IB Math: AI SL

Math AI SL: Projects, concepts, tool kit tasks.

Task: Exponential Modelling (Real World Application Project)

As we have completed our study of sinusoids, we can use our knowledge to apply it to the real world around us. We should now understand that any variable that is cyclical, harmonic, oscillating, or periodic in nature can be modelled graphically by a sine or cosine wave. There are countless applications of sinusoidal modelling in real life. Some of these applications include:

• Changes in Temperature over time
• Hours of daylight over time
• Population growth/decay over time
• Ocean wave heights (high and low tides) over time
• Sound waves
• Biorhythm waves
• Electrical currents
• Ferris wheels and roller coasters
• Tsunamis and tidal waves
• Earthquakes
• Wheels, Trampolines, Swings

TASK:

• Your task is to investigate real-world phenomenon that can be modelled by a sine/cosine function.
• You must research and collect data, develop a predictive model, graph it, and type the whole process in MS-Word Document. You will be given the freedom to choose any topic, and the freedom to be as creative and outside-the-box with this project.
• This project should be done individually by each student.
• This exploration will be worth 20 points and will assessed through the Criteria notes (Criteria-A to E) as shared with you all.

Task Details:

• Collect no less than 40 real-world data points that can be modelled sinusoidally. The more data, the better and its recognition on acquiring the best marks!
• A predictive model of the format y = Asin(Bx + C) + D and y = Acos(Bx + C) + D for the data must be developed manually by hand using algebraic methods & calculations.
• Compare & contrast the two models you came up with. Hence verify your models with use of technology. These models could be used to predict outcomes into the future.
• A neatly organized graph of the original data, and a graph of your developed model must both be embedded in your presentation. To produce these graphs, you may use your graphing calculators, the GeoGebra app, or you may draw the graphs yourselves.
• Tables generated, diagrams/graphs processed must be presented well in order. All the Math Equations must be typed in MS-Word Document alone using the ‘Math Equation’ Editor.
• A reflection must be included in your process which should be in the form of interpreting the results obtained, possible extensions of your chosen Math processes, limitations, strengths/weaknesses discussed.
• This reflection should be neatly and logically written/typed with no grammatical errors and in mathematical contexts and justifications, and should summarize your experience in doing this project. What did you learn? What did you enjoy or dislike? What would you change? How well did you work it out? Etc.

Example Project Ideas for reference and understanding:

Math Sinusoidal Function – Grade 11 Real Life Application

Sinusoidal Function Project: The Pogo Stick

The whole exploration should not be more than 4-6 pages excluding your graphs, diagrams, tables. Bibliography should be included in the end added by Appendix or can be put as footnotes instantly in the same page down wherever used/cited.

Math AI SL – Outline Topic Form

Introduction Paragraph:

• Introduction of topic & the rationale for choosing the topic – include why you are interested in the topic (personal engagement).
• Include any necessary background information.
• Clearly state the topic and the goal of your paper (paper must reflect the goal – goal clearly spells out what steps you will take).

Body Paragraph 1:

1. ---

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   How are you going to collect your data? Or explain where you obtained your data. How do you know that your data is reliable? Why did you only collect this amount of data?

   E.g. interviews, observations, questionnaires, constructing diagrams, playing games, experimenting.

   From: school, home, shops, journeys, newspapers, magazines, books, libraries, photographs, television, video, the internet, etc.

2. Presenting your raw data.
3. Organize your raw data into tables and graphs.
4. Discussion of what the data reveals and what it leads you to do.

Body Paragraph 2:

Which mathematical processes are you going to use?

E.g. sequences and series, inequalities, sets, Venn diagrams, trigonometry, 2-D and 3-D shapes, scatter diagrams, lines of best fit, frequency tables, graphs, percentiles, measures of central tendency and dispersion, probability, correlation coefficients, functions, currency conversions, interest, loan schemes, modeling, etc.

1. Transition sentence – explain that the data has lead you to use this math process.
2. Explain the math process and what you hope to achieve with this process.
3. Define necessary math terms before discussing the math process.
4. Clearly and thoroughly explain the math process.
5. Reflect on the math process. Discuss what the math process reveals (implications). Was there something you could have done differently to make the process better? Did the outcome of the math process lead you to try another method? (If so, do the second math process.) Reflect on the possible limitations of your IA. Make links to different areas of math.

Conclusion Paragraph:

1. Restate your goal and how the task has helped you to achieve your goal.
2. End with what this task has prompted you to do next or to explore next.