4 Math in Motion Copyright © 2026 Pearson Education, Inc. Math in Motion (50 – 60 minutes) Learning Objective(s): Students will combine two or more functions using addition, subtraction, or multiplication in function notation. Students will interpret combined functions to model total costs in budgeting scenarios. Material needed: Student pages: Math in Motion Calculator Graphing software (optional) Lesson Procedure: Warm–Up 10 minutes Prompt: Imagine that you pay for gas and parking separately each day. If gas costs are modeled by one function and parking by another, how could you determine your total cost each day? Discuss: function, combine, total, evaluate Guided Instruction 15 minutes Present: scenario for Math in Motion. Example: A student is earning money from two part-time jobs. The earnings of one job are modeled by the function A(h) = 12h, and the earnings of the second job are modeled by B(h) = 8h + 20. How are the functions similar? How are they different? Both functions are linear and use the same variable, h, for hours worked over a period of time. A(h) is a fixed rate, while B(h) includes a fixed amount in addition to a calculation for hours that are worked. How would you calculate the total earnings if both jobs were worked on the same day? To find total earnings, the functions could be added. Review: key terms – function notation function notation: a way to represent the relationship between inputs and outputs Independent Practice 20 minutes Distribute: student activity Math in Motion Allow students to work individually or in pairs. Closure 10–15 minutes Review Answers: 1. T(x) = R(x) + P(x) = 2x2 + 15x + 40 2. T(2) = 78; cost of 2 days = $78 3. T(5) = 165; cost of 5 days = $165 4. a. T(3) = 103; W(n) = 103n; b. W(n) gives the total transportation cost for n weeks, assuming 3 days of use per week. This helps the student plan for multiple weeks. 5. a. The adjusted function gives a $10 discount for each day after 5 days of rideshare use; b. Td(x) = 2x2 + 5x + 90; T(6) = 202 and Td(6) = 192; the discount saves $10 on day 6. 6. a. Tr(x) = 2x2 + 10x + 40; b. Tr(4) = 112; after the reimbursement, the cost for 4 days is $112. 7. Sample answer: By having a single function that accounts for both costs, students can easily calculate how different choices affect the budget. This helps with planning and making smarter decisions to stay within spending limits. In other situations, such as managing food budgets, combining cost functions allows people to understand overall expenses and identify areas to save money or adjust spending. Discuss: How can combining functions help you manage budgets more effectively? What are other examples where combining functions could help?
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