代写Mathematical Methods代做留学生Matlab程序

Subject   Year 10 Pre-Mathematical Methods

Technique   Problem-Solving and Modelling Task

Topic   Functions and graphs

Conditions
Duration	5 Weeks, including 6 hours class time
Mode	Written Report	Length	Up to 10 pages and 2000 words, excluding appendices
Individual/ group	Individual	Other	N/A
Resources available	The use of technology is required, e.g. non-CAS graphics calculator, spreadsheet program, Desmos and/or other mathematical software.

Context

Ipswich City Council has decided to build a new skate park in the land opposite West Moreton Anglican College. You have been appointed as the architect to design a skate park that is both fun and safe. To ensure you are building both a fun and safe skatepark, the following guidelines have been set by the council:

• The skatepark must consist of at least 3 different sections, including one ramp.

• The height of the ramp should not change more than 1.5m per horizontal 50cm (to avoid skaters in freefall)

• The skatepark must consist of at least 3 different types of mathematical relationships. eg parabola, circle

• The skatepark must have areas of both high-speed and low-speed

• The skatepark is a maximum of 65mm in length

• The skatepark is continuous everywhere

• Transitions between the sections are reasonable for skating (consider the smoothness between functions)

Task

Design a cross section of a skatepark using at least 3 different types of mathematical relationships, justifying how you developed each to meet the guidelines set by the council.

You are required to provide fully labelled images of your skatepark, using appropriate technology.

The stages of the problem-solving and mathematical modelling approach should inform. the development your response. This is provided in the scaffolding workbook.

To complete this task, you must:

 Respond with a range of understanding and skills, such as using mathematical language, appropriate calculations, tables of data, graphs and diagrams.

 Provide a response to the context that highlights the real-life application of mathematics.

 Respond using a written report format that can be read and interpreted independently of the instrument task sheet.

 Develop a unique response.

 Use both algebraic procedures and technology.

Stimulus
Consult your textbook and your class notebooks for key notes and examples.
Checkpoints		Teacher
2 Weeks after start: Students show evidence of their progress to their teacher (preliminary models developed and formulate section written).
3 Weeks after start: Students submit a draft for feedback (via NEST).
4 Weeks after start: Feedback of a general nature is provided to students, but no individual corrections are made. A summary of class feedback is provided.
5 Weeks after start: Students submit their final response via NEST.
Criterion	Marks allocated	Result
Formulate Assessment objectives 1, 2 and 5	4
Solve Assessment objectives 1 and 6	7
Evaluate and verify Assessment objectives 4 and 5	5
Communicate Assessment objective 3	4
Total	20

Authentication strategies

The teacher will provide class time for task completion.

Students will each produce a unique response by using different functions to model their skatepark

Students will provide documentation of their progress at indicated checkpoints.

Students must submit a declaration of authenticity and acknowledge all sources.

The teacher will ensure class cross-marking occurs.

An approach to problem-solving and mathematical modelling

Once students understand what the problem is asking, they must design a plan to solve the problem. Students translate the problem into a mathematically purposeful representation by first determining the applicable mathematical knowledge that is required to make progress with the problem. Important assumptions, variables and observations are identified and justified, based on the logic of a proposed solution and/or model. In mathematical modelling, formulating a model involves the process of mathematisation — moving from the real world to the mathematical world.

Students select and apply mathematical knowledge previously learnt to solve the problem. Possible approaches are wide-ranging and include synthesising and refining existing models, and generating and testing hypotheses with primary or secondary data and information, to produce a complete solution. Solutions can be found using algebraic, graphic, arithmetic and/or numeric methods, with and/or without technology.

Once a possible solution has been achieved, students need to consider the reasonableness of the solution and/or the utility of the model in terms of the problem. They verify their results and evaluate the reasonableness of the solution to the problem in relation to the original issue, statement or question. This involves exploring the strengths and limitations of the solution and/or model. Where necessary, this will require going back through the process to further refine the solution and/or model. In mathematical modelling, students must check that the output of their model provides a complete solution to the real-world problem it has been designed to address. This stage emphasises the importance of methodological rigour and the fact that problem-solving and mathematical modelling is not usually linear and involves an iterative process.

The development of solutions and/or models to abstract and realworld problems must be capable of being evaluated and used by others and so need to be communicated and justified clearly and fully. Students communicate findings logically and concisely using mathematical and everyday language. They draw conclusions, discussing the results, strengths and limitations of the solution and/or model. Students could offer further explanation, justification, and/or recommendations, framed in the context of the initial problem.