Grade 6 Math Module 1 Lesson 6.notebook September 10, 2015 GRADE 6 MODULE 1: LESSON 5 Solving Problems by Finding Equivalent Ratios HOMEWORK PROBLEMS Starter: A cereal company advertised that 3 out of every 24 boxes of cereal had a special prize inside. What is the ratio of boxes with prizes to boxes with no prizes? 1. Last summer, at the Camp OkeyFunOkey, the ratio of boy campers to girl campers was 8:7. If there were a total of 195 campers, how many boy campers were there? How many girl campers? 2. The student to faculty ratio at a small college is 17:3. The total of students and faculty is 740. How many faculty members are there? How many students? 3. The Speedy Fast Ski Resort has started to keep track of the number of skiers and snow boarders who bought season passes. The ratio of skiers who bought season passes to snow boarders who bought season passes is 1:2. If 1,250 more snow boarders bought season passes than the skiers, how many snow boarders and how many skiers bought season passes? 4. The ratio of adults to students at a prom has to be 1:10. Last year there were 477 more students than adults at the prom. If the school is expecting the same attendance this year, how many adults have to attend the prom? Sep 84:55 PM Jun 57:02 AM GRADE 6 MODULE 1: LESSON 6 Solving Problems by Finding Equivalent Ratios CLASS WORK GRADE 6 MODULE 1: LESSON 6 Solving Problems by Finding Equivalent Ratios Exercise 1 The Business District Hotel caters to people who travel for different types of business trips. On Saturday night there is not a lot of business travel so the ratio of occupied rooms to unoccupied rooms is 2:5. However, on Sunday night the ratio of occupied rooms to unoccupied rooms is 6:1 due to the business people attending a large conference in the area. If the business district hotel has 432 occupied rooms on Sunday night, how many unoccupied rooms do they have on Saturday night? SATURDAY NIGHT Occupied Rooms Any suggestions on how to start this problem? STUDENT OUTCOMES Unoccupied Rooms • Use tape diagrams to model SUNDAY NIGHT Occupied Rooms 1. I can use tape diagrams to solve problems for a ratio between two quantities, and a change to those quantities that changes the ratio. Unoccupied Rooms 432 occupied rooms 6 sections on the tape How can we use this information to answer the question? May 234:33 PM Apr 135:36 PM GRADE 6 MODULE 1: LESSON 6 Solving Problems by Finding Equivalent Ratios EXERCISES 2 7 2. Peter is trying to work out by completing situps and pushups in order to gain muscles. Originally, Peter was completing 5 situps for every 3 pushups, but then he injured his shoulder. After the injury, Peter completes the same amount of exercises as he did before his injury, but completes 7 situps for every 1 pushup. During a training session after his injury, Peter completed 8 pushups. How many pushups was Peter completing before his injury? Before Injury Starter: Choose one of the problems from yesterday's exercises (Lesson 6) that your group did not complete to work on. SitUps: PushUps: After Injury SitUps: PushUp: 3. Tom and Rob are brothers who like to make bets about the outcomes of different contests between them. Before the last bet, the ratio of Tom's money to Rob's money was 4:7. Rob lost the latest competition and now the ratio of Tom's money to Rob's money is 8:3. If Rob had $280 before the last competition, how much does Rob have now that he lost the bet? 4. A Sporting goods store ordered new bikes and scooters. For every 3 bikes ordered, 4 scooters were ordered. However, bikes were way more popular than scooters, so the store changed their next order. The new ratio of bikes to scooters ordered was 5:2. If the same amount of sporting equipment was ordered in both orders and 64 scooters were ordered originally, how many bikes were ordered as a part of the new order? 5. At the beginning of 6th grade, the ratio of advanced math students to regular math students was 3:8. However, after taking placement tests, students were moved around changing the ratio of advanced math students to regular math students to 4:7. How many students started in regular and advanced math if there was 92 students in advanced math after the placement tests? Reverse the 4:7 order; 92/4 = 23; 23 x 3 = 69 RM; 23 x 8 = 184 AM before placement. 6, During the first semester, the ratio of students in art class to student in gym class was 2:7. However, the art classes were really small and the gym classes were large, so the principal changed student's classes for the second semester. In the second semester the ratio of students in art to gym class was 5:4. If 75 students are in art class second semester, how many were in art class and gym class first semester? 7. Jeanette is trying to save money, but has not been good at in the past. The ratio of money in Jeanette's savings account to the money in the checking account is 1:6. Because Jeanette is trying to get better at saving money, she moves more money into her savings account. Now the ratio in savings account to checking account is 4:3. If Jeanette has $936 in her checking account before moving money, how much money does Jeanette have in each account after moving money? Sep 910:52 PM May 292:07 PM 1 Grade 6 Math Module 1 Lesson 6.notebook GRADE 6 MODULE 1: LESSON 6 Solving Problems by Finding Equivalent Ratios PROBLEM SET 1. Shelley compared the number of oak trees to the number of maple trees as part of a study of hardwood trees in a woodlot. She counted 9 maple trees to every 5 oak trees. Later in the year there was a bug problem and many of the trees died. New trees were planted to make sure there was the same number of trees as before the bug problem. The new ratio of maple trees to oak trees is 3:11. After planting new trees, there were 132 oak trees. How many more maple trees were in the woodlot before the fire than after the fire? Explain. There were 72 more trees before the bug problem than after because there were 108 maple trees before the bugs and 36 after the bugs. September 10, 2015 GRADE 6 MODULE 1: LESSON 6 Solving Problems by Finding Equivalent Ratios CLOSING THINK: What advice would you have for a friend if they missed class today and they need to do their homework? 2. The school band is comprised of middle school students and high school students, but always has the same maximum capacity. Last year the ratio of middle school students to high school students was 1:8. However, this year the ratio of middle school students to high school students changed to 2:7. If there are 18 middle school students in the band this year, how many fewer high school students are in the band this year? Explain. PAIR There 9 fewer high school student in the band this year. Last year there were 72 HS students, this year there are 63. 72 63 = 9. SHARE If a problem has a ratio that changes, it is best to do one tape diagram for the before and one for the after so you can visualize the change. Jun 57:02 AM GRADE 6 MODULE 1: LESSON 6 Solving Problems by Finding Equivalent Ratios EXIT TICKET Aug 18:50 AM GRADE 6 MODULE 1: LESSON 6 Solving Problems by Finding Equivalent Ratios HOME WORK Jul 274:03 PM Jul 274:09 PM Jul 3110:47 AM 2
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