Benchmark Percentages

5 min

Teacher Prep
Setup
Groups of 2. 1–2 minutes of quiet think time, followed by partner- and whole-class discussion.

Narrative

This Warm-up prompts students to carefully analyze and compare four diagrams with a shaded portion in each. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear how students talk about fractions and percentages, including the number of equal parts, the size of each part, and the size of the whole. The reasoning here can remind students that a fraction is determined in relation to one whole, and similarly, that a percentage is determined in relation to 100%.

Launch

Arrange students in groups of 2–4. Display the four 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 each student to share their response with their group and then together to find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

A

B

C

D

Sample Response

Sample responses:

A, B, C go together because:

  • The length that represents 100% is marked and labeled.

A, B, D go together because:

  • The value of each shaded part is shown.
  • The value for 100% is not shown.

A, C, D go together because:

  • Only one part in each diagram is shaded.
  • The shaded part is a unit fraction (110\frac{1}{10}, 14\frac{1}{4}, and 12\frac{1}{2}).

B, C, D go together because:

  • The shaded regions all have a value of 6.
  • The percentage of shaded regions in each diagram is a multiple of 25 (75%, 25%, 50%).
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 that the reasons given are correct.

During the discussion, prompt students to clarify their reasoning as needed, especially with regard to the percentage of the shaded region and the value of 100% in each diagram. Consider asking:

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

If no students referred to the shaded parts in terms of fractions, ask, “Are there other ways to describe the size of each shaded region in each diagram?” (110\frac{1}{10} of A, 34\frac{3}{4} of B, 14\frac{1}{4} of diagram C, and 12\frac{1}{2} of D)

Standards
Building On
  • 4.NF.B·Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
  • 4.NF.B·Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Building Toward
  • 6.RP.3.c·Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
  • 6.RP.A.3.c·Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

10 min

10 min

10 min