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Calculating Percentages with Double Number Lines

Learn how to calculate percentages using a double number line tool. Explore examples of real-life situations involving percentages like sales and tips.

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Calculating Percentages with Double Number Lines

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  1. Warm Up 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 7 7 7 girls $5 4 boys 7 7 Answer: $15 Answer: 21 girls 14 12 $15

  2. Launch Rihanna is a very popular musical artist. Her 2012 album Unapologetic has sold close to 1 millioncopies 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?

  3. 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?

  4. Launch New Tool: Double Number Lines $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 Sales (in millions) $0 $1.5 $15 percent 40% 50% 60% 10% 20% 30% 70% 80% 90% 0% 100% 5% $15 million sales worldwide 5% or $750,000

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

  6. Explore 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? 0 80 shots percent 100% 0% We are going to make a double number line to compare shots to percentage. Then we can easily find the percent. It says she took 80 total shots, so 80 is 100% of the shots. She took 20 shots, so we have to put 20 in the right position on the number line. First let’s find half.

  7. Explore 1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? 0 20 80 60 40 shots percent 25% 100% 0% 50% 75% The question asks for the percent that is equal to 20 out of 80. Half of the 80 shots, is 40. And half of 100% is 50%. So, where do I put the 20? It’s half of 40! We find halfway between 0 and 40. What percent is that? The answer is 25%.

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

  9. 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? ? 0 candies percent 0% 40% 50% 100% 10% 20% 30% 60% 70% 80% 90% 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% Do you have any ideas?

  10. 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? ? 0 6 candies percent 0% 40% 50% 100% 10% 20% 30% 60% 70% 80% 90% 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?

  11. 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? 0 2 4 6 8 10 12 14 16 18 20 candies percent 0% 40% 50% 100% 10% 20% 30% 60% 70% 80% 90% Here is one way to solve it. There are many ways. Answer: 20 candies

  12. 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? students 300 400 200 0 100 800 600 700 900 1,000 500 percent 30% 0% 80% 70% 20% 40% 10% 60% 50% 90% 100% Answer: 200 students speak Spanish.

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

  14. 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? dollars 0 $12 percent Both of these problems can be solved with the same double number line. 0% 100%

  15. 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! dollars 0 $3.60 $9.60 $8.40 $7.20 $4.80 $10.80 $12.00 $2.40 $1.20 percent Answer: $12.00 + $2.40 = $14.40 $6.00 30% 0% 20% 40% 60% 70% 80% 10% 50% 90% 100%

  16. 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? dollars 5% is halfway between 0% and 10%. What is half of $1.20? 0 $3.60 $9.60 $8.40 $7.20 $4.80 $10.80 $12.00 $2.40 $1.20 percent $6.00 30% 0% 10% 80% 60% 40% 70% 20% 50% 90% 100%

  17. 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. dollars Answer: He does have enough money because $12.00 + $0.60 = $12.60 total cost with tax. 0 $3.60 $9.60 $7.20 $8.40 $4.80 $10.80 $12.00 $2.40 $1.20 percent $0.60 $6.00 30% 0% 20% 80% 70% 10% 60% 40% 50% 90% 100% 5%

  18. 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? I can see that $24 is half of $48. And $12 is half of $24. So, what’s half of 50%? dollars $48 0 percent $48.00 - $12.00 = $36.00 is the cost of the purchase after a 25% discount. $12 $24 Answer: 25% 0% 50% 100% 25% Remember: If the question asks for the total cost you must subtract the discount.

  19. 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?

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