Unit 6, Lesson 12
Solving Problems about Percent Increase or Decrease
Grade 7
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Arrange students in groups of 2. Give students 1 minute of quiet work time followed by 2 minutes to compare their responses with their partner. During the partner discussion, tell students to discuss the expressions they have in common and ones they don’t, and then try to come to an agreement on the correct expressions that represent the price of the item after the discount. Follow with a whole-class discussion.
An item costs dollars and then a 20% discount is applied. Select all the expressions that could represent the price of the item after the discount.
Some students may choose expressions that represent the discount itself instead of the price of the item after the discount is applied. Ask those students to refer back to the situation to identify which part of the problem the expression they chose represents. If students are still unclear, it may be helpful to give students a price for such as \$10 and ask them if 20% of \$10 makes sense as the new price of the item after the discount and then what part of the problem they found.
The purpose of this discussion is to review how to solve for percentage change and represent these situations with expressions.
Possible discussion questions:
In this activity, students interpret a sequence of tape diagrams and an equation that represents a percentage increase situation.
The last question is review of previous work in this unit. This fourth question can be used for additional practice, but it can be safely skipped if time is short.
The focus of this task is critiquing the work presented and explaining their reasoning, so students are critiquing the reasoning of others (MP3).
Keep students in the same groups. Tell students to work on the first three questions and pause for discussion. Give 5 minutes of quiet work time and time to share their responses with a partner, followed by a whole-class discussion. If time permits, the last question can be used as more practice on work from earlier in the unit.
Mai started a new exercise program. On the second day, she walked 5 minutes more than on the first day. On the third day, she walked for 42 minutes. This was a 20% increase from the second day.
Mai drew a diagram to show her progress.
Explain how the diagram represents the situation.
Three tape diagrams, day 1, day 2, day 3. Diagram Day 1, 1 part, labeled d. Diagram Day 2, 2 parts, first part, d, same length as d above, second part labeled 5. Diagram day 3, has 6 equal parts with no labels, The first five parts together are the length of the Day 3 diagram above, the total is 42.
Mai writes the equation to represent the situation. Do you agree with Mai? Explain your reasoning.
If students bring up that the diagram represents 120% or , or if they refer to each equal part as 20% or , ask what whole the fraction or percent refers to. They should understand that the whole is the amount from Day 2, .
The purpose of this discussion is to ensure students understand strategies for representing a percentage increase situation. Select groups with different approaches to share their responses to the first three questions.
Possible discussion questions:
We can solve problems where there is a percent increase or decrease by using what we know about equations. For example, a camping store increases the price of a tent by 25%. A customer then uses a \$10 coupon for the tent and pays \$152.50. We can draw a diagram that shows first the 25% increase and then the \$10 coupon.
Three tape diagrams of unequal length. Top diagram, original price, one part labeled p. Middle diagram, labeled 25% increase, 4 equal parts which total to the same length as p above, with another equal part on the end labeled point 25 p. Third diagram, same total length as diagram above, labeled 10 dollar coupon, first part labeled 152 point 50, second part, dotted outline, labeled 10.
The price after the 25% increase is or . An equation that represents the situation including the \$10 off for the coupon is . To find the original price before the increase and discount, we can add 10 to each side and divide each side by 1.25, resulting in . The original price of the tent was $130.