Connecting Equations to Graphs (Part 1)

5 min

Narrative

Throughout this lesson, students will use a context that involves two variables—the number of games and the number of rides at an amusement park—and a budgetary constraint. This Warm-up prompts students to interpret and make sense of some equations in context, familiarizing them with the quantities and relationships (MP2). Later in the lesson, students will dig deeper into what the parameters and graphs of the equations reveal. 

Launch

Arrange students in groups of 2. Give students a couple of minutes of quiet work time and then another minute to share their response with their partner. Follow with a whole-class discussion.

Student Task

Jada has $20 to spend on games and rides at a carnival. Games cost $1 each and rides are $2 each.

  1. Which equation represents the relationship between the number of games, xx, and the number of rides, yy, that Jada could spend money on if she spends all her money?

    A: x+y=20x + y = 20

    B: 2x+y=202x + y = 20

    C: x+2y=20x + 2y = 20

  2. Explain what each of the other two equations could mean in this situation.

Sample Response

  1. Equation C
  2. Sample responses: 
    • A: Jada spends $20 on games and rides, which are $1 each.
    • A: The combined number of games and rides that Jada enjoys is 20.
    • B: Jada spends $20 on games and rides, where games are $2 each and rides are $1 each.
Activity Synthesis (Teacher Notes)

Invite students to share their interpretations of the equations.

Most students are likely to associate the 20 in the equation with the $20 that Jada has, but some students may interpret it to mean the combined number of games and rides Jada enjoys. (This is especially natural to do for x+y=20x+y=20.) If this interpretation comes up, acknowledge that it is valid. 

Standards
Building On
  • A-SSE.1.a·Interpret parts of an expression, such as terms, factors, and coefficients.
  • A-SSE.1.a·Interpret parts of an expression, such as terms, factors, and coefficients.
  • A-SSE.1.a·Interpret parts of an expression, such as terms, factors, and coefficients.
  • A-SSE.1.a·Interpret parts of an expression, such as terms, factors, and coefficients.
  • A-SSE.1.a·Interpret parts of an expression, such as terms, factors, and coefficients.
  • A-SSE.1.a·Interpret parts of an expression, such as terms, factors, and coefficients.
  • HSA-SSE.A.1.a·Interpret parts of an expression, such as terms, factors, and coefficients.

20 min

10 min