Math Module 1 Ratios and Unit Rates Topic D: Percent Lesson 24: Percent and Rates per 100 6.RP.3c PowerPoint designed by Beth Wagenaar Material on which this PowerPoint is based is the Intellectual Property of Engage NY and can be found free of charge at www.engageny.org

Lesson 24 Target I can do this! I will understand that percents are related to part-to-whole ratios and rates where the whole is 100. I can model percents and write a percent as a fraction over 100 or a decimal to the hundredths place.

Classwork Example 1: 5 minutes Lesson 24 Imagine that you are shopping. You want to purchase an item for $100, but today it is 20% off. What does this mean?

It means that $20 out of every $100 will be subtracted from the total. Classwork Example 1: 5 minutes Lesson 24 It means that $20 out of every $100 will be subtracted from the total.

What does this look like? Classwork Example 1: 5 minutes Lesson 24 What does this look like?

Classwork Example 1: 5 minutes Lesson 24 It could be a tape diagram with $100 divided into ten sections of $10. 2 of the sections are saved and 8 are still paid for the item.

Classwork Example 1: 5 minutes Lesson 24 It could also be shown on a 10 x 10 grid, where 20 of the squares are part of the discount and 80 still need to be paid.

Classwork Example 1: 5 minutes Lesson 24 How is this related to ratios and rates that we have been working on throughout this unit?

20% off of $100 is $20 off. We are trying to find part of a whole. Classwork Example 1: 5 minutes Lesson 24 20% off of $100 is $20 off. We are trying to find part of a whole.

Classwork Example 1: 5 minutes Lesson 24 http://nlvm.usu.edu/en/nav/frames_asid_333_g_3_t_1.html?from category_g_3_t_1.html Use the website above to visually explore percents in a 10 x 10 grid. I’ve copied and pasted it for you, though, because you must have java and can’t use windows 10 so it just seemed easier!

What does this grid show? Classwork Example 1: 5 minutes Lesson 24 What does this grid show? 100 blocks

How many are shaded in? 20 blocks Classwork Lesson 24 Example 1: 5 minutes Lesson 24 How many are shaded in? 20 blocks

How many are not shaded in? Classwork Example 1: 5 minutes Lesson 24 How many are not shaded in? 80 blocks

How can we use this model to help us think through 20% off of $100? Classwork Example 1: 5 minutes Lesson 24 How can we use this model to help us think through 20% off of $100? From the grid, I can see that when I save 20%, I am paying 80% of the original value.

Classwork Lesson 24 My colors will be black, purple, and green. Exercises 1 - 2: 8 minutes Lesson 24 My colors will be black, purple, and green.

Classwork Exercises 1 - 2: 8 minutes Lesson 24

Classwork Exercises 1 - 2: 8 minutes Lesson 24

Classwork Exercises 3 - 6: 15 minutes Lesson 24

Classwork Exercises 3 - 6: 15 minutes Lesson 24

Classwork Exercises 3 - 6: 15 minutes Lesson 24

Classwork Exercises 3 - 5: 15 minutes

Classwork Exercises 3 - 5: 15 minutes Lesson 24

Classwork Exercises 3 - 6: 15 minutes Lesson 24

Lesson 24

We modeled for Grant Wood’s painting, American Gothic! Lesson 23 Closing What are three things you learned about in this lesson? Share two ways that you can write 2%. What is one thing that you still want to know about from the lesson? I can model percents and write a percent as a fraction over 100 or a decimal to the hundredths place. We modeled for Grant Wood’s painting, American Gothic!

Math Module 1 Ratios and Unit Rates Topic D: Percent Lesson 25: A Fraction as a Percent 6.RP.3c PowerPoint designed by Beth Wagenaar Material on which this PowerPoint is based is the Intellectual Property of Engage NY and can be found free of charge at www.engageny.org

Fractions are my favorite! Lesson 25 Target Fractions are my favorite! I can write a fraction and a decimal as a percent of a whole quantity and write a percent of a whole quantity as fraction or decimal.

Classwork Example 1: 5 minutes Lesson 25 Discuss the image on the next slide with a partner. Create two ratios that would describe the images. Then use the ratios to help you discuss and work through the two claims.

Examples for Part to Whole: Classwork Example 1: 5 minutes Lesson 25 Create two ratios that accurately describe the picture. Examples for Part to Whole: Car to Whole 3:5, 3 to 5 Truck to Whole 2:5, 2 to 5

Classwork Example 1: 5 minutes Lesson 25 Remember: Percents are a form of part-to-whole comparison where the whole is 100.

Classwork Example 1: 5 minutes Lesson 25

Classwork Example 1: 5 minutes Lesson 25 Another example of a possible model used is a 10×10 grid. This model visually shows that 3 out of 5 is not the same as 50 out of 100.

Classwork Example 1: 5 minutes Lesson 25 50% means 50 out of 100 which is equivalent to 1 out of 2 that would have to be cars. In other words, half of the vehicles would have to be cars.

How is the fraction of cars related to the percent? Classwork Example 1: 5 minutes Lesson 25 How is the fraction of cars related to the percent?

. Since percents are out of 𝟏𝟎𝟎, the two are equivalent. Classwork Example 1: 5 minutes Lesson 25 3 5 is equal to 60 100 . Since percents are out of 𝟏𝟎𝟎, the two are equivalent.

Use a model to prove that the fraction and percent are equivalent. Classwork Example 1: 5 minutes Lesson 25 Use a model to prove that the fraction and percent are equivalent.

What other fractions or decimals are equal to the same percent? Classwork Example 1: 5 minutes Lesson 25 What other fractions or decimals are equal to the same percent?

Classwork Example 2: 10 minutes Lesson 25

Classwork Example 2: 10 minutes Lesson 25 Write a fraction to represent the number of people that are happy with their job compared to the total.

30% of the people were unhappy. Classwork Example 2: 10 minutes Why is it helpful to write this fraction with a denominator of 100? Lesson 25 30% of the people were unhappy. Percents are also out of 100.

How would you represent this as a decimal? Classwork Example 2: 10 minutes Lesson 25 How would you represent this as a decimal? 30% of the people were unhappy. 0.70 = 0.7

Classwork Example 2: 10 minutes Lesson 25

How can you model this question using a double number line? Classwork Example 2: 10 minutes Lesson 25 Use percents on one line and values on the other. Fractions with denominators other than 100 can also be changed to percents.

Let’s review how to change a fraction to a percent. Classwork Example 2: 10 minutes Lesson 25 Let’s review how to change a fraction to a percent.

We can scale up or scale down to get 100 as a denominator. Classwork Example 2: 10 minutes Lesson 25 We can scale up or scale down to get 100 as a denominator.

What if the denominator is not a multiple or a factor of 100? Classwork Example 2: 10 minutes Lesson 25 What if the denominator is not a multiple or a factor of 100?

Classwork Example 2: 10 minutes Lesson 25 For example, what if I ate 1 8 of a pizza and wanted to know what percent of the pizza I ate. How would I calculate this?

I can change a fraction to a decimal by dividing. Classwork Example 2: 10 minutes Lesson 25 I can change a fraction to a decimal by dividing.

Classwork Exercises 1-6: 20 minutes Lesson 25 You will work on the practice problems where you will be asked to convert from fraction to decimal to percent.

Classwork Exercises 1-6: 20 minutes Lesson 25

Classwork Exercises 1-6: 20 minutes Lesson 25

Classwork Example 2: 10 minutes Lesson 25 Before we do Exercise 3, let’s review how to change 5 8 into a decimal.

Classwork Example 2: 10 minutes Lesson 25 5 8 = 5 ÷ 8 = 0.625 = 625 1,000 = 62.5 100 = 62.5% This is now a percent because it shows how many (62.5) out of one hundred!

Classwork Exercises 1-6: 20 minutes Lesson 25

Classwork Exercises 1-6: 20 minutes Lesson 25

Classwork Exercises 1-6: 20 minutes Lesson 25

Classwork Exercises 1-6: 20 minutes Lesson 25

Lesson 25

Lesson 23 Closing I will select some of you to post diagrams and explain how the diagram helped you see the relationship between the fractions, percents, and decimals. I can write a fraction and a decimal as a percent of a whole quantity and write a percent of a whole quantity as fraction or decimal. 𝟏 𝟐 (50%) of us is holding a pitchfork. The other 𝟏 𝟐 (50%) of us is not happy about it.