Solving Percent Problems with a Double Number Line Model

Warm Up 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. 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? 21 girls boys 7 7 7 roses cost 8 $10 4 $5 7 7 Answer: 21 girls Answer: $15 14 12 $15 Agenda

Launch 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? Agenda

Launch New Tool: Double Number Lines 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. 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. Let’s use a double number line to determine: How much money is that? Agenda

Launch $0 $1.5 $15 percent Sales New Tool: Double Number Lines 50% 10% $15 per album x 1 million albums sold = $15 million sales of all albums How much money is 5% of $15 million? Rihanna only received about 5% of the total sales of the album. So Rihanna received about $750,000 from the sales of an album that made $15,000,000. $0.75 $0 $1.5 $15 percent Sales (in millions) 50% 10% 20% 30% 40% 60% 70% 80% 90% 0% 100% 5% $15 million sales worldwide 5% or $750,000 Agenda

Launch Let’s learn how to use the double number line tool. New Tool: Double Number Lines Let’s learn how to use the double number line tool. Agenda

Explore New Tool: Double Number Lines 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? 80 percent shots 0% 100% 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 right position on the number line. First let’s find half. First, we set up the zeroes. Zero shots is zero percent. It says she took 80 total shots, so 80 is 100% of the shots. Agenda

Explore 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? 20 40 75% 60 80 percent shots 0% 25% 50% 100% Let’s fill out the other side of the number line. Half of the 80 shots, is 40. And half of 100% is 50%. The question asks for the percent that is equal to 20 out of 80. So, where do I put the 20? It’s half of 40! You can see that every number of shots is lined up with a percent. The answer is 25%. We find halfway between 0 and 40. What percent is that? Agenda

Explore 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? 25% percent shots 0% 100% 80 50% 40 20 75% 60 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%?” Agenda

Explore – Let’s do the next one together! 2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? ? percent candies 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% This time we know the part of the bag and the percent but not the total. We can still use a double number line. Next we need to put 30% in the right position. We can’t just put it anywhere. It has to be the right spot. First we need to mark out zero and 100% Do you have any ideas? Agenda

Explore – Let’s do the next one together! 2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? 6 ? percent candies 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% We know that 30% is equal to 6 candies. So we can put 6 across from 30%. 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. Agenda

Explore – Let’s do the next one together! 2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? 2 4 6 8 10 12 14 16 18 20 percent candies 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Here is one way to solve it. There are many ways. Answer: 20 candies Agenda

On Your Own – Try this one! 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? percent students 0% 100% 1,000 100 10% 200 20% 300 30% 400 40% 500 600 60% 700 70% 800 80% 900 90% 50% Answer: 200 students speak Spanish. Agenda

Percents in Life taxes discounts tips Here are a few examples of situations in which adults calculate with percents in real life. taxes discounts tips Agenda

Taxes and Tips are a percent added on to a cost. 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 tax Is 5%. If Martin has $13, can he purchase the book? Both of these problems can be solved with the same double number line. percent dollars 0% 100% $12 Agenda

Taxes and Tips are a percent added on to a cost. 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! Answer: $12.00 + $2.40 = $14.40 percent dollars 0% 100% $12.00 $1.20 10% $2.40 20% $3.60 30% $4.80 40% $6.00 $7.20 60% $8.40 70% $9.60 80% $10.80 90% 50% Agenda

Taxes and Tips are a percent added on to a cost. 5.) Martin wants to purchase a book that costs $12. The sales tax Is 5%. If Martin has $13, can he purchase the book? 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? percent dollars 0% 100% $12.00 $1.20 10% $2.40 20% $3.60 30% $4.80 40% $6.00 $7.20 60% $8.40 70% $9.60 80% $10.80 90% 50% Agenda

Taxes and Tips are a percent added on to a cost. 5.) Martin wants to purchase a book that costs $12. The sales tax Is 5%. If Martin has $13, can he purchase the book? 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. $0.60 percent dollars 0% 100% $12.00 $1.20 10% $2.40 20% $3.60 30% $4.80 40% $6.00 $7.20 60% $8.40 70% $9.60 80% $10.80 90% 50% 5% Agenda

Discounts are an amount taken OFF of a total cost. 6.) Sam got a $12 discount off a $48 purchase. What percent discount did he get? 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? I can see that $24 is half of $48. And $12 is half of $24. So, what’s half of 50%? $48.00 - $12.00 = $36.00 is the cost of the purchase after a 25% discount. percent dollars 0% 100% $48 $12 $24 Answer: 25% 50% 25% Remember: If the question asks for the total cost you must subtract the discount. Agenda

Try These! Independent Practice 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. How much was the bill? Agenda

What is the answer to this problem? Summary 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? 25% percent shots 0% 100% 80 50% 40 20 75% 60 What is the answer to this problem? Partners – Take turns describing how to solve this problem, step by step. Agenda