Year 10 General Mathematics Student name: Student number: Teacher name: Mr Oneto, Mr Hellier, Ms. Stanton, Mr Baldry, Ms. McCarthy Due Date: Friday 28th May 2021 SubjectGeneral MathematicsTechniqueProblem-solving and modelling taskModule2 & 3TopicStatistics and Straight-line graphs ConditionsDuration4 weeks, including 5 lessonsModeWritten reportLengthup to 10 pages (please see back page for inclusions and exclusions in page and word count)maximum of 2000 wordsappendixes can include raw data, repeated calculations, evidence of authentication and student notes (appendixes are not to be marked).Individual/ groupIndividualOtherTurnitin: Submission page on Year 10 General Mathematics Canvas page.Resources availableThe use of technology is required, e.g. computer/internetspreadsheet program (Excel…)calculator (scientific or NON-CAS graphics)other software/technology (DESMOS, GeoGebra…)Context The odometer reading is one of the essential value factors that should be taken into consideration when purchasing a used car. As a rule of thumb, fewer kms make for a car with a potentially longer lifespan than a car with higher kms. Aussie’s now driving an average of 19,200 kms each year. So, a pre-owned car considered “average mileage”, which is about five years old, will have been driven around 96,000 km. TaskThe distance a car has travelled overall during its life is measured by an instrument on the dashboard called an ‘odometer’. A new car will usually have an odometer reading between 0 and 500 km (it may have been driven from the port or factory to the car yard), and much older cars can have odometer readings of over 300,000 km! Is there a linear relationship between the odometer reading of a car and its price? In this task, we are going to be looking at an estimated (or predicted) linear relationship between the ‘asking price’ (that is, how much a seller of a car wants) for a used car, and the distance that car has travelled in kilometres. To do this, we are going to collect some data, plot it on a scatter plot and use this to determine if a linear algebraic relationship exists. To complete this task complete the “Lead in task” attached.write a mathematical report following the scaffolding guidelines outlining the results of your investigation into the relationship between the odometer reading of a vehicle and its price. CheckpointsWeek 3 (7th May 2021): Email evidence of progress to your teacher of lead in task.Week 4 (14th May 2021): Email evidence of progress to your teacherWeek 5 (21st May 2021): Email evidence of progress to your teacherWeek 6 (28th May 2021): Submit final response as a hard copy via the Assignment box by 8.30amFeedback Authentication strategiesYou will have a unique set of data points from Carsales.com.auYour progress will be observed in class and documentation of your progress will be submitted at the indicated checkpoints.You will use plagiarism-detection software (Turnitin) for submission of your response.You must acknowledge all sources.You must submit a declaration of authenticity (see below)Your teacher will ensure a moderation process occurs.ScaffoldingThe approach to problem-solving and modelling must be used (see over page).Declaration of AuthenticitySTUDENT DECLARATION 1. I declare that the work shown in the following solutions is solely my own and that I have not copied any other student’s work nor have I given any solution or part solution to any other student. 2. I have submitted this assignment to turnitin.com which can be found on the Year 10 General Mathematics CANVAS page 3. I am familiar with the Assignment Policy in the Student record Book/Diary Signature Date_______ Approach to problem-solving and modelling Instrument Specific Marking Guide (ISMG) Problem-solving and modelling task (20%) PSMT Criterion: Formulate Assessment objectives 1. select, recall and use facts, rules definitions and procedures comprehend mathematical concepts and techniques 5. justify procedures and decisions by explaining mathematical reasoning The student work has the following characteristics: Marks documentation of appropriate assumptions accurate documentation of relevant observations accurate translation of all aspects of the problem by identifying mathematical concepts and techniques. 3–4 statement of some assumptions statement of some observations translation of simple aspects of the problem by identifying mathematical concepts and techniques. 1–2 does not satisfy any of the descriptors above. 0 Criterion: Solve Assessment objectives 1. select, recall and use facts, rules, definitions and procedures 6. solve problems by applying mathematical concepts and techniques The student work has the following characteristics: Marks accurate use of complex procedures to reach a valid solution discerning application of mathematical concepts and techniques relevant to the task accurate and appropriate use of technology. 6–7 use of complex procedures to reach a reasonable solution application of mathematical concepts and techniques relevant to the taskuse of technology. 4–5 use of simple procedures to make some progress towards a solution simplistic application of mathematical concepts and techniques relevant to the task superficial use of technology. 2–3 inappropriate use of technology or procedures. 1 does not satisfy any of the descriptors above. 0 Criterion: Evaluate and verify Assessment objectives evaluate the reasonableness of solutions justify procedures and decisions by explaining mathematical reasoning The student work has the following characteristics: Marks evaluation of the reasonableness of solutions by considering the results, assumptions and observations documentation of relevant strengths and limitations of the solution and/or model justification of decisions made using mathematical reasoning. 4–5 statements about the reasonableness of solutions by considering the context of the task statements about relevant strengths and limitations of the solution and/or model statements about decisions made relevant to the context of the task. 2–3 statement about a decision and/or the reasonableness of a solution. 1 does not satisfy any of the descriptors above. 0 Criterion: Communicate Assessment objective 3. communicate using mathematical, statistical and everyday language and conventions The student work has the following characteristics: Marks correct use of appropriate technical vocabulary, procedural vocabulary and conventions to develop the response coherent and concise organisation of the response, appropriate to the genre, including a suitable introduction, body and conclusion, which can be read independently of the task sheet. 3–4 use of some appropriate language and conventions to develop the response adequate organisation of the response. 1–2does not satisfy any of the descriptors above. 0 Criterion Marks allocatedResultFormulate Assessment objectives 1, 2, 5 4 Solve Assessment objectives 1, 6 7 Evaluate and verify Assessment objectives 4, 5 5 Communicate Assessment objective 3 4 Total 20 How to write a report Set out your PSMT with the following headings. Introduction Helpful video: Writing the introduction https://www.youtube.com/watch?v=CZDgmqmQ-Ds Write 2 – 3 sentences which explain what your report is investigating. Write in FUTURE tense and THIRD person. 1. Formulate Helpful video: How to write observations and assumptions Part 1 https://www.youtube.com/watch?v=rkp5MDeisIY Helpful video: How to write observations and assumptions Part 2 https://www.youtube.com/watch?v=1Yl9npOBbfU 1.1 Documentation of Observations Use dot points.Minimum of 2Observations are data or information needed to solve the mathematical problem.Observations must be documented, not just stated i.e. what impact does your observation have on the work you will be investigating?Use linking words such as ‘hence’, ‘therefore’, ‘thus’.. Here is an example of a documented observation: All the data points collected are a mixture of automatic and manual vehicles and therefore we will consider the transmission as having no effect on the price of the vehicle. 1.2 Documentation of Assumptions Use dot points.Minimum of 2Assumptions must be documented, not just stated i.e. what impact does your observation have on the work you will be investigating?Use linking words such as ‘hence’, ‘therefore’, ‘thus’. Here is an example of a documented assumption: The vehicles will have no structural damage therefore this will not effect the selling price of the vehicle. 1.3 Procedure Use PAST tense and THIRD personDot points or numbered sequenceThe plan should be complete. Someone should be able to read this section and repeat exactly what you have done without needing to refer to the task sheet. Here are the first few steps of the procedure: 1. Go to Carsales.com.au and collect the price and odometer reading from 20 vehicles 2. Created a scatterplot showing the price and odometer reading of the twenty vehicles. 3. ……… 1.4 Technology and formulae used State what technology you have usede.g. Microsoft Excel was used to organise data into tables and create graphs 2. Solve Helpful video: How to write a PSMT: Solve: Part 1 https://www.youtube.com/watch?v=bXUeLOvoz3Y Helpful video: How to write a PSMT: Solve: Part 2 https://www.youtube.com/watch?v=5wYpdwaTb_Q Helpful video: How to write a PSMT: Solve: Part 3 https://www.youtube.com/watch?v=WOhWbx9PNYc Clearly show your calculations and all the steps in your workingYou must use equation editor in Word: Helpful video: using Equation Editor in Word https://www.youtube.com/watch?v=QNOm03MFPK0 Present all graphs as expected: appropriate type of graph, titles, axis titles, appropriate scales.Ensure your solutions are accurate: check your work!Use tables to reduce white space.Are you able to verify your manual calculations using Excel? 3. Evaluate & Verify 3.1 Reasonableness of results Helpful video: Writing a PSMT: How to Evaluate the reasonableness of results. https://www.youtube.com/watch?v=gMq_7GekL_A How could you improve your results?Do you have any recommendations? 3.2 Documentation of strengths and limitations Helpful video: Writing a PSMT: How to evaluate strengths and limitations. https://www.youtube.com/watch?v=k4TAqchJrOg&t=17s Set up in a table Strengths – consider: What aspects of your solution make it useful?Was a solid data source used?Is it applicable to a real life situation? Limitations – consider: What prevents your solution from being useful?Is your solution limited to only a small context?Were any of your assumptions flawed? 3.3 Justification of decisions made using mathematical reasoning Helpful video: Writing a PSMT: How to justify your decisions with mathematical reasoning. https://www.youtube.com/watch?v=6fJtoxjHUnQ Consider: Do the solutions make sense? Are they what you expected?Could you confidently use your equation to predict the sale price of a vehicle with 100000 km? 4. Conclusion Summarises the entire task. Ensure you answer the question in the task, that is “Does a linear algebraic relationship exist between the odometer reading on a car and its price?” 5. Appendices Can contain calculations, diagrams, Excel formulas, screen shots, etc.Label your appendices as Appendix 1, Appendix 2, etc. 6. Reference List Correctly reference all sourcesUse: Citemaker (library website) to create your reference list (if any) Determining word length in a response Lead in activity Name:________________________ Grab your phone or a laptop with a browser, and go to the ‘Car Sales.com’ website by clicking on the following URL: https://www.carsales.com.au/ Choose a make and model of car from the following:Suzuki Swift,Mazda 2,Toyota Yaris,Hyundai i20. Select the ‘Used’ car tab;Set your search for ‘Queensland’ region only;Select vehicles ranging in age between the years 2010 and 2020 only (if that option is not available on the front page menu, you can set the date range later, after you have hit ‘Show Me Cars’Do not add any other ‘key words’. Choose 5 or 6 cars from the results and note down (a) the price of each car, and (b) the kilometres it has travelled (from the ‘Odometer’ field). Write your sets of these two data variables into the table below. Now… select a different make of car from the four makes above, repeat the process, select another 5 or 6 car prices and odometer readings and write these into the table. Repeat this until you have 20 sets of data filled in the table on the next page. Each of these 20 sets of data (car price and car odometer reading) we will refer to as ‘data points’. Data Point Km Travelled (‘Odometer’) ( Car Price ( )113 20813 500235 93311 99035025911 880461 00010 500569 7507 5006683221 9907887117 990825 00015 500970 19512 3881090 568938811831119 9801214 98116 9441323 50013 9901477 86312 0001584 16711 000166 70018 9001710 14416 990185436114 9901958 83812 00020112 3819 995 Complete the following activities relating to the data set you have collected from CarSales.com and the relationship between used car price and kilometres travelled. Understanding Linear Relationships Considering these two variables ( = Price of Used Vehicle and = Odometer Reading or ‘km travelled’), which of these do you think is the ‘independent variable’ and which is the ‘dependent variable’, and why? The independent variable is the odometer reading and the dependent variable is the priced of the used vehicle as the price is determined by km travelled. Use the graph paper on the next page to create a scatterplot with the 20 data points you have collected from CarSales.com. Look carefully at the overall pattern of the distribution of points on your scatterplot. Using your own visual judgement, draw a straight line of ‘best fit’ on your scatterplot that you think most closely approximates the trendline of your data. For example, if your scatterplot was as follows, you might use a ruler and a pencil to draw a line a bit like this: Scatterplot – Price of Used Vehicle and Odometer Reading of Used Vehicle Derive (work out) an algebraic equation for your ‘line of best fit’, in the form where is the gradient of the trendline (that is, the value we multiply ‘ by); and a fixed or constant value ‘ ’ that is the same for all the data points (that we add (or subtract) to the multiplied value). Use Excel yourself to compose an electronic version of the graph for your data Your Excel scatterplot should include each of: Labels and title for the scatterplot graph.trend line for the ‘line of best fit’ through the data; andthe algebraic linear equation that expresses the trendline. Insert a picture of your excel graph here. Look at your scatterplot graph and the trendline you have inserted. Using your Excel data as a guide, how much would you expect to pay (all other factors being equal), for a car that has travelled 100,000 km? (vi) What do each of the ‘ ’ and the ‘ values represent in your linear equation? (vii) What does the linear relationship between and mean in the context of buying a used car? (viii) What is the ‘constant’ (‘ ’) in your electronically generated linear equation, and what does this tell us about buying this type of used car in the local used car market?
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