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* *Reflection: Connection to Prior Knowledge
The 10% Benchmark - Section 2: Guided Problem Solving

I made an assumption again. What is it they say about assuming? My students seemed to grasp finding 10% of a number without much difficulty. I thought that meant they were ready for the problems in the guided problem solving section. As students were working, I noticed strange answers to the circle graph problems. Students were saying there were .1 books. I quickly realized they didn't realize that the circle graph represents the total number of books - 400. They did not understand that to find the total number of history books, for example, it would be necessary to find 20% of 400.

Before common core standards, there was a state standard for 7th grade that specifically mentioned circle graphs. I always made sure to write a couple of lessons about interpreting these graphs. Here, I took it for granted that students would figure out how to read the graph. I had to stop students from working to explain how to interpret a circle graph. I do not think an entire lesson is necessary, but in the future, I'll make sure to discuss the circle graph first.

*Assuming and Circle Graphs*

*Connection to Prior Knowledge: Assuming and Circle Graphs*

# The 10% Benchmark

Lesson 2 of 15

## Objective: SWBAT find the percent of a number using 10% as a benchmark

*50 minutes*

#### Introduction

*10 min*

Before I begin with the essential question, I will want to make sure that all students can easily divide a number by 10 by shifting the decimal 1 place to the left. While they should have already learned this shortcut, I know many will need a reminder. I will **cold call** students here. I'll present a number, call a name, and expect them to provide that number divided by 10. I will go through the entire class. I will scaffold the difficulty of the problems as necessary. Because this skill is so basic (it goes back well before 7th grade), I have an anchor chart posted in the room that all can see. It shows how to divide a number by ten by moving the decimal. I will refer to this poster often throughout the unit as needed.

I will then present the essential question: How can you find the percent of a number using 10% as a benchmark? I think this may be one of the most useful skills to know in the "real world". I'll let students know this - when finding a discount, leaving a tip at a restaurant, etc. This benchmark is vital.

A simple problem is presented with a bar model. We will complete the bar model and answer the questions. This is so that we can see that to find 10% of a number, you can simply divide that number by 10 (**MP8**). I'll ask students to explain why this works. They should feel free to point to the bar model above to help explain their answers.

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#### Guided Problem Solving

*15 min*

Students now find quantities in a circle graph. Some of my struggling readers will over look that the circle graph represents 400 new books. It might be necessary to point this out or ask someone in the class to answer the question: "How many books does the entire circle graph represent."

I am focusing on multiples of 10% for this lesson, but I could not resist including a question here or there with a multiple of 5%.

GP2 and GP3 ask students to calculate a tip and discount respectively. We will have a formal lesson on discounts later, but I didn't think it would hurt to include a problem here.

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#### Independent Problem Solving

*20 min*

The independent section again follows the same format as the guided section with only a few changes. I have included a percent over 100%, but it is still a multiple of 10%! Also the extension section has percents that are not multiples of 10%. The 3 given questions should be answerable by all. I will ask the more advanced students to see if they can determine the value of each category.

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#### Exit Ticket

*5 min*

Before we begin the exit ticket we will summarize. 1) How can you find 10% of any number? 2) How can you use 10% to find any other multiple of 10%?

Students will then answer 5 questions. The first 4 questions involve a multiple of 10%. Therefore, a successful exit ticket would have these 4 problems answered correctly. Hopefully students can reason their way through question 5. Even if they are not quite sure how to find 5% they should be able to say that 10% of $500 = $50, therefore less than $50 was spent on invitations.

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##### Similar Lessons

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

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Environment: Urban

- 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