Engage New York Grade 6 Module 1 Full Module Review
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Module 1 Review Lessons 1 & 2 Write each ratio two ways. 1. At the fair for every 8 games, there are 6 rides. 2. At the burger shop, for every 5 chocolate shakes sold, there are 7 vanilla shakes sold. 3. Margaret s recipe calls for 2 eggs and 1 cup of flour. Describe a scenario for each ratio. 4. 6 : 1 5. 4 : 9 Lessons 3 & 4 Determine if the ratios are equivalent. If they are, tell the factor relating them. If they are NOT, create a ratio that would be equivalent. 6. 36 : 54 and 4 : 9 Yes No 7. 32 : 18 and 16 : 9 Yes No Lessons 5 & 6 Use tape diagrams ratios to solve each problem. 8. Xochitl is making guacamole. She uses 3 tablespoons of cilantro for every 4 avocados. How many tablespoons of cilantro will she need for 16 avocados? 1
9. Aisha can walk 9 miles in 2 hours. At this rate, how many miles will she walk during the week if she walks a total of 6 hours? Lesson 7 Fill in the table with ratios associated to the given ratio. Remember that equivalent ratios are NOT the same as associated ratio. Description Ratio Associated Ratio Part-to-Part 10. For every 3 white eggs, there 3 : 2 are 2 brown eggs. 11. For every 9 teaspoons of sugar, 9 : 4 there are 4 teaspoons of salt. Find the value of each ratio. Then write an equation using the value. Associated Ratio Part-to-Whole 12. With every 162 bead, Diane makes 3 necklaces. Ratio: Value in lowest terms: Equation: Ratio: Value in lowest terms: Equation: 13. Mr. Heimler grades 126 tests in 3 hours. Ratio: Value in lowest terms: Equation: Ratio: Value in lowest terms: Equation: 2
Lessons 9 & 10 Mario has a new job designing websites. He is paid at a rate of $500 for every 2 pages of web content that he builds. 14. Create a ratio table to show the total amount of money Mario has earned in ratio to the number of pages he has built. Pages Money 15. Mario is saving up to purchase a used car that costs $4000. How many web pages will Mario need to build before he can pay for the car? Lesson 11 Jack and Angela are making orange juice. Jack has mixed 12 cups of water with 4 cups of juice concentrate. Angela has made her juice by mixing 10 cups water with 3 cups of juice concentrate. 16. Compare the ratios of juice concentrate to water using ratio tables. State which beverage has a higher juice concentrate-to-water ratio. 3
Samirah is making recipes for smoothies. Her first recipe calls for 3 cups of blueberries and 8 cups of other ingredients. Her second recipe says that 2 cups of blueberries are combined with 7 cups of other ingredients. 17. Which smoothie recipe has more blueberries compared to other ingredients? Use ratio tables to justify your answer. Lesson 12 Use double number lines to solve. 18. For every 4 hours babysitting Kristin makes $32. How much money will she make if she babysits 7 hours? 19. If Justin ran 6 miles in 48 minutes, how long would it take him to run 9 miles at the same rate? Lesson 13 During a particular Comic Con event, the ratio of the number of men to the number of women was 7:2. 20. Use the ratio table provided below to create at least two equations that model the relationship between the number of men and the number of women attending the Comic Con event. 4
Lesson 15 A pastry chef from a popular bakery demonstrated how she makes fresh croissants daily for her restaurant. The recipe for her croissant is below: 4 cups unbleached all-purpose flour 1/2cup cold water 1/2 cup cold whole milk 1/4 cup granulated sugar 3 Tbs. soft unsalted butter 1 Tbs. instant yeast 2-1/4 tsp. table salt 21. Determine the ratio of tablespoons of butter to cups of flour. 22. Provided the information in the table below, complete the table to determine ordered pairs. 23. Use the ordered pairs to graph the relationship of the number of tablespoons of better to the number of cups of flour.! Butter Flour 3 4 5
Lesson 16 24. Pork roast is on sale at both Super Mart and Grocery Giant. At Super Mart, a 6 lb. roast cost $14.04, and at Grocery Giant an 8 lb. roast costs $19.76. Which store offers the better deal on pork roast? How do you know? How much better is the deal? Lesson 17 25. Ella and her family went on vacation. Her father set the cruise control at 75 miles/hour and drove 4 hours. Ella s mother took over after a quick stop for lunch and drove for 5 hours with the cruise control set at 60 miles/hour. How far did Ella and his family travel altogether? Lesson 18 26. Felix earns $11 per hour working at a local gourmet donut shop. a. If Felix worked 14 hours this week, how much money did he earn this week? b. If Felix worked for 26.5 hours last week, how much money did he earn last week? 27. The local ice hockey rink is being prepared for a special event by having wooden planks placed over raised pallets. The rink is a total of 17,000 square feet and, volunteers can cover 170 square feet of rink with planking per minute. The special event will begin in 2 hours. Will the volunteer team have enough time to complete flooring for the special event? Explain your answer. 6
Lesson 19 Carson is trying to decide which new car to buy. He has narrowed it down to two models and has decided to use the vehicles gas efficiency to help him determine which one he should purchase. The more miles a car gets per gallon, the better the gas efficiency of the car. He found the following gas mileage data online. Gallons of Gasoline Miles 5 120 10 240 15 360 20 480 28. Based on gas efficiency, which car should Carson buy? Provide support for your answer. Lesson 20 The table below shows the amount of money Mallory earns working at Toys Galore. Hours 4 8 12 Pay 52 104 156 29. How much does Mallory earn per hour? 7
30. Nancy is the manager of Toys Galore. The amount of money she earns is represented by the equation: m =21.5h, where h is the number of hours Nancy works and m is the amount of money she earns. How much more money does Nancy make an hour than Mallory? Explain your thinking. Lesson 21 31. 15 ft. = in. 32. 7 yd. = ft. 33. 5100 cm = m 34. Andrew buys a 5-pound bag of his favorite candy. He eats 4 ounces of candy per day. How many days will this bag of candy? 35. An Aston Martin DB9 weighs 3,880 pounds. How many tons is this? (Hint: Your answer will be a decimal number.) Lesson 22 36. Marisol is taking a trip across the US with her family. On the first leg of the trip, her family traveled at a constant speed of 72 miles per hour. If they traveled for six hours before stopping, how far did they travel? 37. A rabbit ran 45 yards in 5 seconds. How fast did it run? 38. An F-15 fighter jet travels at a top speed of 1665 miles/hour. If it traveled at this constant speed for 3 hours, how far would it have traveled? 8
Lesson 23 39. Who walks at a faster rate: someone who walks 84 feet in 12 seconds or someone who walks 70 feet in 8 seconds? 40. Who walks at a faster rate: someone who walks 72 feet in 12 seconds or someone who takes 5 seconds to walk 35 feet? Lesson 24 41. Greg is creating a tri-color wall in his living room. The wall he has chosen to use is 100 square feet. He will be using red, black and gray on the wall. The distribution of each color is shown in the table below. Color the model to show how the distribution. Then complete the table. Color Percentage Fraction Decimal Red 15% Black 35% Gray 50% 42. Rowan has been working on a mural for the local community center all day. Now, only 40 percent of the wall is left unfinished. Shade the grid to represent the space that is left to decorate. a. What does each block represent? b. What percent of this wall has been painted? 9
Lesson 25 43. Use the 10 x 10 grid to express the fraction 14 25 as a percent. 44. Use a tape diagram to relate the fraction 14 25 to a percent. 45. How are the diagrams related? 46. What decimal is also related to the fraction? 47. Which diagram is the most helpful for converting the fraction to a decimal? Explain why. Lesson 26 48. What is 30% of 70? Create a model to prove your answer. 49. If 25% of a number is 23, what was the original number? Create a model to prove your answer. 10
50. In a 10 x 10 grid that represents 600, one square represents. 51. Use the grids below to represent 27% and 73% of 600. 27% 73% 27% of 600 is. 73% of 600 is. Lesson 27 52. Mr. Thomas has 150 papers. He graded 90 papers, and he had a student teacher grade the rest. What percent of the papers did each person grade? 53. Mrs. Hewitt has graded 30% of her 180 students papers. How many papers does she still need to finish grading? Lesson 28 54. The Yum-Yum Baking Company has delivered products to 30 customers so far this week. If this number represents 20% of the total number of customers the company is contracted to supply, how many total customers will the company supply by the end of the week? 11
55. Brandy delivered 45 homemade cards to the local boutique. If the owner has agreed to sell 15% of the total number of Brandy s cards, how many cards does Brandy have in all? Lesson 29 56. Martin has 12 lawns mowed out of a total of 60 lawns. What percent of the lawns does Martin still have to mow? 57. Talia got an 75% on her social studies test. She had 30 questions correct. How many questions were on the test? 58. Wendell read 40% of his book containing 520 pages. What page is he going to read next? 12
Module 1 Review KEY Lessons 1 & 2 Write each ratio two ways. 1. At the fair for every 8 games, there are 6 rides. _8:6 8 to 6_ 2. At the burger shop, for every 5 chocolate shakes sold, there are 7 vanilla shakes sold. _5:7 5 to 7_ 3. Margaret s recipe calls for 2 eggs and 1 cup of flour. _2:1 2 to 1_ Describe a scenario for each ratio. 4. 6 : 1 For every 6 crayons, there is one sharpener. 5. 4 : 9 For every 4 pens, there are 9 pencils. Lessons 3 & 4 Determine if the ratios are equivalent. If they are, tell the factor relating them. If they are NOT, create a ratio that would be equivalent. 6. 36 : 54 and 4 : 9 Yes _X_No 36:54 with either 4:6 or 6:9 7. 32 : 18 and 16 : 9 _X_Yes No The factor is 2. Lessons 5 & 6 Use tape diagrams ratios to solve each problem. 8. Xochitl is making guacamole. She uses 3 tablespoons of cilantro for every 4 avocados. How many tablespoons of cilantro will she need for 16 avocados? Since there are 16 avocados represented by 4 boxes each box must represent 4. Therefore, 3 boxes worth 4 each would be 12 tablespoons of cilantro. 1
9. Aisha can walk 9 miles in 2 hours. At this rate, how many miles will she walk during the week if she walks a total of 6 hours? Since two boxes are used to represent 6 hours, each box must be worth 3. Nine boxes each worth 3 would equal 27 miles Aisha could walk Lesson 7 Fill in the table with ratios associated to the given ratio. Remember that equivalent ratios are NOT the same as associated ratio. Description Ratio Associated Ratio Part-to-Part Associated Ratio Part-to-Whole 10. For every 3 white eggs, there 3 : 2 2:3 3:5 or 2:5 are 2 brown eggs. 11. For every 9 teaspoons of sugar, there are 4 teaspoons of salt. 9 : 4 4:9 9:13 or 4:13 Find the value of each ratio. Then write an equation using the value. 12. With every 162 bead, Diane makes 3 necklaces. Ratio: Value in lowest terms: Equation: 162:3 162 = 54 = 54 b = 54n 3 1 Ratio: Value in lowest terms: Equation: 3:162 3 162 = 1 54 13. Mr. Heimler grades 126 tests in 3 hours. Ratio: Value in lowest terms: Equation: 126:3 126 = 42 = 42 t = 42h 3 1 Ratio: Value in lowest terms: Equation: 3:126 2 3 126 = 1 42 n = 1 b or n = b 54 54 h = 1 t or h = t 42 42
Lessons 9 & 10 Mario has a new job designing websites. He is paid at a rate of $500 for every 2 pages of web content that he builds. 14. Create a ratio table to show the total amount of money Mario has earned in ratio to the number of pages he has built. Pages 2 4 6 8 10 12 14 16 Money 500 1000 1500 2000 2500 3000 3500 4000 15. Mario is saving up to purchase a used car that costs $4000. How many web pages will Mario need to build before he can pay for the car? Mario will need to build 16 web pages before he can pay for the car. Lesson 11 Jack and Angela are making orange juice. Jack has mixed 12 cups of water with 4 cups of juice concentrate. Angela has made her juice by mixing 10 cups water with 3 cups of juice concentrate. 16. Compare the ratios of juice concentrate to water using ratio tables. State which beverage has a higher juice concentrate-to-water ratio. Water Jack Juice Con. Water Angela Juice Con. 12 4 10 3 24 8 20 6 36 12 30 9 48 16 40 12 60 20 50 15 Both Jack and Angela have juice concentrate amounts of 12. Jack pairs this 12 cups with 36 cup of water while Angela pairs it with 40 cups of water. Therefore, Jack has the higher juice concentrate to water ratio. 3
Samirah is making recipes for smoothies. Her first recipe calls for 3 cups of blueberries and 8 cups of other ingredients. Her second recipe says that 2 cups of blueberries are combined with 7 cups of other ingredients. 17. Which smoothie recipe has more blueberries compared to other ingredients? Use ratio Recipe1 tables to justify your answer. Recipe 2 Blueberries Other Blueberries Other 3 8 2 7 6 16 4 14 9 24 6 21 12 32 8 28 Recipe 1 pairs 6 cups of blueberries with 16 cups of other ingredients while recipe 2 pairs the same 6 cups of blueberries with 21 cups of other ingredients. So, recipe 1 has more blueberries compared to other ingredients. Lesson 12 Use double number lines to solve. 18. For every 4 hours babysitting Kristin makes $32. How much money will she make if she babysits 7 hours? Kristin will make $56 babysitting for 7 hours. Seven is 3 out of 4 spaces between four and eight. 32 divided into 4 pieces makes each piece worth 8. Three pieces worth 8 = 24. 24 + 32 = 56 4a
19. If Justin ran 6 miles in 48 minutes, how long would it take him to run 9 miles at the same rate? It will take Justin 72 minutes to run 9 miles. Nine is halfway between 6 and 12. Half of 48 is 24. 48 + 24 = 72 Lesson 13 During a particular Comic Con event, the ratio of the number of men to the number of women was 7:2. 20. Use the ratio table provided below to create at least two equations that model the relationship between the number of men and the number of women attending the Comic Con event. Men 7 14 21 28 35 Women 2 4 6 8 10 4b
Cups of Flour Lesson 15 A pastry chef from a popular bakery demonstrated how she makes fresh croissants daily for her restaurant. The recipe for her croissant is below: 4 cups unbleached all-purpose flour 1/2cup cold water 1/2 cup cold whole milk 1/4 cup granulated sugar 3 Tbs. soft unsalted butter 1 Tbs. instant yeast 2-1/4 tsp. table salt 21. Determine the ratio of tablespoons of butter to cups of flour. 3:4 22. Provided the information in the table below, complete the table to determine ordered pairs. (3,4) (6,8) (9,12) (12,16) (15,20) 23. Use the ordered pairs to graph the relationship of the number of tablespoons of better to the number of cups of flour. Butter Flour 3 4 6 8 9 12 12 16 15 20 22 20 18 16 14 12 10 8 6 4 2 0 Croissant Recipe Ratios 0 3 6 9 12 15 18 Tablespoons of Butter 5
Lesson 16 24. Pork roast is on sale at both Super Mart and Grocery Giant. At Super Mart, a 6 lb. roast cost $14.04, and at Grocery Giant an 8 lb. roast costs $19.76. Which store offers the better deal on pork roast? How do you know? How much better is the deal? $14.04 6 = $2.34 $19.75 8 = $2.47 Therefore, Super Mart has the better deal on pork roast by $0.13/lb. Lesson 17 25. Ella and her family went on vacation. Her father set the cruise control at 75 miles/hour and drove 4 hours. Ella s mother took over after a quick stop for lunch and drove for 5 hours with the cruise control set at 60 miles/hour. How far did Ella and his family travel altogether? Ella s family drove 600 miles altogether. Dad 75 x 4 = 300 Mom 60 x 5 = 300 300 + 300 = 600 Lesson 18 26. Felix earns $11 per hour working at a local gourmet donut shop. a. If Felix worked 14 hours this week, how much money did he earn this week? Felix earned $154.00 this week. b. If Felix worked for 26.5 hours last week, how much money did he earn last week? Felix earned $291.50 last week. 27. The local ice hockey rink is being prepared for a special event by having wooden planks placed over raised pallets. The rink is a total of 17,000 square feet and, volunteers can cover 170 square feet of rink with planking per minute. The special event will begin in 2 hours. Will the volunteer team have enough time to complete flooring for the special event? Explain your answer. Yes, the volunteer team will have enough time. 17000 170 = 100 minutes to lay all the flooring 100 minutes = 1 hour (60 minutes) and 40 minutes The team has 20 minutes left before the event begins. 6
Lesson 19 Carson is trying to decide which new car to buy. He has narrowed it down to two models and has decided to use the vehicles gas efficiency to help him determine which one he should purchase. The more miles a car gets per gallon, the better the gas efficiency of the car. He found the following gas mileage data online. Gallons of Gasoline Miles 5 120 10 240 15 360 20 480 120 5 = 24 mpg 110 4 = 27.5 mpg 28. Based on gas efficiency, which car should Carson buy? Provide support for your answer. Carson should buy vehicle number 2 because it gets 3.5 more miles per gallon than vehicle 1. Lesson 20 The table below shows the amount of money Mallory earns working at Toys Galore. Hours 4 8 12 Pay 52 104 156 29. How much does Mallory earn per hour? Mallory earns $13 per hour. 52 4 = 13 7
30. Nancy is the manager of Toys Galore. The amount of money she earns is represented by the equation: m =21.5h, where h is the number of hours Nancy works and m is the amount of money she earns. How much more money does Nancy make an hour than Mallory? Explain your thinking. Nancy makes $8.50/hr more than Mallory. Nancy s pay per hour is $21.50 and Mallory s is $13. 21.5 13 = 8.5 Lesson 21 31. 15 ft. = 180 in. 15 x 12 = 180 32. 7 yd. = 21 ft. 7 x 3 = 21 33. 5100 cm = 51 m 5100 100 34. Andrew buys a 5-pound bag of his favorite candy. He eats 4 ounces of candy per day. How many days will this bag of candy? He has enough candy for 20 days. 1 pound = 16 ounces 16(ounces) x 5(pounds) = 80(ounces) 80 4 = 20 35. An Aston Martin DB9 weighs 3,880 pounds. How many tons is this? (Hint: Your answer will be a decimal number.) 3880 2000 = 1.94 Lesson 22 36. Marisol is taking a trip across the US with her family. On the first leg of the trip, her family traveled at a constant speed of 72 miles per hour. If they traveled for six hours before stopping, how far did they travel? They traveled 432 miles. D = rt d = 72 x 6 = 432 37. A rabbit ran 45 yards in 5 seconds. How fast did it run? The rabbit runs 9 yards per second. 45 5 = 9 38. An F-15 fighter jet travels at a top speed of 1665 miles/hour. If it traveled at this constant speed for 3 hours, how far would it have traveled? 8 The jet would travel 4995 miles. 1665 x 3 = 4995
Lesson 23 39. Who walks at a faster rate: someone who walks 84 feet in 12 seconds or someone who walks 70 feet in 8 seconds? The person walking 70 feet in 8 seconds is walking faster. 84 12 = 7 70 8 = 8.75 40. Who walks at a faster rate: someone who walks 72 feet in 12 seconds or someone who takes 5 seconds to walk 35 feet? The person walking 35 feet in 5 seconds is walking faster. 72 12 = 6 35 5 = 8.75 Lesson 24 41. Greg is creating a tri-color wall in his living room. The wall he has chosen to use is 100 square feet. He will be using red, black and gray on the wall. The distribution of each color is shown in the table below. Color the model to show how the distribution. Then complete the table. Color Percentage Fraction Decimal Red 15% Black 35% Gray 50% 15 100 = 3 20 35 100 = 7 20 50 100 = 1 2 0.15 0.35 0.50 42. Rowan has been working on a mural for the local community center all day. Now, only 40 percent of the wall is left unfinished. Shade the grid to represent the space that is left to decorate. a. What does each block represent One hundredth or 1% b. What percent of this wall has been painted? 60% of the wall has been painted. 9
Lesson 25 43. Use the 10 x 10 grid to express the fraction 14 25 as a percent. 44. Use a tape diagram to relate the fraction 14 25 to a percent. 45. How are the diagrams related? Both express the same value. 46. What decimal is also related to the fraction? 0.56 47. Which diagram is the most helpful for converting the fraction to a decimal? Explain why. Answers will vary depending on the student. Lesson 26 48. What is 30% of 70? Create a model to prove your answer. 49. If 25% of a number is 23, what was the original number? Create a model to prove your answer. 10
50. In a 10 x 10 grid that represents 600, one square represents. 51. Use the grids below to represent 27% and 73% of 600. 27% 73% 27% of 600 is 162. 73% of 600 is 438. Lesson 27 52. Mr. Thomas has 150 papers. He graded 90 papers, and he had a student teacher grade the rest. What percent of the papers did each person grade? Mr. Thomas graded 60% of the papers and his student teacher graded 40%. 90 = n 150 100 3 = n 5 100 3 20=60 5 20=100 53. Mrs. Hewitt has graded 30% of her 180 students papers. How many papers does she still need to finish grading? Mrs. Hewitt still needs to grade 126 papers. n = 70 180 100 Lesson 28 n 180 = 7 10 7 18=126 10 18=180 54. The Yum-Yum Baking Company has delivered products to 30 customers so far this week. If this number represents 20% of the total number of customers the company is contracted to supply, how many total customers will the company supply by the end of the week? 30 = 20 n 100 supply. 11 30 = 10 n 50 10 3=30 50 3=150 They have a total of 150 customers to
55. Brandy delivered 45 homemade cards to the local boutique. If the owner has agreed to sell 15% of the total number of Brandy s cards, how many cards does Brandy have in all? Brandy has 300 cards in all. 45 n = 15 100 15 3=45 100 3=300 Lesson 29 56. Martin has 12 lawns mowed out of a total of 60 lawns. What percent of the lawns does Martin still have to mow? 12 = n 60 100 1 = n 5 100 1 20=20 5 20=100 Martin has mowed 20% of the lawns, leaving 80% left to mow. 57. Talia got an 75% on her social studies test. She had 30 questions correct. How many questions were on the test? There were 40 question on Talia s social studies test. 30 n = 75 100 30 n = 3 4 3 10=30 4 10=40 58. Wendell read 40% of his book containing 520 pages. What page is he going to read next? The last page Wendell read was 208. Therefore the next page he will read is 209. n = 40 520 100 n 520 = 4 10 4 52=208 10 52=520 12
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