MTH1W Culminating Assignment

Throughout this course, you explored various mathematical topics, investigated their importance, and learned to work with them. In this culminating assignment, you will complete four (4) tasks that assess your expertise in the course material.

Task 1: Principles of Mathematics

Consider the number sets integers, rational numbers, and real numbers. In one day, record at least 25 different numbers that you encounter in your everyday life. Your observations must include at least one of each set: integers, rational numbers that are not integers, and real numbers that are not rational numbers.

• Part A:
  In an organized table, record your 25 or more observed numbers in order, state where you observed that number, and classify it as an integer, a rational number that is not an integer, or a real number that is not a rational number.
• Part B:
  Write a paragraph that explains the importance of each of those three number sets. Your paragraph should explain why each number set is used, and its limitations that require the use of another set.
• Part C:
  Consider a person from a culture that counts in base-6. Assume that they use the number symbols 0, 1, 2, 3, 4, and 5. Write a paragraph to them that explains our base-10 system.
• Checklist:
  • I have shared my observations.
  • I have classified each number as a real number, a rational number, or an integer.
  • I have written a paragraph explaining the importance of each number set.
  • I have written a paragraph explaining the base ten system.

Task 2: Financial Literacy

Imagine that you need to save $12,000. In this task, you will create and analyze investments to reach this goal.

• Part A:
  Describe two possible financial goals for which you may require $12,000. Classify each as a want or a need. Do research to ensure that amount is enough for your goal.
• Part B:
  Create and describe three possible investments to reach your goal within five (5) years. Investment 1 is a simple interest investment with 3% annual interest. How much would you need to invest at the beginning? Investment 2 is a compound interest investment, with 3% annual interest compounded monthly. How much would you need to invest at the beginning?
  
  Investment 3 is a regular deposit in an account that earns 3% compound interest, compounded once per year. How much do you need to deposit, and how often will you deposit it, to reach your goal? State the details of the three investments and explain the pros and cons of each.
• Part C:
  Calculate and describe the total interest earned on each of your three investments. Explain your thinking and show your work.
• Checklist:
  • I have described a financial goal.
  • I have created a recurring payment, a simple interest investment, and a compound interest investment that reaches a goal.
  • I have calculated the interest earned on various investments.

Task 3: Geometry and Coding

Now it is time to connect your geometry and coding experience. Refer back to the Scratch program you used in Unit 3.

• Part A:
  Create a flow chart that could be used to solve a problem involving data, and one that could be used to solve a problem involving financial decisions.
• Part B:
  Create code that will ask for values of a and b, then graph the lines $y=ax+b$, $y=bx+a$, and announce their point of intersection. Include a screenshot or printout of your code, and an example of it in use.
• Part C:
  Write a paragraph sharing your thinking process, and any trouble you had while creating the code in parts A and B.
• Checklist:
  • I have created code that will draw a triangle according to given parameters.
  • I have created code that will find the point of intersection of two lines.
  • I have written a paragraph reflecting on my experience.

Task 4: Data and lines

Review the data you collected in Learning Activity 4.6: Data investigation.

• Part A:
  Consider the data for your 20 cities. Create three scatter plots: One graphing the latitude against the average temperature, another graphing the longitude against the average hours of daylight, and a third comparing annual precipitation to distance to closest international airport.
• Part B:
  For each of the three graphs, find the line of best fit using technology. State the equation of the line, and its coefficient of determination. Describe the relationship in each of the three plots.
• Part C:
  Select four of your cities, and plot their longitude on the x-axis and their latitude on the y-axis. Draw line segments connecting the four points (4 lines forming the outside of a quadrilateral, and 2 diagonals). Find the equation of the line that forms each of the line segments, and the point of intersection of the quadrilateral’s two diagonals. Show your work, and be sure to specify which points and lines you are describing.
• Checklist:
  • I have plotted points on a Cartesian plane.
  • I have found a line of best fit, and its coefficient of determination.
  • I have described a system of equations.
  • I have found the point of intersection of two lines.