Unit 6, Lesson 6
Percent Increase and Decrease with Equations
Accelerated 6
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This Math Talk focuses on finding the factor that scales 50 to another number. It encourages students to think about increase and decrease in terms of fractions, decimals, or percentages and to rely on properties of operations to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students write equations to represent percent increase or decrease situations.
As students use results from the previous equation to help solve the next equation, they are making use of repeated reasoning (MP8).
Tell students to close their books or devices (or to keep them closed). Reveal one problem at a time. For each problem:
Keep all previous problems and work displayed throughout the talk.
Solve each equation mentally.
To involve more students in the conversation, consider asking:
If all students give their answers as fractions, encourage them to express the fraction as a decimal. This will help prepare students for working with equations where decimals are used to represent percent increase or decrease.
If any student expresses their reasoning in terms of percentages, for example, by saying that 60 is a 20% increase from 50, highlight this strategy for all to see.
MLR2: Collect and Display
To Gather
Four-function calculators
Introduce the context of this activity by asking students, “Have you ever taken a plain piece of fabric and decorated it somehow? What are some ways you can think of to decorate fabric?” Then explain that zardozi (zar-DOO-zee) and molas (MOH-lah) are two different ways that some people decorate fabric. Zardozi is a Persian art form that involves sewing metal threads and beads onto silk or other fabrics. Molas are made by the Guna people. They sew multiple layers of fabric together and cut out pieces to make a colorful pattern.
Give students 4–5 minutes of quiet work time followed by time for partner discussion. Then hold a whole-class discussion.
Write an equation to represent each situation. Then, solve the equation.
A piece of fabric weighed 15 ounces. After it was decorated with zardozi, the weight had increased by 82%. What is the weight of the finished piece?
Before making a mola, the layers of fabric weighed 4.7 ounces. When the mola was finished, the weight had decreased by 17%. What is the weight of the finished mola?
Another finished mola weighs 4.9 ounces. This is a 21% decrease from the original weight of the fabric. What was the original weight?
Optional
MLR1: Stronger and Clearer Each Time
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In this activity, students practice writing equations to represent situations involving percent increase or decrease. The situations are the same ones that students previously represented with double number line diagrams in a previous lesson.
In this partner activity, students take turns sharing their initial ideas and first drafts. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3). As students revise their writing, they have an opportunity to attend to precision in the language they use to describe their thinking (MP6).
Show students the double number line from the activity in the previous lesson.
Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to the first question, about the equation
If time allows, display these prompts for feedback:
Close the partner conversations and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer.
After Stronger and Clearer Each Time, give students 3–4 minutes of quiet work time to answer the rest of the questions.
Select students to share the different equations they came up with. Points of discussion could include:
We can use equations to express percent increase and percent decrease.
For example, if
So if someone makes an investment of
Here is another example: if
So if the amount of water in a tank decreased 7% from its starting value of
Often, an equation is the most efficient way to solve a problem involving percent increase or percent decrease.
Help us improve by sharing suggestions or reporting issues.
Last year, scientists counted 12 foxes in a conservation area. This year, they counted 50% more than that. How many foxes did they count this year?
Explain why this situation can be represented by the equation
Students may continue to struggle to recognize the original amount and new amount with the proper percentages on the double number line. Remind them that the original amount always corresponds to 100%.