Algebra I Task: Speeding Ticket Problem

Algebra I Task: Speeding Ticket Problem

Standards & Objectives

Academic standards
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions,...
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or...
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the...
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one...
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function...
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Essential and guiding questions: 
  • How did you calculate the cost of each ticket?
  • Would you need to calculate the 27 miles per hour? Why or why not?
  • How did you use the calculations in Part A to write an equation in Part B?
  • How did you define your variables in your equation? Why do the labels matter?
  • How does your equation relate to the scenario? Where is each part of your equation in the scenario?
  • Do the equations shared have the same solution? Explain.
  • Does your equation represent a function? Justify your reasoning.
  • How did you define the domain and range of your function? How does your domain and range relate to the scenario?
  • Could you receive a ticket for going 30.2 miles per hour? Explain. How does this relate to your domain and range?
  • How did you determine the speeds at which a driver is considered reckless?

Activity/Task Variations

Blooms taxonomy level: 
Differentiation suggestions: 

If students can’t get started….
Assessing Questions:

  • What is the question asking?
  • Describe what each number in your calculations represents. Where is the fee? Where is the cost charged for every mile per hour over the speed limit?
  • Talk me through how you would find the cost of a ticket.
  • How did you determine what to multiply the $8 by?
  • How do you know that the 27 miles per hour would not generate a ticket? or Why did you not calculate a number for the 27 miles per hour?

Advancing Questions:

  • How could you use your number sentences in Part A to help write an equation?
  • What do you notice is changing and what is staying the same in the scenario?
Extension suggestions: 

If students finish early….
Assessing Questions:

  • Show me how your equation relates to the scenario.
  • Why did you decide to use this equation?
  • How do you know that your equation represents a function?
  • How does your domain and range relate to the scenario?

Advancing Questions:

  • Group or pair students who have different equations
  • How are your methods similar and different? How are all of your equations related?
  • The mayor of Cautionville wants to change the fee for a regular speeding violation, but keep the same maximum cost and criteria (miles per hour over the speed limit) for distinguishing between a regular and reckless violation. Write an equation that would allow this to happen. Mathematically show how your equation fits the mayor’s criteria.