Unit 6, Lesson 14
Percentage Increase and Decrease
Extra Support Materials for Algebra 1
14.1
Warm-up
Visualizing Percent Change
Instructional Routines
Notice and Wonder
Materials
None
Activity Narrative
The purpose of this activity is for students to understand that a percentage increase of 25% corresponds to 125% of the original amount, and a percentage decrease of 25% corresponds to 75% of the original amount. Students may be familiar with tape diagrams from earlier grades. This activity reminds students how tape diagrams show relative quantities, and illustrates how tape diagrams can show percent change. Students look for and make use of the structure (MP7) of tape diagrams to understand percent change.
Launch
Tell students to close their books or devices (or to keep them closed). Display the images for all to see. Give students 1 minute of quiet think time, and ask them to be prepared to share at least one thing they notice and one thing they wonder. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the images.
If the meaning of the 25% in each image does not come up during the conversation, ask students to discuss this idea.
Tell students to open their books or devices and complete the Task Statement.
Activity
None- Match each situation to a diagram. Be prepared to explain your reasoning.
- Compared with last year’s student population, this year’s student population increased 25%.
- This year’s student population is 75% of last year’s.
- Compared with last year, this year’s student population decreased 25%.
- This year’s student population is 125% of last year’s student population.
- Draw a diagram to represent these situations.
- The number of ducks living at the pond increased by 50%.
- The number of mosquitoes decreased by 20%.
Activity Synthesis
The goal of this discussion is to connect the idea of percentage increase and decrease with visual representations. Share the correct matches and ensure everyone understands how the given diagrams are connected to the descriptions. Then ask students to share their diagrams for the second question and explain their thinking. Here are some questions for discussion:
- “The ducks increased by 50%. That means the new number of ducks is what percentage of the old number?” (150%)
- “The mosquitoes decreased by 20%. That means the new number of mosquitoes is what percentage of the old number?” (80%)
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