# Multiple Representations of Percents

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## Objective

SWBAT convert fractions and decimals to percents (and vice versa) by writing equivalent fractions with a denominator of 100

#### Big Idea

Review conversions between benchmark fractions, decimals, and percents.

## Percent Introduction

5 minutes

This lesson is to provide a review for how to convert between fractions, decimals, and percents.  I especially want to hone in on the meaning of percent since this is a relatively new concept for 7th grade common core students.

This introductory activity is meant as a way to gauge what students already know about percents.

I may present this in one of two ways.  The first is to allow students to work for about 5 minutes with a partner to match the statements to the percents.  The other method is a group discussion.  I'll ask a student to read a statement and then we will discuss the statement.  Either way it is a simple way for students to exercise MP1.

As we review problems, I will ask students how they determined their answers.  I will annotate the statements as we go along.  I anticipate only a few of my students having difficulty with the first statement "I am half of a half."  If they are having difficulty, I will simply ask what is half as a percent?  When they respond, I will ask them what is half of that?  So 1/2 is 50% and half of the half is 25%.

I expect a large number of students to confuse 50% with 1/2%.  That's great since this gets us to the heart of what percent means!  A number out of 100.

## Examples

5 minutes

Before we work through the examples, we will remind ourselves of the definition of percent.  I have a hundredths grid with 8 out of 100 squares shaded.  I will give students a minute to see if they can write this value in word form, fraction form, decimal form, and percent form.  I expect to see some students write the value 0.8.  If so I'll ask, how do we say 0.8?  If a students says "zero point eight" I'll probably say that is like its nickname and how most people say it, but how did your 5th grade teacher INSIST you say it using place value.

Once we are cleared with the 8/100 in all its forms, I'll work through each example follow by a check for understanding.  I will not initially take short cuts.  I will not say "to convert 0.7 to a percent, just move the decimal two places to the right....".  I'll model 0.7 = 7/10 = 70/100 = 70%.  I don't mind the shortcut but I want to be sure students understand the conversion conceptually.

On example 3, I will have students first write the value as a fraction out of 100.  So 37.5% will be 37.5/100.  We will then rewrite this as 375/1000 to make 0.375.  We can then also simplify the fraction.

## Guided Problem Solving

15 minutes

Next students will work in pairs to fill in a table of equivalent values - fractions, decimals, and percents.  I am not going to insist that fractions be presented in lowest terms.  I will make sure that all the fractions are represented in lowest terms as we review the answers.

There are a few tricky problems that we did not discuss in the examples.  I'll be interested to see how students choose to convert 1 3/4 to a decimal and a percent.  Will they write 1 3/4 as 7/4 = 175/100?

Problem GP2 asks students to determine if 0.25 is equal to 1/4%.  Many students will quickly say yes.  I will ask them what the meaning of percent is to lead them to seeing that 0.25 is 25 out of 100 and 1/4% is 1/4 out of 100.  Two different values.

## Independent Problem Solving

20 minutes

The majority of the independent work is similar to the guided problem solving work.  Students complete a table of values and also discuss whether 1/2% is equal to 50%.  The first 3 problems are presented though as a bit of scaffolding to the practice.  I gives students a chance to work with hundredths grids to visualize various percents.

## Exit Ticket

5 minutes

Before we begin, I will call on students to discuss the meaning of percent.  How does this relate to fractions?  How does this relate to decimals?

Students then have 3 multiple choice (1 point each) and 1 open ended question (2 points- 1 point for saying "no" and 1 point for a valid explanation).  I have tried to include the common distractors for the wrong multiple choice answers.    Students will need to answer at least 4 out of 5 to show a successful effort.