Solving Multi-step Percentage Problems

5 min

Teacher Prep
Setup
Students in groups of 2. 2 minutes quiet work time followed by partner then whole-class discussion.

Narrative

This Warm-up prompts students to compare four equations. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Launch

Arrange students in groups of 2–4. Display the equations for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three equations that go together and can explain why. Next, tell students to share their response with their group and then together find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

A

1.0825=271.08 \boldcdot 25 = 27

B

1.0825=x1.08 \boldcdot 25 = x

C

1.08x=271.08x = 27

D

(1+x100)25=27\left( 1 + \dfrac{x}{100} \right) \boldcdot 25 = 27

Sample Response

Sample responses:

A, B, and C go together because:

  • They have the number 1.08.
  • The percentage of the increase is known.

A, B, and D go together because: 

  • They have the number 25.
  • The original value before the increase is known.

A, C, and D go together because: 

  • They have the number 27.
  • The new value after the increase is known.

B, C, and D go together because: 

  • They have a variable.
  • A value is unknown.
Activity Synthesis (Teacher Notes)

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology they use, such as “variable,” “coefficient,” “product,” “factor,” and “percent increase,” and to clarify their reasoning as needed. Consider asking:

  • “How do you know . . . ?”
  • “What do you mean by . . . ?”
  • “Can you say that in another way?”

If time allows, invite 2–3 students to briefly share what they notice that all of the equations have in common. (For example, they could all represent an 8% increase from 25 to 27.) The purpose of this concluding share out is to remind students how an equation can represent a situation involving percent increase or decrease, which will be helpful for this lesson. 

Standards
Building On
  • 6.EE.2·Write, read, and evaluate expressions in which letters stand for numbers.
  • 6.EE.A.2·Write, read, and evaluate expressions in which letters stand for numbers.
Building Toward
  • 7.RP.3·Use proportional relationships to solve multistep ratio and percent problems.
  • 7.RP.A.3·Use proportional relationships to solve multistep ratio and percent problems. <span>Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.</span>

20 min