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STANDARDS RATIONS & PROPORTIONALITY TEACHER GUIDE 6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed. d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. VOCABULARY & KEYWORDS proportion: two equal ratios rate: a comparison between two quantities with different units of measure ratio: a comparison between two different quantities scale factor: the ratio of two corresponding sides in a set of similar figures unit rate: a comparison of two measurements with a denominator of 1 COMMON MISTAKES & MISCONCEPTIONS Students may incorrectly set up a proportion. Students may not recognize that the ratio is a part-to-part or a part-to-whole. Students may struggle to read a problem and to determine which information is the part and/or the whole.

WARM -UP 1. Mrs. Matthis can grade 2 essays every 15 minutes. At this rate, how many essays can Mrs. Matthis grade in 1.5 hours? Name Date Pd 2. A recipe for salad dressing calls for 2 tsp of vinegar to 3 tsp of oil. Based on the data complete the table. How many tsp of oil will be used if 18 tsp of vinegar are used? VINEGAR (TSP) OIL (TSP) 2 12 10 27 WARM -UP 1. Mrs. Matthis can grade 2 essays every 15 minutes. At this rate, how many essays can Mrs. Matthis grade in 1.5 hours? Name Date Pd 2. A recipe for salad dressing calls for 2 tsp of vinegar to 3 tsp of oil. Based on the data complete the table. How many tsp of oil will be used if 18 tsp of vinegar are used? VINEGAR (TSP) OIL (TSP) 2 12 10 27

CHEAT SHEET - A RATIO: a comparison of TWO quantities Must be set up correctly; be sure to use labels Can be part-to-part or part-to-whole RATE: a ratio with TWO DIFFERENT UNITS $5.25 6 LB UNIT RATE: a ratio with a quantity of ONE PRICE 1 LB 250 MI 4 HRS MILES 1 HR 49 FT 5 SEC FEET 1 SEC Measurement conversions MEASUREMENT CONVERSION: converting units in one measurement system Label the various units Use the measurement chart if necessary to find the conversion Set up and solve the proportion IN YDS 3 BOYS 4 GIRLS Ratios & rates = 36 1 = 1X = 180 X = 180 7 STUDENTS: 4 GIRLS 4 GIRLS TO 3 BOYS INCHES TO YARDS KILOGRAMS TO GRAMS X 5 5 YARDS = 180 INCHES Name Date Pd PROPORTION: two equal RATIOS proportions Can be used to find a missing quantity Must be set up correctly; be sure to use labels Solve for the missing quantity Reread the problem to make sure you answer the question MILES HR MILES (m) = EQUATIONS m = 150h GRAPHS 500 450 400 350 300 250 200 150 100 50 0 432 X = 6 8 3,456 = 6X 576 = X HOURS (h) 576 MILES IN 8 HOURS TABLES MILES (m) 2 150 4 300 7 525 10 1500 1 2 3 4 5 6 7 8 9 10 HOURS (h) RATIO REPRESENTATIONS

CHEAT SHEET - B RATIO: a comparison of quantities Name Date Pd proportions Must be set up correctly; be sure to use labels Can be part-to-part or part-to-whole PROPORTION: two equal 3 BOYS 4 GIRLS RATE: a ratio with $5.25 6 LB 7 STUDENTS: 4 GIRLS 4 GIRLS TO 3 BOYS 250 MI 4 HRS 49 FT 5 SEC UNIT RATE: a ratio with a quantity of Can be used to find a missing quantity Must be set up correctly; be sure to use labels Solve for the missing quantity Reread the problem to make sure you answer the question MILES HR = 432 6 = X 8 PRICE 1 LB MILES 1 HR FEET 1 SEC Ratios & rates Measurement conversions MEASUREMENT CONVERSION: INCHES TO YARDS KILOGRAMS TO GRAMS Label the various units Use the measurement chart if necessary to find the conversion Set up and solve a proportion IN YDS = 36 1 = X 5 MILES (m) EQUATIONS GRAPHS 500 450 400 350 300 250 200 150 100 50 0 HOURS (h) 2 7 TABLES 1 2 3 4 5 6 7 8 9 10 HOURS (h) MILES (m) 300 1500 RATIO REPRESENTATIONS

CHEAT SHEET - C Name Date Pd proportions Ratios & rates Measurement conversions RATIO REPRESENTATIONS

INSTRUCTIONS HE SAID, SHE SAID TO PREP Print cards on cardstock and cut the cards apart. Print and copy a recording sheet for each student. TO USE Students can begin at any card with their recording sheet. Students will analyze the card to determine which student made a correct statement. Students will record the name of the student who is correct, along with a justification on their recording sheet. OTHER TIPS This activity works well when students are in partners or groups of 3-4. Laminate cards to protect them for future use. You can choose to have one set of cards for the entire class to share, or multiple sets of cards that could be put on binder rings for individual groups.

HE SAID, SHE SAID RECORDING SHEET Name Date Pd Each of the 10 cards will have statements from two students. Read carefully and choose the name of the student who made the correct statement. Then, justify your answer in the space provided. 1 is correct because 2 is correct because 3 is correct because 4 is correct because is correct because 5 6 is correct because is correct because 7 8 is correct because is correct because 9 10 is correct because

CARD 1: Jamie received a piggy bank for her birthday. Every five days she earned $4.00 in allowance for completing her chores. At this rate, how many days did it take for Jamie to save $60.00 in her piggy bank? Alex says that it will take 75 days. Adrianna says that it will take 45 days. CARD 2: The table below shows how far the Martinez family traveled on family Bryson says that the Martinez family traveled at a rate of 66 miles per hour. vacation. HOURS (h) MILES (m) 3 198 5 330 8 528 11 726 Brenda says that the Martinez family traveled at a rate of 76 miles per hour.

CARD 3: Each morning Mrs. Sheppard takes 500 milligrams of Vitamin C. How many grams of Vitamin C does Mrs. Sheppard take? Charlie says that she takes 0.5 grams of Vitamin C. Candace says that she takes 5 grams of Vitamin C. CARD 4: The high school marching band has a select number of spots for each instrument. For every two tuba players, there are 11 clarinet players. How many tuba players can be expected if there are 33 clarinet players? Damien says that there are 10 tuba players. Dakota says that there are six tuba players.

CARD 5: A city is analyzing its family friendly environment. There are 36 parks for 5,796 residents. What is the relationship between the number of parks and the number of residents? Enrique says the ratio of parks to residents is 1:161. Emma says the ratio of residents to parks is 1:161. CARD 6: The table below shows the cost to make a wreath. How much does it cost to make one wreath? Frankie says that it costs $12.50 to make a wreath. WREATH, w 3 5 7 9 COST, d $37.50 $62.50 $87.50 $112.50 Fiona says that it costs $13.50 to make a wreath.

CARD 7: A punch recipe calls for 4 cups of lemonade to 3 cups of sparking juice. If Sara is making 42 cups of punch, then how many cups of lemonade does she need? Greg says that she needs 16 cups of lemonade. Grace says that she needs 24 cups of lemonade. CARD 8: A large container holds a sports drink for the soccer team. It holds 6 gallons of sports drink. How many cups of sports drink does the container hold? Hugo says that it will hold 96 cups. Harper says that it will hold 48 cups.

CARD 9: A wedding reception seats eight people at each table. The relationship is represented by the equation p=8t, where p is the number of people and t is the number of tables. Ian says that to host a wedding with 192 people, 22 tables will be needed. Ivy says that if you have 13 tables, 104 people will be able to be seated. CARD 10: The graph below shows the number of miles traveled during a family road trip. How many miles per hour did the family travel? Jack says that family traveled 70 miles per hour. 500 450 TOTAL MILES 400 350 300 250 200 150 100 50 Jaqueline says that the family traveled 75 miles per hour. 0 1 2 3 4 5 6 7 8 9 10 HOURS

QUICK CHECK Name Date Pd 1. A bike travels 24 miles in 3 hours. At this rate how many miles will the bike travel in 10 hours? A. 192 B. 80 C. 32 D. 124 2. Edgar pays $67.86 for 7.8 pounds of fertilizer. What is the price per pound of fertilizer? F. $6.98 G. $5.65 H. $8.70 J. $10.26 1. A B C D 2. F G H J 3. A B C D 4. F G H J 5. A B C D 6. F G H J 7. A B C D 8. F G H J 9. A B C D 10. Use the grid below. 3. Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. When company comes she makes 96 fluid ounces of coffee. How many grams of coffee beans does Diana use when company comes? A. 160 B. 60 C. 98.2 D. 14.4 4. Sarah Beth babysits and earns $10.50 per hour. Which of the following best represents the relationship between the number of hours, h, and the total earnings, t. F. t = 10.50 + h G. t = 10.50h H. h = 10.50 + t J. h = 10.50t 5. The model below shows the ratio of gray to white squares. Which of the following is not an equivalent ratio of gray squares to total squares? A. 9/24 B. 21/60 C. 15/40 D. 27/72

6. Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges? F. CARDS, c 2 9 11 15 G. DOLLARS, d 9 40.5 50.5 67.5 CARDS, c 9 18 27 36 DOLLARS, d 2 4 6 8 H. J. CARDS, c 2 4 7 10 DOLLARS, d 9 18 31.5 45 CARDS, c 2 3 4 5 DOLLARS, d 9 10 11 12 7. The graph shows the amount of money that Janice saves each week from her summer job. Which equation best represents the graph? 2000 1800 8. Which of the following tables best represents the ratio of minutes it takes to fill a bathtub to the total number of gallons? 50 45 40 Total Savings ($) 1600 1400 1200 1000 800 600 400 Total Gallons 35 30 25 20 15 10 5 200 0 1 2 3 4 5 6 7 8 9 10 Weeks 0 1 2 3 4 5 6 7 8 9 10 Minutes F. G. Minutes Gallons Gallons Minutes A. y = 200x B. y = x + 200 C. x = 200y D. x = y + 200 2 5 5 15 8 20 12 25 H. J. Gallons Minutes 5 2 10 5 15 3 20 4 2.5 1 5 2 7.5 3 9 4 Minutes Gallons 2 5 5 12.5 7 17.5 11 27.5 9. Miguel weighs himself and discovers he weighs 83,600 grams. How many kilograms does Miguel weigh? A. 8.36 kg 10. Jameson pays $39.90 for 3.8 pounds of almonds. What is the price per pound of almonds? Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value. B. 83.6 kg C. 8,360 kg D. 83,600,00 kg

ANSWER KEYS

WARM -UP 1. Mrs. Matthis can grade 2 essays every 15 minutes. At this rate, how many essays can Mrs. Matthis grade in 1.5 hours? Name Answer Key Date Pd 2. A recipe for salad dressing calls for 2 tsp of vinegar to 3 tsp of oil. Based on the data complete the table. How many tsp of oil will be used if 18 tsp of vinegar are used? VINEGAR (TSP) OIL (TSP) 2 3 8 12 10 15 18 27 12 essays WARM -UP 1. Mrs. Matthis can grade 2 essays every 15 minutes. At this rate, how many essays can Mrs. Matthis grade in 1.5 hours? Name Date Pd 2. A recipe for salad dressing calls for 2 tsp of vinegar to 3 tsp of oil. Based on the data complete the table. How many tsp of oil will be used if 18 tsp of vinegar are used? VINEGAR (TSP) OIL (TSP) 2 12 10 27

HE SAID, SHE SAID RECORDING SHEET Answer Key Name Date Pd Each of the 10 cards will have statements from two students. Read carefully and choose the name of the student who made the correct statement. Then, justify your answer in the space provided. 1 Alex is correct because 2 Bryson is correct because *Check students work. Explanations will vary. 3 Charlie is correct because 4 Dakota is correct because Enrique is correct because 5 6 Frankie is correct because Grace is correct because 7 8 Hugo is correct because Ivy is correct because 9 10 Jaqueline is correct because

QUICK CHECK Name Answer Key Date Pd 1. A bike travels 24 miles in 3 hours. At this rate how many miles will the bike travel in 10 hours? A. 192 B. 80 C. 32 D. 124 2. Edgar pays $67.86 for 7.8 pounds of fertilizer. What is the price per pound of fertilizer? F. $6.98 G. $5.65 H. $8.70 J. $10.26 3. Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. When company comes she makes 96 fluid ounces of coffee. How many grams of coffee beans does Diana use when company comes? A. 160 B. 60 C. 98.2 D. 14.4 1. A B C D 2. F G H J 3. A B C D 4. F G H J 5. A B C D 6. F G H J 7. A B C D 8. F G H J 9. A B C D 10. Use the grid below. 1 0 5 4. Sarah Beth babysits and earns $10.50 per hour. Which of the following best represents the relationship between the number of hours, h, and the total earnings, t. F. t = 10.50 + h G. t = 10.50h H. h = 10.50 + t J. h = 10.50t 5. The model below shows the ratio of gray to white squares. Which of the following is not an equivalent ratio of gray squares to total squares? A. 9/24 B. 21/60 C. 15/40 D. 27/72