Planning a Party

5 min

Narrative

This Warm-up elicits the idea that an equation can contain only letters, with each letter representing a value. It also reminds students that an equation is a statement that two expressions are equal, and that different expressions could be used to represent a quantity. Later in this lesson and throughout the unit, students will create, interpret, and reason about equations with letters representing quantities.

Launch

Arrange students in groups of 2. For the last question, ask each partner to come up with a new equation.

Student Task

Here are some letters and what they represent. All costs are in dollars.

  • mm represents the cost of a main dish.
  • nn represents the number of side dishes.
  • ss represents the cost of a side dish.
  • tt represents the total cost of a meal.
  1. Discuss with a partner: What does each equation mean in this situation?
    1. m=7.50m=7.50
    2. m=s+4.50m = s + 4.50
    3. ns=6ns = 6
    4. m+ns=tm + ns = t
  2. Write a new equation that could be true in this situation.

Sample Response

  1. Sample response:
    1. A main dish costs $7.50.
    2. A main dish costs $4.50 more than a side dish.
    3. Ordering nn side dishes at ss dollars each costs $6.00.
    4. The total cost of the meal is the cost of a main dish plus the cost of nn side dishes at ss dollars. 
  2. Sample responses:
    • n=2n=2
    • m−s=4.5m-s=4.5
    • m+6=13.5m + 6 = 13.5
Activity Synthesis (Teacher Notes)

Invite students to share their interpretations of the given equations and the new equations that they wrote. Then discuss with students:

  • "What is an equation? What does it tell us?" (An equation is a statement that an expression has the same value as another expression.)
  • "Can equations contain only numbers?" (Yes.) "Only letters?" (Yes.) "A mix of numbers and letters?" (Yes.)
  • "The last question asked you to write an equation that could be true. Could this equation be true: m+5=tm + 5 = t? How do you know?" (It could be. Example: If mm is 7.50 and tt is 12.50, then the equation is true.)
  • "When might the equation be false?" (Example: If mm is 7.50 and tt is anything but 12.50, or if the value of tt is not 5 more than mm, then it is false.)
  • "One equation tells us that a main dish is $7.50. Another equation tells us that it is equal to the expression s+4.50s + 4.50. Could both be true? Are they both appropriate for expressing the cost of a main dish?" (Yes. The first one tells us the price in dollars. The second tells us how the price compares to a side dish.)

Math Community

After the Warm-up, display the Math Community Chart. Remind students that norms are agreements that everyone in the class shares responsibility for, so it is important that everyone understands the intent of each norm and can agree with it. Tell students that today’s Cool-down includes a question asking for feedback on the drafted norms. This feedback will help identify which norms the class currently agrees with and which norms need revising or removing.

Standards
Building On
  • 7.EE.A·Use properties of operations to generate equivalent expressions.
  • 7.EE.A·Use properties of operations to generate equivalent expressions.
Addressing
  • A-CED.2·Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A-CED.2·Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A-CED.2·Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A-CED.2·Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A-CED.2·Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • A-CED.2·Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • HSA-CED.A.2·Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

20 min

10 min