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# Finding an Original Value

Lesson 9 of 15

## Objective: SWBAT find an original (or whole) value given a part and percent by scaling values in a table

*45 minutes*

#### Introduction

*5 min*

I will begin with the essential question: How can you find an original value (or whole) when given the part and the percent?

Then I'll ask a simple question: "The donor gave $20. This was 10% of their total pledge. How much did the donor pledge in all?" The common error will be for a student to say $2. When this happens (yes, I said "when") I'll ask: Do we want 10% of $20 or 10% of their total pledge? Or I may ask: if $20 represents 10% of their total pledge will the total pledge be less than or greater than $20?. A quick bar model drawing will help students see that the total pledge is $200.

All problem can be solved as easily mentally or using a bar model, so today we will use a table.

This is a direct instruction lesson. At the beginning I have given 3 steps to solve any of the problems. Students will be expected to use this method throughout the lesson.

We will work through the 3 examples by filling in any missing values in the table. Calculators will be on hand to speed up compuations.

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#### Guided Problem Solving

*15 min*

Before students begin the problems on this page, we will discuss how you can find an original value. I will cold call a student to tell me each step. If a student draws a blank, I will ask them or where this information can be found. Answer: the first page of notes.

Students will then work on the 5 problems with their partners. I anticipate students having problems with GP2 and GP3. Students will need to recall that a 40% discount means the sale price is 60% of the original cost or that the total with tax is 109% of the original cost. Drawing a simple bar model should help remind students of this.

GP5 gives the value 0.3%. Some students may mistakenly think of this as 30%. Others may be confused as to how to scale this "down" to 1%. I will ask them to look at how they scaled other values to 1%. They'll notice that they divided by that percent amount, so the same should work with 0.3%. I may even say any number divided by itself equals...?

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#### Independent Problem Solving

*20 min*

Students will work on this set of problems independently. The first 5 problems are similar to the first 5 of the previous section.

Problem 6 requires students to find an original amount given a total with tax based on a discount. It is somewhat scaffolded in two parts.

The last problem presents data in a circle graph. Students are given the value and percent of 1 section and then must find the values of all other sections.

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#### Exit Ticket

*5 min*

Before beginning the exit ticket, we will review the 3 steps to find an original value. Students then have 5 problems to solve. These are similar to the first 5 guided practice problems and the first 5 independent practice problems.

A successful exit ticket will have at least 4 correct answers.

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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