Algebra I Task: Speeding Ticket Problem

Algebra I Task: Speeding Ticket Problem

Standards & Objectives

Academic standards
CCSS.Math.Content.HSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions,...
CCSS.Math.Content.HSA-CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or...
CCSS.Math.Content.HSA-REI.A.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the...
CCSS.Math.Content.HSF-IF.A.1
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...
CCSS.Math.Content.HSF-IF.B.5
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: 
Understanding
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.