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YEAR 9 MATHEMATICS – SA5 - ASSIGNMENT – TERM 3, 2022 Student Guide: How to use the Problem Solving and Modelling approach Formulate Describe how you plan to solve the problem and document any appropriate assumptions, observations, and variables. You will need to: Identify the variables you will be using – either given to you or you have researched, yourself Document your observations Document your assumptions Outline the steps you plan to take to solve this problem Create a table to explain the Mathematics you will use to solve this problem Identify the technology you used and how or why you used it Solve Apply the concepts, techniques and steps you discussed to solve the problem. It is important for you to show the highest level of mathematical technique you can achieve. Remember to use your observations and assumptions. All graphs must be digitally produced. Determine a rate that is “reasonable” Convert all rates to the same units Convert all rates to a mathematical model (equation) Create graphs using the equations you have developed Interpret your graphs to determine whether any of the claims are “reasonable” Evaluate and Justify Is your solution reasonable and valid? Make a judgement about your response. Have you shown all the necessary calculations and verified all of your solutions and conclusions? Consider any issues that may be relevant. Is there another way you could determine a rate that is “reasonable”? • Refer to the “Stimulus” in the task sheet for ideas • How does this other way compare with your original method? • Does this other way lead you towards the same conclusion? Evaluate your observations, assumptions and results • Is there anything in your observations – that if it was different – it would change your results? • Is there anything in your assumptions – that if it was different – it would change your results? • Is your final conclusion sensible and realistic? Discuss the strengths of your method to solve this problem Discuss the limitations of your method to solve this problem Refine where necessary (can you make your results more accurate?) Justify your decisions Communicate Ensure you show all working including relevant formulas Round all answers to 2 decimal points Include appropriate units of measure Ensure your report has an Introduction, Body and Conclusion Ensure your report can be read independently of the task sheet Check you have answered the original problem posed YEAR 9 MATHEMATICS – SA5 - ASSIGNMENT – TERM 3, 2022 - PAGE 1 Brisbane School of Distance Education Task Sheet - Assignment Subject 9 Mathematics Class name Student name Teacher name Task title Draft due date Final due date Dripping down the drain 5pm Wednesday 31 st August 5pm Monday 12th September Technique Problem solving and modelling task Mode Written: up to 10 pages, max 1000 words (excl. Appendices) Text type Mathematical Report Duration 3 weeks Task purpose Apply the problem-solving and modelling approach (formulate, solve, evaluate and communicate) to investigate and model a situation to formulate a conclusion. Explore the relationship between graphs and equations corresponding to simple rate problems. Sketch linear relations. Context Water is a limited, precious resource. Wasting water is environmentally irresponsible and increases a household’s water bill. Governments run awareness campaigns to encourage citizens to fix leaking taps and therefore decrease wasting water. The following three water awareness claims have been made by government agencies in different parts of the world: 1 2 Another source states “One slowly dripping tap can waste 9,000 litres of water a year …” 3 Sources: 1 https://twitter.com/cpcb_official/status/1082979006570319877 2 https://www.southwestwater.co.uk/save-water/top-tips/ 3 https://www.qld.gov.au/environment/water/residence/use/home/leaks#:~:text=One%20slowly%20dripping%20tap%20can,and%20equipment%20in%20good%20condition. https://www.southwestwater.co.uk/save-water/top-tips/ https://www.qld.gov.au/environment/water/residence/use/home/leaks#:%7E:text=One%20slowly%20dripping%20tap%20can,and%20equipment%20in%20good%20condition YEAR 9 MATHEMATICS – SA5 - ASSIGNMENT – TERM 3, 2022 - PAGE 2 Task details Your task is to use your mathematical knowledge of rates, equations and graphs to determine whether any of the three “Dripping tap” claims are reasonable. You need to create a formal mathematical report that includes the following: • Outline your plan to determine whether any of the “Dripping tap” claims are reasonable. • Develop a mathematical model (an equation) for the loss of water from a dripping tap • Use your mathematical model to sketch a graph of the loss of water from a dripping tap • Interpret your model to determine whether any of the “Dripping tap” claims are reasonable. • Justify your conclusions mathematically. Scaffolding • You are required to use the problem-solving and modelling approach – see the “Student Guide” provided in Blackboard for further information. • Your solution needs to be communicated using a presentation genre (introduction, body and conclusion) which can be understood independently of this task sheet – see the “Report Template” provided in Blackboard. Stimulus Some recommended resources: • How much water are you wasting?: https://dorringtonplumbing.com.au/water-wasted-from-leaking-tap/ • Experiment – Water leaking from a dripping tap: https://www.youtube.com/watch?v=sCwJwTBLdIE • Convert water weight to millilitres: https://calculator-converter.com/milliliters-to-grams.htm • Convert drips to ml: http://convert-to.com/conversion/volume/convert-drop-to-ml.html • Desmos: https://www.desmos.com/calculator Due Dates • 5pm Wednesday 31st August: Students submit their draft to Draft via Blackboard dropbox. • 5pm Monday 12th September (Due date): Students submit their final to Final via Blackboard dropbox. Conditions • Students are encouraged to use the BrisbaneSDE Writing Guide. • Students are permitted to access computers, student notes, books and / or learning materials. • Students are expected to use technology to complete this assignment, including calculators, spreadsheet programs such as Microsoft Excel and the internet for research. Student declaration By submitting this item, I declare that the work submitted: • is my own work and has not been written by any other person, • contains no plagiarised material, and has not been obtained from any other source except where due acknowledgement has been made. https://dorringtonplumbing.com.au/water-wasted-from-leaking-tap/ https://www.youtube.com/watch?v=sCwJwTBLdIE https://calculator-converter.com/milliliters-to-grams.htm http://convert-to.com/conversion/volume/convert-drop-to-ml.html https://www.desmos.com/calculator YEAR 9 MATHEMATICS – SA5 - ASSIGNMENT – TERM 3, 2022 - PAGE 3 Marking Criteria Student Name: Teacher Name: UF: PSR: Overall Grade: A B C D E Un de rs ta nd in g an d Fl ue nc y Co m m un ica te Mathematical language and symbols • Accurate 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. • Use of technical vocabulary, procedural vocabulary and conventions to develop the response • Organisation of the response, including a suitable introduction, body and conclusion. • Use of some appropriate language and conventions to develop the response • Adequate organisation of the response • Use of everyday language to develop a response • Basic organisation of the response • Unclear and disjointed organisation of the response. Fo rm ul at e Conceptual Understanding • Accurate translation of all aspects of the problem by identifying mathematical concepts and techniques • Explanation of appropriate assumptions • Accurate explanation of relevant observations • Translation of simple and complex aspects of the problem by identifying mathematical concepts and techniques • Statements of appropriate assumptions • Statements of relevant observations • Translation of simple aspects of the problem by identifying mathematical concepts and techniques • Statement of some assumptions • Statement of some observations • Translation of some aspects of the problem by identifying mathematical concepts and techniques • Statement of an assumption or an observation • Statement of an assumption, observation or translation of an aspect of the problem Procedural Fluency • Appropriate, accurate use of facts, definitions, mathematical concepts and procedures to reach a valid conclusion • Considers assumptions and observations when accurately determining various, verified rates of water loss • Considers assumptions and observations when accurately constructing linear graphs for various, verified rates of water loss • Use of facts, definitions, mathematical concepts and procedures to reach a reasonable conclusion • Accurately converts all rates to the same units • Accurately constructs linear graphs for multiple rates • Use of facts, definitions, mathematical concepts and procedures to make progress towards a conclusion • Converts rates to the same units • Constructs a linear graph • Some use of facts, definitions, mathematical concepts and simple procedures • Calculates a rate or constructs a linear graph • Partial use of facts, definitions, mathematical concepts or simple procedures • Attempts to calculate a rate or construct a graph Pr ob lem -S ol vi ng an d Re as on in g So lve Problem-solving approach • Appropriate, systematic application of the problem-solving and modelling approach (formulate, solve, verify , evaluate) • Application of the problem-solving and modelling approach (formulate, solve, evaluate) • Attempts to methodically formulate, solve and evaluate • Some attempt to methodically solve the problem • Disjointed attempt to solve the problem Mathematical modelling • Considers assumptions and observations to develop accurate mathematical models for various, verified rates of water loss • Develops accurate mathematical models (linear equations) for all rates • Develops a mathematical model (linear equation) that matches a rate • Develops an equation • Attempts to develop an equation Ev alu at e a nd v er ify Reasoning and justification • Evaluation of the reasonableness of the solution by considering the results, assumptions and observations • Explanation of relevant strengths and limitations of the model and solution • Logical justification of decisions and/or