Using Equations to Solve Problems

5 min

Narrative

In this Warm-up, students write a story and an equation that could be represented by a tape diagram. The purpose is to reactivate students’ understanding of tape diagrams to make it more likely that tape diagrams are accessible as a representation for them to choose in this lesson. The diagram was deliberately constructed to encourage some students to write an equation like 24=3(a+2)24=3(a+2) and others like 24=3a+624=3a+6. Monitor for one student who writes each type of equation.

Launch

Arrange students in groups of 2. Give 5 minutes of quiet think time and time to share their work with a partner followed by a whole-class discussion.

Student Task

Tape diagram, 6 parts, a, 2, a, 2, a, 2, total 24.  Across the top, brackets above an a and 2 indicate a + 2.

  1. Write a story that could be represented by this tape diagram.
  2. Write an equation that could be represented by this tape diagram.

Sample Response

  1. Sample response: A baker put aa cookies in each of 3 boxes. Then he put 2 more cookies in each box, so there were a total of 24 total in the 3 boxes.
  2. 24=3(a+2)24=3(a+2) or 24=3a+624=3a+6 (or equivalent)

Synthesis

The purpose of this discussion is to help students see that an equation representing the diagram can be written in either form, 3(a+2)=243(a+2)=24 or 3a+6=243a+6=24. After students have had a chance to share their work with their partner, select a few students to share their stories. Then select one student to share each type of equation and explain its structure.

Standards
Addressing
  • 7.EE.4.a·Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. <em>For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?</em>
  • 7.EE.B.4.a·Solve word problems leading to equations of the form <span class="math">\(px + q = r\)</span> and <span class="math">\(p(x + q) = r\)</span>, where <span class="math">\(p\)</span>, <span class="math">\(q\)</span>, and <span class="math">\(r\)</span> are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. <span>For example, the perimeter of a rectangle is <span class="math">\(54\)</span> cm. Its length is <span class="math">\(6\)</span> cm. What is its width?</span>

20 min

10 min