Represent Situations with Equations

5 min

Teacher Prep
Setup
1-2 minutes quiet think time, followed by a whole-class discussion.

Narrative

The purpose of this Warm-up is to elicit observations about possible unknown quantities in a situation and to make explicit that a variable can be used to represent such a quantity. The reasoning here builds on students’ previous work in using a “?” to represent an unknown value or quantity.

This activity uses the Co-Craft Questions math language routine to advance reading and writing as students make sense of a context and practice generating mathematical questions.

Launch

Tell students to close their books or devices (or to keep them closed). Arrange students in groups of 2. Introduce the context of daily reading routine or reading a certain number of pages regularly to finish a book. Use Co-Craft Questions to orient students to the context and elicit possible mathematical questions.

Give students 1–2 minutes to write a list of mathematical questions that could be asked about the situation before comparing questions with a partner.

Student Task

Jada reads 25 pages of a book every day. After several days, she has read the entire book.

Sample Response

Sample responses:
  • How many pages long is the book?
  • How many days does it take her to read the entire book?
  • Does she read exactly 25 pages on the last day?
  • How many minutes does it take her to read 25 pages?
  • How many minutes does it take her to read the entire book?
Activity Synthesis (Teacher Notes)

Invite several partners to share one question with the class and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as “how many days,” “how many pages,” and “how long.”

To connect the idea of an unknown quantity in a situation to a variable, display the equation 25n=20025n=200 for all to see and ask students:

  • “Suppose Jada finishes a 200-page book by reading 25 pages a day. If this equation represents the situation, what might the variable nn represent?” (The number of days Jada reads the book.) 
  • “What value of nn makes the equation true?” (8) 
  • “What does that number mean in this situation?” (Jada reads the book in 8 days.)

If time permits, display another equation, 25t=5025t=50, and ask students:

  • “Suppose Jada spends 50 minutes reading 25 pages each day. If this equation represents the situation, what might the variable tt represent?” (The number of minutes Jada spends reading one page) 
  • “What value of tt makes the equation true?” (2) 
  • “What does it mean in this situation?” (Jada reads at a rate of 2 minutes a page.)

Highlight that a variable can also be used to represent an unknown quantity in a situation, such as the number of days or the number of minutes in Jada’s reading example.

Standards
Addressing
  • 6.EE.6·Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
  • 6.EE.B.6·Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

15 min

15 min