2.10 Sports statisticians: Working with systems of equations
Essential question: How can using elimination or substitution in a system of equations determine important statistics in sports?
Students will solve real-world problems involving systems of equations by using either the substitution or the elimination method.
- Basketball statistics worksheet (Includes answer key.)
- Overhead projector and pens
- Overhead transparency
Time required for lesson
Approximately 40 minutes
- (5 minutes) As a class, review with the process it takes to solve a system of equations using the substitution method. Example:
2x + 3y = 1 2x + 3(3x + 15) = 1 -3x + y = 15 → y = 3x + 15 2x + 9x + 45 = 1 11x + 45 = 1 11x = -44 x = -4
*Once the class has found the value for x, plug in this value to either equation and solve for y. The system of equation has one solution (-4, 3)
- (5 minutes) Using the same system of equations, solve using the elimination method. Example:
2x + 3y = 1 → 3(2x +3y =1) → 6x + 9y = 3 -3x + y = 15 → 2(-3x + y = 15) → -6x + 2y = 30 11y = 33 y = 3
*Once the class has found the value for y, plug in this value to either equation and solve for x. The system of equation has one solution (-4, 3)
- (10 minutes) Using the basketball scenario worksheet, have the students work cooperatively to solve the system of equations on the statistics on basketball players Chris Paul and Deron Williams. (For more information on these players, see the ESPN.com profile pages for Deron Williams and Chris Paul.) Students should be prepared to share their equations and the process they used to solve for the total number of 2-point and 3-point field goals for the 2007-2008 season.
- (10 minutes) Ask for a volunteer to come to the overhead and explain the system of equations they used to solve these real-world problems and the meaning of the solution to these problems. Ask other volunteers to come to the overhead and explain different approaches to solving these problems.
- (5 minutes) Answer the additional questions on the worksheet.
- (5 minutes) Use the career information below to discuss how the ability to solve systems of equations may be relevant in the careers of statisticians and accountants.
Some of the information below comes from the Bureau of Labor Statistics’ Occupational Outlook Handbook.
- Statisticians work in many different areas, such as analyzing data collected from experiments in science, determining the number of households that watch a television show, and surveys measuring unemployment for the government. Statisticians design many surveys and set the procedures to be followed from how to sample the population to the questions being asked. Then using computers, they analyze the data collected and summarize and present the results of the data. Systems of equations can help with the summarizing of specific data.
In basketball, statisticians are used to help make sure that the team they work for does not overpay for a player, and to find the players that can best play in that team’s style of play. Statisticians look at statistics for players over their entire college and professional careers to decide which players the team should attempt to add to their team. Based on what a statistician can infer, statistics can also help to determine how much money a team will offer the player. These statistics will be used to predict the future statistics of the player for the upcoming season.
- Education: Master’s degree in statistics or mathematics
- Pay: $37,000 - $108,000
- Growth: Average growth; 9% increase over the next 10 years
- Accountants record and maintain the financial records of a company. Accountants may analyze the financial statements of the company, or analyze the cost of different items and provide feedback to executives so the executives can make informed financial decisions. Systems of equations can help with the analysis of these costs.
- Education: Bachelor’s degree in accounting
- Pay: $42,000 - $72,000
- Growth: Faster than average growth; 18% increase over the next 10 years
North Carolina curriculum alignment
Grade 9–12 — Algebra 1
- Goal 4: Algebra - The learner will use relations and functions to solve problems.
- Objective 4.03: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results.
- Next: 8th grade math