Module 2 - Ratios and Proportional Relationships Unit 4, Packet 1 - Percent Change

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1 Name: Packet Due Date: Friday, Oct. 19th Module 2 - Ratios and Proportional Relationships Unit 4, Packet 1 - Percent Change Standard 7.RP.A.3 Description Use proportional relationships to solve multistep ratio and percent problems. Lesson I can represent percentages as a part and a whole and solve to find the part, whole, or percent; and convert between fractions, decimals and percents. solve for the missing part, whole, or percent through equivalent ratios. represent a markup up and markdown rate as a percentage of 100 and solve for the markdown, markup, selling price, and original price of an item using equivalent ratios. Schedule Weds.,Oct. 17th Thurs., Oct. 18th Fri., Oct. 19th Lesson 4.1 HW: Page 5 Lesson 4.2 HW: Page Lesson 4.3 HW: Page Packet Completion Rubric Nothing in packet is missing. Responses consistently meet ALL of the criteria for high quality work. Exemplary effort is evident throughout entire packet. Packet is % complete/accurat e. Work/effort misses the criterion for high quality consistently. Packet is 50-75% complete/accurate. Work/effort has evidence of quality but not consistently. More than 50% of the packet is incomplete or incorrect. Work does not meet the expected level of quality. Packet is entirely incomplete or not turned in. Grading Breakdown: = F = D = C = B = A

2 Unit 4 Lesson 4.1 DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. Direct Instruction Key Vocabulary: - A percent is a ratio that compares a number to - We compare the to the and use the symbol to represent a percent Converting decimals to fractions! 1. Write the decimal over 1 2. Multiply the top and the bottom by Simply! Convert 0.75 to a fraction You Try! 1) Shade the grid to represent the ratio 35:100 a. Write this ratio as a proportion where the equivalent fraction is out of : 100 = b. How would you write the new equivalent ratio as a decimal? c. How would you write the new equivalent ratio and decimal as a percent? 1

3 2) Shade the grid to represent the ratio 24/25 d. Write this ratio as a proportion where the equivalent fraction is out of /25 = e. How would you write the new equivalent ratio as a decimal? f. How would you write the new equivalent ratio and decimal as a percent? 3) Shade the grid to represent the ratio 22/50 g. Write this ratio as a proportion where the equivalent fraction is out of = h. How would you write the new equivalent ratio as a decimal? i. How would you write the new equivalent ratio and decimal as a percent? 4) Shade the grid to represent the ratio 7 20 a. Write this ratio as a proportion where the equivalent fraction is out of /20 = b. How would you write the new equivalent ratio as a decimal? c. How would you write the new equivalent ratio and decimal as a percent? Convert each of the following... Percent Fraction Decimal 37.5% 100% You try! ½% 2

4 Fraction Decimal Percent 350% ⅛ Guided Practice 1 Write these decimals as fractions: 0.3 = 0.5 = 0.6 = 0.02 = 0.05 = 0.25 = 0.36 = = 2 Write these fractions as decimals: 7/10 = 1/5 = 2/5 = 3/4 = 7/8 = 2/3 = 9/10 = 7/25 = 3 Write these percentages as decimals: 3% = 30% = 25% = 80% = 8% = 12% = 67% = 17.5% = 4 Write these percentages as fractions: 3

5 20% = 75% = 5% = 30% = 40% = 15% = 24% = 35% = 5 Write these decimals as percentages: 0.25 = 0.5 = 0.7 = 0.07 = 0.45 = 0.09 = 0.4 = = 6 Write these fractions as percentages: 1/10 = 1/5 = 3/4 = 4/5= 6/15 = 3/8 = 7/12 = 11/12 = Independent Practice: Please use a separate piece of paper when needed! 4

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7 Unit 4 Lesson 4.2 DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. Direct Instruction Explore! Cassandra likes jewelry. She has five rings in her jewelry box. a. In the box below, sketch Cassandra s five rings. b. Draw a double number line diagram relating the number of rings as a percent of the whole set of rings. c. What percent is represented by the whole collection of rings? What percent of the collection does each ring represent? Finding a Percent Increase Cassandra s aunt said she will buy Cassandra another ring for her birthday. If Cassandra gets the ring for her birthday, what will be the percent increase in her ring collection? Strategy 1: = x 6

8 Strategy 2: You try! Exercise 1: a. Jon increased his trading card collection by 5 cards. He originally had 15 cards. WHat is the percent increase? Use the equation Quantity = Percent x Whole to arrive at your answer and then justify your answer using a numeric visual model. b. Suppose instead of increasing the collection by 5 cards, Jon increased his 15-card collection by just 1 card. Will the percent increase be the same as when Cassandra s ring collection increased by 1 ring (in Example 1)? Why or why not? Explain. c. Based on your answer to Part B, how is displaying change as a percent useful? Finding a Percent Decrease Ken said that he is going to reduce the number of calories that he eats during the day. Ken s trainer asked him to start off small and reduce the number of calories by no more than 7%. Ken estimated and consumed 2,200 calories per day instead of his normal 2,500 calories per day until his next visit with the trainer. Did Ken reduce his calorie intake by no more than 7%? Justify your answer. a. Using mental math and estimation, was Ken s estimate close? Why or why not? 7

9 b. How can we use an equation to determine whether Ken made a 7% decrease in his daily calories? We can use our strategies: Strategy 1: = x Strategy 2: Thinking about percent increase and percent decrease Sign of Percent Increase: Sign of Percent Decrease: Why? Finding One Hundred Percent Given Another Percent Explore! A sports store received a shipment of 400 hockey pucks. 30% of them arrived damaged. How many damaged hockey pucks were in the shipment? a. 30% means out of 8

10 b. Write this ratio as a fraction: As a decimal: c. So, there were damaged pucks for every regular hockey puck. d. Use a percent bar to solve this problem. 0 0% D? e. How did you determine the labels along the bottom of the bar model in Step A percent is to the ratio of a part of a whole. To find a percent of a number, you can write a ratio to represent the percent and find an equivalent ratio that compares the part to the whole. A sports store received a shipment of 400 hockey pucks. 30% of them arrived damaged. How many damaged hockey pucks were in the shipment? Our goal is to find % of hockey pucks We can use proportional reasoning to solve this problem. part part Our unit rate for this module: whole Proportion: whole = So 30% of 400 is. Write a complete sentence to answer this question. There are. 30 x Is 0.30 x 400 the same as =? Reasoning: You try! 1. Bob s Tire Outlet sold a record number of tires last month. One salesman sold 165 tires, which was 60% of the tires sold in the month. What was the record number of tires sold? 9

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13 Extra Practice with your group! 1. Tanner collected 360 cans and bottles while fundraising for his baseball team. This was 40% of what Reggie collected. How many cans and bottles did Reggie collect? 2. An animal shelter only houses cats and dogs and there are 25% more cats than dogs. IF there are 40 cats, how many dogs are there, and how many animals are there in total? 3. At a playoff basketball game, there were 370 fans cheering for Wahiawa Middle School and 555 fans cheering for Wheeler Middle School. A. Express the number of fans cheering for Wahiawa Middle School as a percent of the number of fans cheering for Wheeler Middle School. B. Express the number of fans cheering for Wheeler Middle School as a percent of the number of fans cheering for Wahiawa Middle School. C. What percent more fans were there for Wheeler Middle than Wahiawa Middle? 4. Bella spent 15% of her paycheck at the mall and 40% of that was spent at the movie theater. Bella spent a total of $13.74 at the movie theater for her ticket, popcorn and a soft drink. How much money was in Bella s paycheck? 12

14 Independent Practice 1. Justin earned 8 badges in Scouts as of the Scout Master s last report. Justin wants to complete 2 more badges so that he will have a total of 10 badges earned before the Scout Master s next report. a. If Justin completes the additional 2 badges, what will be the percent increase in badges? b. Express the 10 badges as a percent of the 8 badges. c. Does 100% plus your answer in Part A equal your answer in Part B? Why or why not? 2. Alexis and Tasha challenged each other to a typing contest. Alexis typed 54 words in one minute, which was 120% of what Tasha typed. How many words did Tasha type in one minute? 3. Yoshi is 5% taller today than she was one year ago. Her current height is 168 cm. How tall was she one year ago? 4. Rectangle A has a width of 8 cm and a length of 16 cm. Rectangle B has the same area as the first, but its width is 62.5% of the width of the first rectangle. Express the length of Rectangle B as a percent of the length of Rectangle A. What percent more or less is the length of Rectangle B than the length of Rectangle A? 5. A plant in Mikayla s garden was 40 inches tall one day and was 4 feet tall one week later. By what percent did the plant s height increase over one week? 6. Grace and her father spent 4 ½ hours over the weekend restoring their fishing boat. This time makes up 6% of the time needed to fully restore the boat. How much total time is needed to fully restore the boat? 13

15 7. Skyla is answering the following problem: The value of an investment decreased by 10%. The original amount of the investment was $ What is the current value of the investment? A. Skyla said that 10% of $75.oo is $7.50 and since the investment decreased by that amount, you have to subtract $7.50 from $75.00 to arrive at the final answer of $ Create one equation that can be used to arrive at the final answer of $ Write an explanation of your thought process. B. Skyla wanted to show the proportional relationship between the dollar value of the original investment, x, and its value after a 10% decrease, y. She creates the table of values shown. Does it model the relationship? Explain. Then, provide a correct equation for the relationship that Skyla wants to model. x y Ted is a supervisor and spends 20% of his typical work day in meetings and 20% of that meeting time in his daily team meeting. If he starts each day at 7:30 am, and his daily team meeting is from 8:00 am to 8:20 am, when does Ted s typical work day end? 14

16 Unit 4 Lesson 4.3 DO-NOW Complete today s Do-Now on the Do-Now sheet, located at the back of this packet. Direct Instruction Explore #1: A $300 mountain bike is markdown by 30% a. Find the sale price of the bicycle. b. How much has the bicycle been discounted in dollars? Explain. A is one kind of. You can rewrite the equation using the sale price of an item. = - For Example: = - The (discount rate) is the percent decrease in the price. Use this to find the sale price of an item. You Try: A $60 pair of Nike s is markdown by 25% for the Thanksgiving Sale A. How much would you pay for the Nike s? Original Price: Markdown Rate: Markdown: 15

17 B. How much did you save? C. If you buy the shoes online you save an extra 10% with the gobble gobble gonline discount. What would be the price of the shoes with the additional 10% off? Explore #2: A ski shop has a markup rate of 50%. Find the store s selling price of skis that cost the store owner $300. A is one kind of. You can rewrite the equation using the retail price of an item. = + For Example: = - The is the percent increase in the price Use this to find the retail price of an item. Written as a proportion this is: Input the information that is in the problem and then use the proportion to solve. YOU TRY! 1. You and your friend decide to go to subway for dinner. There is a promotion going on in which you buy 1 footlong and you get the second 50% off. The price of a footlong sandwich is $6. In addition, you have a 16

18 discount card that you purchased from you friend Eli in band. The discount is 20% off your total order. a. How much would you pay before applying the additional 20% discount? b. How would you apply the additional 20% to find the total savings? c. How much did you save in total with both discounts? 2. A $500 Xbox One X console is marked up by 10% and then marked down by 10%. What is the final price? a. Explain your answer. 17

19 LET S GET READY TO PLAY SHOWDOWN!! 18

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21 Independent Practice Directions : On your own, answer the questions that follow. Use the space in the margins if you need extra room to complete each question, or you may show your work on graph paper. 1. Complete the following table by listing the markup and retail price of each item. Round to two decimal places when necessary. 2. Find the sale price of each item. Round to two decimal places when necessary. a. Original Price: $45.00; Markdown: 22% b. Original Price: $23.99; Markdown: 44% a. Original Price: $89.00; Markdown: 33% b. Original Price: $279.00; Markdown: 75% 2. Timmy wants to buy a scooter and the price was $50. When he goes to the store a second time, he found that price was marked down by 20%. What is the sale price? Be sure to show all of your work and write an expression to determine the sale price. 20

22 3. A new flatscreen TV is on sale at Costco. The television cost $360. The TV was marked up by 25% so that Costco can make a profit off of it. What is the retail price of the TV? Be sure to show all of your work and write an expression to determine the retail price. 4. The new H&M has a limited edition Halloween sweater in stores that costs $20. The sweater was marked up by 60%. If Mrs. Constantino wants to get the sweater how much money will she need? Be sure to show all of your work and write an expression to determine your answer. 5. Challenge Problem: Harold works at a men s clothing store, which marks up its retail clothing by 27%. The store purchases pants for $74.00, suit jackets for $325.00, and dress shirts for $ How much will Harold charge a customer for two pairs of pants, three dress shirts, and a suit jacket? 21

23 Date Do-Now Lesson 4.1 Percent- Date: Lesson 4.2 Date: Lesson 4.3 Date: End of Packet Reflection 1. What do you feel were your strengths during the lessons from this packet? 2. What areas do you feel like you need more support? Are there any lessons that you feel like you need to develop the skills further? 3. What can you do to improve your understanding? 4. How can I (your teacher) support your learning better and improve your understanding? 22