21 st Century Lessons Solving Percent Problems with a Double Number Line Model Primary Lesson Designer: Lisa Schad 1.

21st Century Lessons

Solving Percent Problems with a Double Number Line Model

Primary Lesson Designer:Lisa Schad

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Lesson Objective Students will be able to construct and interpret a double number line model for solving percent problems involving finding the whole or a part or the percent.

Lesson Description This lesson extends students’ understanding of ratios to include thinking about the relationship of part to whole in a real-life situation and the percent equivalence. Instead of merely teaching students a quick algorithm for finding the percent of a number, this approach allows students to visualize the percent as representing an equivalent ratio.

This lesson is structured with a mini-lesson and guided practice intended to teach students step by step how to make and use a double number line model. This is followed by independent practice including more sophisticated multi-step non-routine challenge problems.

Lesson Overview (1 of 3)

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Lesson Vocabulary Double number line, model, tool, percent

Materials Powerpoint, class worksheets, homework worksheet

Scaffolding This lesson is great for both special education and EL students. The heavy use of a visual model is an aid to students who can appreciate a tangible demonstration of the mathematical ideas.

Enrichment The application problems in the class work are intended for the advanced students or for a second day of instruction.

Online Resources for Absent Students

http://learnzillion.com/lessons/596-find-the-part-when-the-percent-and-total-are-known This LearnZillion lesson is helpful for learning what a double number line is but it is used differently than in this lesson.

Lesson Overview (2 of 3)

http://learnzillion.com/lessons/596-find-the-part-when-the-percent-and-total-are-known

http://learnzillion.com/lessons/596-find-the-part-when-the-percent-and-total-are-known

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Lesson Overview (3 of 3)Common Core State Standard

6RP3c - Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.http://www.corestandards.org/

Before and After

Other lessons in this series illustrate the use of other ratio problem solving models including the tape diagrams, ratio table and finding the unit rate. The lesson after this one (Lesson 11) has students compare all models and Lesson 12 is a review of all topics in the unit.

Topic Background

“Ratios and percentages are also useful in many situations in daily life, such as in cooking and in calculating tips, miles per gallon, taxes, and discounts. They also are also involved in a variety of descriptive statistics, including demographic, economic, medical, meteorological, and agricultural statistics (e.g., birth rate, per capita income, body mass index, rain fall, and crop yield) and underlie a variety of measures, for example, finances (exchange rate), medicine (dose for a given body weight), and technology (kilobits per second)…Double number line diagrams can help make visible that there are many, even infinitely many pairs in the same ratio, including those with rational number entries.” From Progressions document: http://ime.math.arizona.edu/progressions/

girls

boys

Warm UpCONTENT OBJECTIVE: Students will be able to construct and interpret a double number line model for solving percent problems involving finding the whole or a part or the percent. LANGUAGE OBJECTIVE: Students will be able to describe verbally to another student their understanding of double number lines. They will listen to the other student share.

Agenda

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1. The ratio of the number of girls to the number of boys in a chess club is 3 to 2. There are 14 boys in the chess club. What is the number of girls in the chess club?

2. A florist sells 8 roses for a total of $10. Each rose costs the same amount.

What is the cost of 12 roses?

roses cost

8 $104 $5

12 $15

21

14

7 7

7 7 7

Answer:21 girls

Answer: $15

Agenda:1) Warm Up – Review Ratio Solving with models - Independent

Double Number Line for Percent Problems

3) Guided Practice - Whole Class and Partners

5) Summary/Assessment – Think, Pair, Share - Partners

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CONTENT OBJECTIVE: Students will be able to construct and interpret a double number line model for solving percent problems involving finding the whole or a part or the percent. LANGUAGE OBJECTIVE: Students will be able to describe verbally to another student their understanding of double number lines. They will listen to the other student share.

4) Independent Practice – Independent

2) Launch - Whole Class

Launch

Agenda

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Rihanna is a very popular musical artist.

Her 2012 album Unapologetic has sold close to 1 million copies worldwide.

The album can be bought at most places for $15. How much money would you expect that Rihanna has made from the sales of Unapologetic?

There are many costs that have to be paid from the sale of an album before the artist can receive her share of the profits.

Based on most information we can assume that Rihanna only received 5% of the total sales of the album. How much money is that?

Launch

Agenda

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Today we are going to learn how to calculate the percent of an amount.Today we are going to learn how to calculate the percent of an amount.

We are going to use a tool called the Double Number Line.We are going to use a tool called the Double Number Line.

To find out how much money Rihanna is estimated to have made from the sale of Unapologetic we need the total sales of the album and the percent she received.

$15 per album x 1 million albums sold = $15 million sales of all albums

Again, Rihanna only received about 5% of the total sales of the album.

New Tool: Double Number Lines New Tool: Double Number Lines

Let’s use a double number line to determine: How much money is that?Let’s use a double number line to determine: How much money is that?

Launch

Agenda

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$15 per album x 1 million albums sold = $15 million sales of all albums

Rihanna only received about 5% of the total sales of the album.


percent

Sales (in millions)

0%

$0

100%

$15

50%10% 20% 30% 40% 60% 70% 80% 90%

$1.5

How much money is 5% of $15 million?

$0.75

5%

So Rihanna received about $750,000 from the salesof an album that made $15,000,000.

$15 million sales worldwide

5% or $750,0005% or $750,000

Launch

Agenda

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Let’s learn how to use the double number line tool.


Explore

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Agenda

1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made?

percentshots

0%

0

First, we set up the zeroes. Zero shots is zero percent.

100%

80

It says she took 80 total shots, so 80 is 100% of the shots.We are going to make a double number line to compare shots to percentage. Then we can easily find the percent.

She took 20 shots, so we have to put 20 in the rightposition on the number line. First let’s find half.


Explore

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Agenda

0%

0

Half of the 80 shots, is 40. And half of 100% is 50%.

100%

80

50%

40

So, where do I put the 20? It’s half of 40!We find halfway between 0 and 40. What percent is that?

percentshots

25%

20

Let’s fill out the other side of the number line.

75%

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You can see that every number of shots is lined up with a percent.The question asks for the percent that is equal to 20 out of 80.

The answer is 25%.


Explore

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Agenda

25%

percentshots

0%

0

100%

80

50%

4020

75%

60


Partners: Take turns asking and answering:Partners: Take turns asking and answering:Lefty – Ask Righty “How did we figure out where to put 20?”Righty – Ask Lefty “How do we know that 20 shots = 25%?”

Explore – Let’s do the next one together!

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Agenda

2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag?

percentcandies

This time we know the part of the bag and the percent but not the total. We can still use a double number line.First we need to mark out zero and 100%

0

0% 100%

?

Next we need to put 30% in the right position. We can’t just put it anywhere. It has to be the right spot.

Do you have any ideas?

50%10% 20% 30% 40% 60% 70% 80% 90%


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Agenda


percentcandies

We know that 30% is equal to 6 candies. So we can put 6 across from 30%.

0

0% 100%

?

Can you use this information to find out how much 100% is?Think, Pair, Share: See if you can find an answer. Then, tell your speaking partner. Listen to your partner’s idea.

50%10% 20% 30% 40% 60% 70% 80% 90%

6


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Agenda


percentcandies

Here is one way to solve it. There are many ways.

0

0% 100%50%10% 20% 30% 40% 60% 70% 80% 90%

642 12108 181614 20

Answer:

20 candies

On Your Own – Try this one!

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Agenda

3.) A class conducts a survey of 1,000 students. The survey reveals that 20% of the students speak Spanish. How many students is this?

percentstudents

0%

0

100%

1,000

50%

500100

10%

200

20%

300

30%

400

40%

600

60%

700

70%

800

80%

900

90%

Answer: 200 students speak Spanish.

Percents in Life

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Agenda

Here are a few examples of situations in which adults calculate with percents in real life.

taxestips

discounts

Taxes and Tips are a percent added on to a cost.

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Agenda

4.) Cheryl had breakfast in the diner and the bill came to $12.00. She would like to leave a 20% tip. How much should she leave altogether?

5.) Martin wants to purchase a book that costs $12. The sales taxIs 5%. If Martin has $13, can he purchase the book?

Both of these problems can be solved with the same double number line.

percentdollars

0%

0

100%

$12


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Agenda

4.) Cheryl had breakfast in the diner and the bill came to $12.00. She would like to leave a 20% tip. How much should she leave altogether?

Just remember to add the tip to the total amount if you are looking for the total cost!Just remember to add the tip to the total amount if you are looking for the total cost!

percentdollars

0%

0

100%

$12.00

50%

$6.00$1.20

10%

$2.40

20%

$3.60

30%

$4.80

40%

$7.20

60%

$8.40

70%

$9.60

80%

$10.80

90%

Answer: $12.00 + $2.40 = $14.40Answer: $12.00 + $2.40 = $14.40


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Agenda


percentdollars

0%

0

100%

$12.00

50%

$6.00$1.20

10%

$2.40

20%

$3.60

30%

$4.80

40%

$7.20

60%

$8.40

70%

$9.60

80%

$10.80

90%

How do you find 5% on this number line? Do you have any ideas?How do you find 5% on this number line? Do you have any ideas?

5% is halfway between 0% and 10%. What is half of $1.20?5% is halfway between 0% and 10%. What is half of $1.20?


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Agenda


percentdollars

0%

0

100%

$12.00

50%

$6.00$1.20

10%

$2.40

20%

$3.60

30%

$4.80

40%

$7.20

60%

$8.40

70%

$9.60

80%

$10.80

90%

$0.60

5%

Don’t forget that a tax is also an amount added on to the total.Don’t forget that a tax is also an amount added on to the total.

Answer: He does have enough money because $12.00 + $0.60 = $12.60 total cost with tax.Answer: He does have enough money because $12.00 + $0.60 = $12.60 total cost with tax.

Discounts are an amount taken OFF of a total cost.

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Agenda

6.) Sam got a $12 discount off a $48 purchase. What percentdiscount did he get?

percentdollars

0%

0

100%

$48

50%

$24

25%

I can see that $24 is half of $48. And $12 is half of $24.I can see that $24 is half of $48. And $12 is half of $24.

$12

So, what’s half of 50%?So, what’s half of 50%?The question could have asked: how much did Sam pay for a purchase that was 25% off of the original price of $48. What would the answer be?

$48.00 - $12.00 = $36.00 is the cost of the purchase after a 25% discount.

Answer:

25%Answer:

25%

Remember: If the question asks for the total cost you must subtract the discount.Remember: If the question asks for the total cost you must subtract the discount.

Try These! Independent Practice

Agenda

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1.) Alexis bought a CD player. She does not remember the price, but she does know that the 5% sales tax came to $4.80. What was the price of the CD player? 2.) Customers left Jill $2.50 as a tip. The tip was 20% of the total. Howmuch was the bill?

Summary

Agenda

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25%

percentshots

0%

0

100%

80

50%

4020

75%

60


What is the answer to this problem? Partners – Take turns describing how to solve this problem, step by step.

What is the answer to this problem? Partners – Take turns describing how to solve this problem, step by step.

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21 st Century Lessons Solving Percent Problems with a Double Number Line Model Primary Lesson Designer: Lisa Schad 1.

Documents

lesson descriptionthis

lesson overview

learnzillion lesson

lesson objectivestudents

percent problems

percent materialspowerpoint

percent equivalence

advanced students