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# Solve Problems by Applying Percents of Increase and Decrease

Lesson 6 of 15

## Objective: SWBAT model and apply a percent of increase or decrease using a bar model

#### Introduction

*10 min*

This lesson extends beyond the previous lesson "Drawing Bar Models to Represent Percent of Increase and Decrease". The previous lesson was built to make sure students could accurately draw bar models, today we will apply that to solving "real-world" problems.

I'll start by asking: What is a percent of increase? What is a percent of decrease? Students may need a more concrete question - what does it mean to increase or decrease a value by 10%?

Next we solve the example problems. If the previous day's exit tickets show a high level of mastery, I will given students the opportunity to solve both example problems on their own. If less than 70% of the class did well with the previous exit ticket I will use this as a quick re-teach on drawing bar models.

The last question of each example asks student to identify what percent of the original value is the new value. It may be helpful to have students find this percent of the original value so they can see how this relates to their models. Using example 2, students will find 75% of 460 and see that this value is equal to the 25% decrease seen in the model.

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#### Guided Problem Solving

*15 min*

Students now have 4 problems to solve. The first two can be modeled using the two bar models we have been using.

The last two questions are to see if students can find increases and decreases that are not so easily modeled using a 10% or 25% bar model. Or, the new value is 100% + % increase of the original value for an increase. The new value is 100% - % decrease of the original value for the decrease.

Students may need help drawing these models. It will not be necessary to divide the bar into units; just keep one long bar to represent 100% or the original value. Then, add on a smaller bar for the increase and "x" out a part of the bar for a decrease.

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#### Independent Problem Solving

*20 min*

The independent problem solving has similar problems to the guided problem solving. It goes one step beyond with the bonus question. Now students are asked to find a new value after a 13% increase. This is not merely asking students to identify the percent as before. Students may need a reminder that a percent of increase means we find the percent of the original value and add this to the original value.

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#### Exit Ticket

*5 min*

The exit ticket is set up like the independent practice. There are two problems (3 parts each) where students draw a model, find find the new value, and find the new percent. The last two questions are to see if students have learned the alternative way of finding a percent of increase or decrease. That being said, I will mostly be concerned with the first 6 problems, we'll have more time to discuss the last two problems at a later date.

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###### The Defining Pi Project, Day 1

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- LESSON 1: Multiple Representations of Percents
- LESSON 2: The 10% Benchmark
- LESSON 3: The 1% Benchmark
- LESSON 4: Percent Benchmark Fluency
- LESSON 5: Drawing Bar Models to Represent Percents of Increase and Decrease
- LESSON 6: Solve Problems by Applying Percents of Increase and Decrease
- LESSON 7: Discounts and Sales Tax
- LESSON 8: Finding a Percent of Change
- LESSON 9: Finding an Original Value
- LESSON 10: A Percent Equation
- LESSON 11: Expressions for Percent Increases and Decreases
- LESSON 12: Simple Interest
- LESSON 13: Increasing and Decreasing Quantities by a Percent (Day 1 of 2)
- LESSON 14: Increasing and Decreasing Quantities by a Percent (Day 2 of 2)
- LESSON 15: Percent Assessment