One Hundred Percent

5 min

Teacher Prep
Setup
Students in groups of 2. Give students 1 minute of quiet think time, followed by partner- and whole-class discussions.

Narrative

This Warm-up prompts students to compare four diagrams that represent percent increase or percent decrease. 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 diagrams in comparison to one another.

Launch

Arrange students in groups of 2–4. Display the diagrams for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three diagrams 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
<p>A tape diagram. Five white sections, labeled 100 percent. With a smaller blue section labeled 20 percent that extends past the 100 percent.</p>

B
A tape diagram. Four white sections, labeled 100 percent. With a smaller blue section labeled 25 percent that extends past the 100 percent.

C
A tape diagram. Three white sections, labeled 75 percent. With a smaller blue section labeled 25 percent that extends past the 75 percent.

D
<p>A double number line with 6 evenly spaced tick marks.</p>
A double number line with 6 evenly spaced tick marks. On the top number line, starting with the first tick mark, zero, 5, 10, 15, 20 and 25 are labeled. On the bottom number line, starting with the first tick mark, zero percent, 25 percent, 50 percent, 75 percent, 100 percent and 125 percent are labeled.

Sample Response

Sample responses:

A, B, and C go together because:

  • They are tape diagrams.

A, B, and D go together because: 

  • They represent a percent increase.
  • They show a percentage that is greater than 100%

A, C, and D go together because: 

  • The value 20 is 100%.

B, C, and D go together because: 

  • They are counting in increments of 25%.
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 “original amount,” “new amount,” “increase,” and “decrease,” 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 not mentioned by students, ask them to discuss the amount that corresponds to 100% for each diagram.

Standards
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>

15 min

10 min