch Overtime and Special allowance tutorial (Integrated Technology) . Pause the video at different times and randomly picks students to summarize the calculation steps. • Demonstrate how to calculate overtime and special allowances. ( Learning by comparison). Example: (Powers,2018) Barak earns $24.20 an hour. He earns normal time during the week and time and a half during the weekends. Last week he worked 36 hours during the week and 8 hours during the weekend, calculate (a) His wage during the week (b) His wage on the weekend (c) His total wage (d) His yearly Income Correct Worked example

EDME394 Incorrect Worked example Student activity • Students examine the correct and incorrect examples,identify the differences and similarities, share and justify their findings. • Students practice more problems for homework from Cambridge Mathematics Book- Exercise 2C (1,3,5,6,9,11,15,17,18,19)( Powers,2018) Earning Income • Commission Lesson 3 Key Concepts • Calculate earnings based on commission (ACMGM002)

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EDME394 Learning activities • Discuss the terms commission and retainer, providing examples. • Revise concepts around percentages and modal examples (Appendix 2.2) . • Students practice a few problems on calculating the percentage of an amount (Appendix 2.3) . • Demonstrate how to calculate earnings involving commission in various contexts, relating it to students' prior knowledge on calculating the percentage of an amount. (Learning by Analogy) Example: (Powers,2018) Sam the salesman sold a car worth $28 400. Find his commission if he gets 5% of the selling price. Student Activity: • Students solve the problem and swap their solutions to make each other's workand suggest what was done well, clarify the misconception and suggest the next step. (Appendix 1.6) (A salesperson earns a monthly commission of 5% of sales on the first $1000 of sales, 4% on the next $2000 and 3.5% thereafter (ie the commission is based on a sliding scale). Calculate the pay for a month in which total sales were $4800.) (NSW Department of Education, 2019) • Provide answer key and observe students, clarifying any gaps in understanding.

EDME394 • Students practice more problems from Cambridge Mathematics Book-Exercise 2D (1,3,4,6,7,9,11,12) ( Powers,2018) Earning an income • Piecework, royalties, and Income from the government Lesson 4 Key Concepts • Calculate earnings based on piecework and royalties(ACMGM002) Learning activities • Discuss the terms piecework and royalties, providing examples. • Watch the following tutorials (a) How to calculate royalties (b) How to calculate piecework Pause the video at different points and randomly pick students to summarize the calculation steps. • Demonstrate how to calculate earnings involving piecework, royalties, and Income from the government in various contexts. (Cognitive Load Theory ) Worked Example 1: Emilio earns a royalty of 24% on net sales for writing a fiction book. There were $18640 net sales in the last financial year. What is Emilio's royalty payment? (Powers,2018)

EDME394 Partially completed example Mr Boris wrote a book called Selling Ice to Eskimos. The publisher pays him 4% royalties on sales. On the opening day his book sales earn $4532. Calculate his royalty. (Powers,2018) Worked Example 2: Noah is a tiler and charges $47 per square metre to lay tiles. How much will he earn in a room whose area is 14 square metres? Find his hourly rate if he works 6 hrs a day.

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EDME394 Partially worked example Larry Landscaper builds rock walls. He is paid $18 ⋅ 50 per linear metre. On a day he makes 14 metres of rock wall. (Powers,2018) (a) How much will he earn on this day? (b) Find his hourly rate if he worked for 7 hours.

EDME394 Student Activity: • Students complete the partially worked examples and share their answers. • Students complete an online quiz on commission, royalties, and piecework https://quizizz.com/admin/quiz/59ae936e99be86170041649c/u1-p3-commission- royalties-piecework-2020-2021 • Observe students and clarify gaps in understanding. • Students practice more problems for homework from Cambridge Mathematics Book- Exercise 2E (1,3,5,6,8,9,10,12,13) ( Powers,2018) Annual Leave Loading and Bonus Lesson 5 Key Concepts • Calculate annual leave loading and Bonus. Learning Activities • Students explore Employ sure Workplace Confidence and Fair work ombudsman's website for annual leave entitlement, including annual leave loading and share their findings. (Constructivist Theory) • Revise percentage concepts and provide examples (Appendix 2.2) . • Students to practice more percentage problems written on the board (Appendix 2.3).

EDME394 • Demonstrate how to calculate Annual Leave loading and Bonuses. (Learning by Analogy) Example 1: A business pays 17.5% holiday loading on 4 weeks normal pay. Calculate the holiday leave loading for Nicholas who earns $62490 normal pay for 4 weeks. (Powers,2018) Example 2: Fred receives an extra 8% of his annual salary as a Bonus at the end of the year. If his salary is $68900, what will be the Bonus. (Powers,2018) Student Activity • Students work in pairs and choose a range of professions and calculate • Annual leave loading • Total holiday pay • Weekly holiday pay • Observe students and clarify gaps in understanding

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EDME394 • Students practice assigned problems for homework from Cambridge Mathematics Standard Book- Exercise 2B (1,4,5,7,8,11) ( Powers,2018) • Exit Ticket: Students use the 3-2-1form (Appendix 1.5) to show their understanding of the topic. (NSW Department of Education,2021) Understanding tax, calculating tax deductions and taxable Income Lesson 6 - 7 Key Concepts • Identify allowable tax deductions • Calculate Taxable Income after allowable tax deductions are taken from gross pay Learning activities • Watch the Taxable Income video to understand the term income tax, Taxable Income, and tax deductions and share their understanding. • Students investigate types of deductions using the ATO website and summarise their findings ( Constructivist theory) • Conclude by explaining income tax, taxable Income, gross pay, net pay, deductions, refund, and liabilities.

EDME394 • Students work in pairs to • play the Payslip Label Game to familiarise themselves with the terms and their meaning. • locate the discussed terms on an Individual Payslip Allowable Tax Deductions • Watch the following tutorials on calculating deductions • Calculate total yearly deductions • Calculate travel cost as a deduction • Calculate depreciation as a tax deduction Pause the video at different points and randomly pick students to summarize the calculation steps. • Demonstrate how to calculate tax deductions. (Learning by comparison) Example 1: Sam can claim tax deduction based on number of business kilometres travelled in a year. Maximum kilometres allowed per car: 5000 Tax Deduction rate: 66 cents/kilometre Calculate the tax deduction if Sam travelled 3560 km in the year. (Powers,2018) Example 2: Syed has an investment property that contain furnishings valued 412600. The furnishings are an allowable tax deduction with the rate of depreciation of 15% p.a. How much can be claimed for depreciation in the first year?

EDME394 How much can be claimed for depreciation in the second year? (Powers,2018) Student activity: • Students compare the solutions and share the differences and similarities, justifying their findings. • Students practice more problems for homework from Cambridge Mathematics Standard Book- Exercise 2F (1,2,5,6,8,9,10) ( Powers,2018 )

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EDME394 Taxable Income • Revise the terms income tax, tax deductions, gross pay and net pay . • Watch the following tutorial on calculating taxable Income • Calculate taxable income p art 1 • Calculate taxable income part 2 • Pause the video at different points and randomly pick students to summarize the calculation steps. • Demonstrate how to calculate taxable Income. (Cognitive Load Theory)

EDME394

EDME394 Student Activity • Students complete the partially completed solutions and share their answers. • Students create three problems, swapping with their peers and solving each other's problems. In the end, students share their answer keys to mark the problems. • Observe students and clarify any gaps in understanding. • Students practice more problems for homework from Cambridge Mathematics Standard Book- Exercise 2G (1,2,4,6,8,9) (Powers,2018)

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EDME394 Assessment Proposed formative assessment 1. Questioning: Throughout the unit there is a continuous interaction between the teacher and students. While watching the tutorials in lesson 4 and lesson 7 , the teacher pauses the tutorial at different stages to ask students to summarize the steps to solve financial problems. 2. Peer feedback: In lesson 1 and lesson 3 , the students solve a given word problem and swap their solutions to mark each other's work. Students fill out the "Plus, Minus and what's next" form (Appendix1.6) to provide feedback. Justification for an assessment approach 1. Questioning provides students with opportunities to discuss, argue and express their opinion. allowing teachers with significant insight into the degree and depth of student understanding of the topic, providing immediate feedback to students on the gaps and misconceptions in their learning, simultaneously improving teaching strategies. (Victoria Education & Training,2019) 2. Peer feedback acts as a metacognitive tool, engaging students in the learning process and developing their capacity to evaluate their learning and skill development critically. (NSW Department of Education,2021) Peer Feedback also encourages collaborative learning, enhancing students' capacity for judgement. (AITSL,2017) Unit Rationale Learning theory Explain how the learning theory supports the learning activities Cognitive Load Theory Consumer Arithmetic unit involves understanding many financial terms, concepts, formulas, and problem-solving, increasing the load on the working memory. According to Miller (1956) & Kaliyuga (2006), even though the learners can process seven separate parts of information, the number significantly declines when it must be compared (as cited in Chinnappan & Chandler,2010). When students solve word problems, a high-level extraneous load is involved consuming a high proportion of limited working memory, leaving few resources for constructing schemas. (Chinnappan & Chandler,2010). To minimize the extraneous load, I have used worked examples (lesson 1) , including partially worked examples (lesson 4) , in my unit sequence. As a result, students can use their limited working memory to focus on the solutions, accruing the related schemas to solve similar problems in the future, reducing the cognitive load and improving problem-solving strategies. (Sweller, Merrienboer & Pass,1998). Also, integrating the modular approach into the worked solutions (lesson 1) has broken down the solution into meaning solution

EDME394 elements that can be isolated, reducing the load on the working memory. (Gerjet, Scheiter & Catrambone,2004) Learning by Analogy The analogical transfer is critical for problem-solving instruction as it enables the mapping of prior mathematical concepts to new problems resulting in the transfer of skills facilitating understanding of new mathematical concepts. (Ngu &Yeung,2012). In lesson 5 , I utilized the students' prior knowledge of percentages and mapped structural elements of calculating Annual leave loading to calculating an amount's percentage. Co nstructivist learning theory According to Vygotsky (1977), students learn better when learning experiences involve social interactions with peers and adults (Jones, Jones & Vermette,2010). Throughout the unit, there is continuous interaction between the teacher and students. In lesson 1 , students explore the ATO and Fairworks Ombudsman websites to understand and exchange ideas on the various financial terms like wages, salaries, royalties, tax deductions etc., relating to real-life scenarios. According to Bruner (1966), effective instruction engages and stimulates student minds by using what they already know and have experienced to teach new concepts (Jones, Jones & Vermette,2010). In lesson 3 , the student's prior knowledge of percentages was integrated to calculate commission. Technology-based learning environment Technology can provide videos, interactive worksheets, and instructional games, enabling teachers to create individualized instruction or meet students in the Zone of Proximal development, engaging them and assisting through scaffolding (Prieto,2016). Apart from modelling examples to solve financial scenarios, I have also included tutorials at different stages (lesson 6) , allowing students to understand solving financial problems at their own pace.

EDME394 Lesson Title: Salary and Wages Lesson overview In this lesson, students explore various ways to earn Income and learn mathematical skills to calculate salaries and wages. Students should: • Work in groups/pairs • Brainstorm and discuss • Use worked examples • Compare salary cards • Complete partially completed examples Materials/Equipment/Resources • Cambridge Maths Standard Book • Chart with the time- period conversions • IWB • Calculators • Laptops/iPad Online resources • Art Of Smart : Tutorials to understand the Financial calculations • Fair Work Ombudsman Website : E xplore salaries and wages for a range of jobs Outcomes • calculate weekly or monthly wage from an annual salary, wages from an hourly rate including situations involving overtime and other allowances and earnings based on Assessment area and strategies • Understanding the various financial terms • Observing students during classroom discussion and providing oral clarification and feedback on discussion and ideas presented in the sharing stage affirms students' responses to financial terms/scenarios.

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EDME394 commission or piecework (ACMGM002) • Calculations involving monthly, fortnightly, weekly, daily, or hourly pay rates from given salary. • Student participation in the calculation process, making comments and answering questions. • Students check each other's work and provide feedback. • Students complete the partially completed solution. • Students complete assigned problems from the Cambridge Maths Textbook (Powers,2018) Step 1 (15 minutes) • Students brainstorm different ways of earning Income, including wage, salary, commission, piecework,royalty Key learning activities/experiences/questions/discussions (a) Teacher starts a discussion on the student jobs and how they are paid? (i.e., hours worked, overtime or salary) (b) Think, pair, and share Students work in pairs to access various job profiles on Fair Work Ombudsman Website to find different ways of earning Income and summarise their findings in a table (Glossary of terms) (Appendix 1) Step 2 (25 minutes) • Demonstrate examples to calculate earnings from given salary and wage Key learning activities/experiences/questions/discussions • Demonstrate problems to calculate weekly, fortnightly, monthly, and yearly Income from o A salary o Wage ( Appendix 2.4) • Students summarize the steps to calculation. • Demonstrate how to use a spreadsheet to calculate wages/salary. (Appendix 2.1)

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EDME394 Step 3 (20 mins) • Assess student knowledge and clarify the gaps in understanding Key learning activities/experiences/questions/discussions • Challenge Question (Appendix 2.4) Students work in pairs and calculate the salary to decide on the best pay options, discussing the following questions? (Education World,2022) (a) Which one was the best salary option? Why? (b) How does the length of the workday affect the salary choice? (c) What is the difference in the daily salary between the highest-paying option and the lowest-paying option? • Partially worked problem (Appendix 2.6) Students complete the solution and share their answers. • Swap Solutions: Students solve the problem and swap their solutions to mark each other's work and suggest what was done well, clarify the misconception and suggest the next step. (Appendix 1.6) (A programmer is paid an annual salary of $56 230. Calculate the equivalent hourly, weekly, fortnightly, and monthly pay if an average week is 42 hours of work.) (NSW Department of Education, 2019) Lesson Evaluation • Working in groups/pairs in Step 1 created an environment for students to contribute, share and compare their learning with the class. (Killen,2009). Did I spend more time in Step 1? • In step 2 are students able to summarize the calculation steps. Worked examples act as analogies reducing the cognitive load, decreasing mathematical errors. (Sweller, Ayers& Kalyuga,2011) • In Step 3 do students apply their knowledge appropriately to mark peer solutions? Homework • Students complete the spreadsheet and discuss the answers in the next lesson • Students complete the assigned problems from Cambridge Standard Math Textbook. (Powers,2018) Exercise 2A – 1,2,4,8,9,10,13,14.18,22,24)

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EDME394 Appendix 1 1.2 Ways of earning Term Definition Examples Advantages Disadvantages Salary Wages Commission Piecework Overtime Royalties 1.3 Time period conversions 1 year = 52 weeks 1 year = 26 weeks 1 year = 12 months 1 fortnight = 2 weeks 1.4 Types of Deductions Expenses Definition Examples Work-related expenses Self-education expenses Travel expenses Clothing expenses Tools gifts 1.5 Exit Ticket (3-2-1 form) (NSW Department of Education,2021) Name three things you learnt in the lesson today List 2 questions you have about the learning today Give one reason why it is essential to learn about Annual leave loading and Bonus 1.6 Plus, minus and what next (AITSL,2017) Plus Minus What's next

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EDME394 Appendix 2 2.1 Calculate wages and salaries on spreadsheet 2.2 Calculating Percentage Example 1 Find 12.5% of $340 12.5% of 340 (Convert % into decimal) =0.125 × 340 =$42.5 Example 2: Find 4% of $640 4% of $640 (Convert % into decimal) =0.04 × $640 =$25.60 2.3 Percentage worksheet 1. What is 40% of $300 2. What is 4% of $5467? 3. What is 11.5% of $2880?

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EDME394 2.4 Worked Examples Example 1: (Powers,2018) Timecard – Sam Solution:

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EDME394 Example 2: (Powers,2018) Dylan earns a salary of $564885 per annum. He is paid fortnightly. • How much does he receive each fortnightly? Assume there are 52 weeks. • What is his hourly rate if he works 8 hours a day for a 5-day week? Solution: 2.5 Challenge Question (Education world,2019) Which salary is best You are newly hired store manager and must choose from the offered salary options. Determine the best choice based on a 5 day work week. Calculate the monthly salary (based on four weeks per month) and the annual salary (based on 52 weeks per year) for each pay option for an eight-hour workday. Pay Periods Pay Option A Pay Option B Pay Option C Pay Option D Eight-Hour Day $255.00 $96.00 $75.00 $90/day

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EDME394 2.6 Partially worked problem (Powers,2018) 1 year = 52 weeks 1 year = 26 weeks 1 year = 12 months 1 fortnight= 2 weeks Harrison is a civil engineer who works 6 hours a day for a 5 - day week and earns a salary of $1500 per week a) What is Harrisons hourly wage? b) How much does he receive per fortnight? c) How much does he receive per year? Harrison's Salary Per week = $1500 Harrison's wage per day = $1500÷_____ =$300 Harrisons hourly wage =______÷______ =$50 Harrisons fortnight pay =1500×___ =$____ Harrison's yearly salary =1500×____ =$7800

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EDME394 References Australian Institute for Teaching and School Leadership [AITSL]. (2017). Peer feedback . Retrieved from https://www.aitsl.edu.au/docs/default-source/feedback/aitsl- peer-feedback-stratedy.pdf?sfvrsn=372dec3c_2 Chinnappan, M. & Chandler, P. A. (2010). Managing cognitive load in the mathematics education . Australian Mathematics Teacher, 66 (1), 5-11. Education world(2022). Lesson idea: Salary Math . retrieved from https://www.educationworld.com/a_lesson/math-lesson-salaries.shtml Gerjets, P., Scheiter, K., & Catrambone, R. (2004). Designing instructional examples to reduce intrinsic cognitive load: Molar versus modular presentation of solution procedures . Instructional Science, 32(1-2), 33-58. doi:10.1023/b: truc.0000021809.10236.71 Goos, M. (2010). Using Technology to support effective mathematics teaching and learning: what counts? Published in the proceedings of the Australian Council for Educational Research Conference, Camberwell, Victoria, January 2010. Jones, K., Jones, J., & Vermette, P. (2010). The constructivist mathematics classroom, Mathematics Teaching , 219, 33-35. Killen, R. (2009). Effective Teaching Strategies . South Melbourne, Victoria: Cengage Ngu, B. H. (2010). Analogical approach to facilitate learning of trigonometry problems . Reflections, 35(1), 10-13. Ngu, B. H., & Yeung, A. S. (2012). Fostering analogical transfer : The multiple components approach to algebra word problem solving in a chemistry context . Contemporary Educational Psychology, 37(1), 14-32. doi: http://dx.doi.org/10.1016/j.cedpsych.2011.09.001

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EDME394 NSW Department of Education. (2019). Mathematics Stage 6 . Retrieved from https://education.nsw.gov.au/content/dam/main-education/teaching-and- learning/curriculum/key-learning-areas/mathematics/media/documents/ms-f1- money-matters-sample-unit-s6.docx NSW Department of Education. (2021). Learning Activities: Exit Ticket . Retrieved from https://app.education.nsw.gov.au/digital-learning- selector/LearningActivity/Card/543 NSW Department of Education. (2021). Peer and self-Assessment for students . Retrieved from https://education.nsw.gov.au/teaching-and-learning/professional- learning/teacher-quality-and-accreditation/strong-start-great-teachers/refining- practice/peer-and-self-assessment-for-students Powers,GK.(2018). Mathematics Standard: Earning and Managing Money . Sydney Australia: Cambridge. Prieto, Jaime. (2016). Accommodating Students Different Learning Styles with the Use of Technology. Capstone Projects and Master's Theses. 35.Retrived from https://digitalcommons.csumb.edu/caps_thes_all/35 Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive load theory. New York, NY: Springer. doi:10.1007/978-1-4419-8126-4. Sweller, J., van Merrienboer, J. G., & Paas, F. (1998). Cognitive architecture and instructional design . Educational Psychology Review, 10(3), 251-296. DOI: 10.1023/a:1022193728205 VICTORIA Education and Training. (2019). High Impact Strategies . Retrieved from https://www.education.vic.gov.au/school/teachers/teachingresources/practice/i mprove/Pages/hits.aspx

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