Lesson 1C ~ Measurement Determine the best unit of measurement you would use in each situation. 1. distance from your home to the nearest airport. best customary unit: best metric unit: 2. mass of a marble. best customary unit: best metric unit: 3. length of a fence. best customary unit: best metric unit: Complete each conversion. 4. 360 inches = yards 5. 2 miles = inches 6. 500 millimeters = centimeters 7. 4 hours = seconds 8. 250 centimeters = meters 9. 128 ounces = pounds 10. Sami ran 1,320 feet in 2 minutes. a. At this rate, how many feet would Sami run in 1 hour? b. Find Sami s speed in miles per hour. 11. a. Find the surface area of the cube in square feet. b. Find the volume of the cube in cubic feet. 2 yards 2 yards 2 yards 12. Find the area of the triangle in square centimeters. 5 m 12 m 13 m
Lesson 2C ~ Fractions and Decimals Find each sum, difference, product or quotient. Convert the answer to a decimal. 1. 1 1 7 2 7 3 + 2. 3. 4 2 10 5 8 8 4. 1 1 1 2 3 1 2 5. 4 3 2 3 6. 2 14 7 16 7. 1 3 + 8. 5 3 8 4 41 9. 1 1 + 2 3 Find each sum, difference, product or quotient. Convert the answer to a fraction or mixed number in simplest form. 10. 0.2 + 1.3 11. 2.4 1.1 12. (0.25)(1.4) 13. 3.5 0.7 14. 3.75 + 0.625 15. (3.125)(0.8) 16. 0.4 0.25 17. 1.5 4.5 18. 0. 6 + 0.5 19. a. Find the sum: 2.3 + 0. 6. b. Convert each number in part a to a fraction or mixed number and then find the sum. c. Do your two answers match? Explain why or why not. 20. a. Shade the figure so it shows a decimal value between 0.55 and 0.7. b. Write the shaded part of the picture as a fraction and a decimal.
Lesson 3C ~ Ratios 1. The basketball team won 12 games and lost 18 games. a. Write the ratio of wins to losses. b. Write the ratio of wins to total games played. c. Write the ratio of losses to total games played. 2. The ratio of dogs to all pets in a pet store was 32. a. Write the ratio of dogs in the pet store to other types of pets in the pet store. b. If there were 12 dogs in the pet store, how many other types of pets were in the pet store? c. If there were 21 total pets in the pet store, how many would be dogs? 3. A rectangle has a base and a height in a ratio of 1 : 1. a. What is the most specific name for this shape? Draw one example of the shape. b. If one side has a length of 5 centimeters, what is the perimeter of the shape? c. If one side has a length of 3 centimeters, what is the area of the shape? There are special rules for the lengths of the sides of a right triangle. One set of sides that creates a right triangle is 3 cm, 4 cm and 5 cm. These sides can also be written as a ratio 3 : 4 : 5. In fact, any triangle with sides in a simplified ratio of 3 : 4 : 5 creates a right triangle. 3 cm 5 cm 4 cm A triangle with sides 6 in, 8 in and 10 in has sides in a ratio 6 : 8 : 10 which simplifies to 3 : 4 : 5 since every side has a factor of 2. When writing the ratio, you do not need to write the units when they are the same for every side length. 4. a. One set of sides that creates a right triangle has sides in a ratio of 3 : 4 : 5. Find two different sets of sides in centimeters that would create a right triangle using this ratio. b. Another set of sides that creates a right triangle has sides in a ratio 5 : 12 : 13. Find two different sets of sides in feet that would create a right triangle using this ratio. Write a ratio using a colon that has a value between the other two ratios given. 5. 1 9,, 2 to 5 6. 4 to 5,, 4 10
Lesson 4C ~ Unit Rates Find each unit rate. 1. 320 miles 8 gallons 2. 55 words 2 minutes 3. 522 miles 9 hours 4. Write three rates equivalent to the unit rate 40 miles. 1hour 5. A store sells 3 dozen large cookies for $30.60. Find the price per cookie. 6. Kendra walked 12 miles in 3 hours. How many feet per hour did she walk? 7. Mandy can buy a 12-ounce box of crackers for $6.60 or a 15-ounce box of the same crackers for $7.80. Which is the better deal? Explain using unit rates. 8. Tabitha bought one dozen socks for $9.00. How much would 18 socks have to sell for in order to be a better deal? Explain using unit rates. 9. Tram rode his bike at a steady rate of 12 miles per hour. a. At this rate, how far had Tram ridden after 15 minutes? b. At this rate, how far had Tram ridden after 1 hour and 20 minutes? 10. Marta walked 6 miles in 1.5 hours. At this rate, how long will it take her to walk 16 miles? 11. Lionel typed 320 words in 4 minutes. At this rate, how long will it take him to type 800 words?
Lesson 5C ~ Rate Conversions Complete each fraction so it is equal to 1. [ ] mile 1. 5280 feet 2. 1[ ] 60 minutes 3. [ ] millimeters 1kilometer Convert each rate. 4. 8 miles 1 hour feet to hour 5. 160 meters 1 minute to meters hour 6. 30 feet 1 second yards to minute 7. 2 kilometers per hour to meters per day 8. 3600 words 1 hour words to second 9. 3 miles per hour to feet per minute 10. Jacob ran at a rate of 7 miles per hour. At this rate, how far does he run in 30 minutes? 11. Dale drove 270 miles in 4.5 hours. At this rate, how far did he travel in 20 minutes? 12. Lucinda drove for 30 minutes at a rate of 60 miles per hour. Then she travelled 20 minutes at a rate of 36 miles per hour. Overall, what was her average rate of speed in miles per hour?
Lesson 6C ~ Write and Solve Proportions Solve each proportion. 2 x 1. = 2. 5 20 4 28 6 2a = 3. = 7 y 42 7 4. 3 x = 18 8 24 5. 33 2y = 6. 75 50 2 5 = 9 b 7. 1 24 = x 36 8. 15 5x = 9. 30 12 5 20 4 = y + 2 10. Bob walked 20 miles in 4 hours. Kelly walked 14 miles in 3 hours. Are these rates proportional? Explain why or why not. 11. Tami typed 120 words in 2 minutes. Carl typed 30 words in 30 seconds. Are these rates proportional? Explain why or why not. 12. Sherlock put two tomato plants in his garden. The first tomato plant produced 20 tomatoes in a 2-day period. The second tomato plant produced 35 tomatoes in a 3.5-day period. Are these rates proportional? Explain why or why not. 13. Write a proportion for the phrase and solve it: 9 pounds for $5.85; 20 pounds for d dollars 14. Write a proportion using the variable x. The solution to the proportion should be x = 5.
Lesson 7C ~ Problem-Solving With Proportions Solve each proportion. 3 6x 1. = 2. 9 45 10 4 = y 25 30 Solve each problem using a proportion. The answers are listed at the bottom of the page out of order without units. Cross out each answer once you find it. 3. A bicyclist rides 16 miles in 2 hours. How far will the bicyclist ride at this speed in 7 hours? 4. Six candles cost $15.00. How many candles can you buy for $22.50? 5. You paid $32.00 for 10 gallons of gasoline. How much would you pay for 25 gallons of gasoline? 6. Laura ran 6 miles in 1.5 hours. How many minutes will it take her to run 9 miles at this rate? 7. Ken painted 14 meters of fencing in 1 hour. How many centimeters of fencing can he paint in 45 minutes? 8. Nick typed 275 words in 2.5 minutes. At this rate, how many hours will it take him to type 9,900 words? 9. Marta drove her car 448 miles before it ran out of gas. When she started her trip, her car had 14 gallons of gas. At this rate, how many gallons of gas would she need to travel 84,480 feet? 10. Cassie hiked at a rate of 3 miles per hour. At this rate, how many yards does she travel in 15 minutes? Answers: 9 1050 80 0.5 56 1.5 135 1320 2010 SM C Curriculum Oregon Focus on Proportionality
Lesson 8C ~ Similar and Congruent Figures 1. a. Is Δ MAN congruent or similar to Δ BOY? Explain. 4 in A 4 in O 10 in 10 in b. Determine the scale factor between Δ MAN and Δ BOY. M 2 in N B 5 in Y c. Find the perimeter of Δ MAN and Δ BOY. What is the ratio of their perimeters? 2. Suppose rectangles ABCD and WXYZ are congruent to each other. Which side of WXYZ corresponds to AD? Determine the scale factor for each pair of similar figures. 3. 4. 45 in 15 in 4 cm 6 cm In Question #1d, you learned that the ratio of the perimeters of two similar figures is equal to the ratio of the sides of the two figures (scale factor). Use this to write a proportion and solve for the missing perimeter in the similar figures below. 5. 6. 15 mm 24 mm Perimeter = 50 mm Perimeter =? mm 15 yd Perimeter =? yd 9 yd Perimeter = 30 yd 7. 5 m 15 m 8. 4 m Perimeter = 12 m 12 m Perimeter =? m 12 ft 21 ft Perimeter =? ft Perimeter = 56 ft 2010 SM C Curriculum Oregon Focus on Proportionality
Lesson 9C ~ Proportions and Similar Figures The shapes below are similar. Use proportions to solve for each variable. 18 in 1. 6 in 2. 12 ft 5 in 3x in 14 ft y ft 3 ft 2 in ( x +1) in 3. 4. 4 in 6 in 25 ft 20 ft 10 ft 2y ft 5. 16a ft 6. 10 ft 96 ft 12 ft 27 in 36 in 0.5x in 6 in 7. Mike wanted to find the height of his house. He measured the shadow from his house on the ground to be 20 feet. He measured his own shadow on the ground to be 5 feet. Mike is 6 feet 6 inches tall. Find the height of his house. 8. Paula used a mirror to find the height of a telephone pole. She found her eye height to be 2 meters and 60 centimeters. Her distance to the mirror was 1 meter 20 centimeters. The mirror was 15 meters from the telephone pole. Find the height of the telephone pole. 2010 SM C Curriculum Oregon Focus on Proportionality
Lesson 10C ~ Special Ratios for Similar Figures For each pair of similar figures: a. Find the scale factor (units must be the same). b. Find the ratio of the perimeters. c. Find the ratio of the areas. 1. 2. 2 in 3 in 25 ft 30 ft 3. 4. 14 m 18 m 2 m 50 cm 5. 1 ft 6 in 6. 40 ft 100 ft 7. Use the similar figures to the right. a. If the smaller hexagon has a perimeter of 24 m, find the perimeter of the larger hexagon. 3 m 4 m b. If the larger hexagon has area 32 m 2, find the area of the smaller hexagon. 8. Use the similar figures to the right. a. If the smaller rectangle has a perimeter of 18 inches, find the perimeter of the larger rectangle. 6 in b. If the larger rectangle has an area of 50 square inches, find the area of the smaller rectangle. 10 in 9. Two octagons are similar. They have a scale factor of 2 : 3. a. If the larger octagon has a perimeter of 36 centimeters, what is the perimeter of the smaller octagon? b. If the smaller octagon has an area of 24 square centimeters, what is the area of the larger octagon? 2010 SM C Curriculum Oregon Focus on Proportionality
Lesson 11C ~ Scale Drawings A map has a scale 3 inch : 10 miles. Use the given map distance to find the actual distance. 1. 9 in 2. 1 ft A map has a scale 2 inches : 5 kilometers. Use the given actual distance to find the map distance. 3. 30 km 4. 1,500 m 5. Two cities are 24 miles apart. On a map, the cities are 6 inches apart. Find the scale of the map. 6. A fence is 8 inches long in a scale drawing. The actual fence is 36 feet long. Find the scale of the drawing. 7. A blueprint of a park has a scale 2 centimeters : 3 meters. On the blueprint, the area for the play structure is 80 square centimeters. What is the actual area of the play structure area? 8. A blueprint of a house has a scale of 1 inch : 2 feet. a. Find the actual length of a wall that is 9.5 in on the blueprint. b. The actual height of a door is 7 feet. How many inches is this on the blueprint? 9. You are building a model of a statue. The scale is 4 : 49. The model is 6 inches tall. How tall is the actual statue? 10. You are remodeling your house. The ratio of measurements from the scale drawing to the actual floor is 1 inch : 5 feet. The floor on the scale drawing is 4 inches by 3 inches. a. You need to buy baseboards. What is the perimeter of the actual floor? b. You need to buy carpet. What is the area of the actual floor? 2010 SM C Curriculum Oregon Focus on Proportionality
Lesson 12C ~ Fractions, Decimals and Percents Write a fraction in simplest form that has a value between the two percents. 1. 75% and 80% 2. 0.3% and 0.4% 3. 340% and 400% Write a percent that has a value between the two decimals. 4. 0.4 and 0.5 5. 4.3 and 4.6 6. 0.004 and 0.005 Write a decimal that has a value between the two fractions. 7. 3 1 and 2 1 9 8. 1000 11 and 1000 2 1 and 13 2 9. 5 10. Penelope read that 52% of people liked action movies. a. What fraction of people like action movies? b. What decimal represents the portion of people who do not like action movies? 11. On the grid to the right: a. Shade 6 1 red, 25% blue, and the rest of the grid yellow. b. What part of the grid is shaded yellow? Write as a fraction, a decimal and a percent. 12. The ratio of wins to losses for a soccer team was 1 : 3. a. What percent of the team s total games were losses? b. What percent of the team s total games were wins? 13. A house blueprint has a scale of 1 inch : 2 feet. The family room has an actual length of 16 feet. a. What is the length of the family room on the blueprint? b. What percent of the length of the actual family room is the length of the family room on the blueprint? 14. There is a 40% chance Tamara will choose a red marble from a bag of marbles. a. Write 40% as a fraction in simplest form and as a decimal. b. What is the chance Tamara will NOT choose a red marble from the bag of marbles? Write your answer as a fraction in simplest form and as a decimal. c. If there are 12 red marbles in the bag, how many total marbles are in the bag?
Lesson 13C ~ Probability A bag has 4 red marbles, 3 green marbles, 8 blue marbles and 5 yellow marbles. Find the probability that Susan will randomly choose the specified marble from the bag. Write as a fraction in simplest form. 1. P(red) 2. P(red or blue) 3. P(black) 4. P(yellow) 5. P(red, green or yellow) 6. P(green) Suppose Susan chooses one marble out of the bag, replaces it, and then chooses a second marble out of the bag. The probability she would choose a red marble and then a green 1 3 marble is 3 5 20 = 100 or 3%. You multiply the probability of choosing each color together and the product is the probability she will choose both colors. Use this to find each probability below assuming she chooses one marble, replaces it, and then chooses a second marble. 7. P(red and then blue) 8. P(blue and then yellow) 9. P(red and then red) 10. Connie has 1 blue marble, 1 green marble and 1 red marble. She randomly chooses one marble, replaces it, and then randomly chooses a second marble. a. List all of her possible outcomes (example: BG means blue first, then green) b. What is the probability she will choose a green marble and then a red marble? 11. Jane and Kyle decided to roll a number cube to see who would start the game. Jane will start if a 1, 2 or 3 appears and Kyle will start if a 4, 5 or 6 appears. Suppose they rolled the number cube 10 times and Jane s numbers appeared 4 times while Kyle s numbers appeared 6 times. a. What is the experimental probability Jane s numbers will appear on the next roll? b. What is the experimental probability Kyle s numbers will appear on the next roll? c. What is the theoretical probability Jane s numbers will appear on the next roll? d. Why are the probabilities in parts a and c different? 12. A bag has 40 marbles. a. How many marbles should be red if the probability of randomly choosing red is 30%? b. How many marbles should be green if the probability of randomly choosing green is 51? c. How many marbles should be blue if the probability of randomly choosing blue is 0.5?
Lesson 14C ~ Use Probability To Predict 1. You plant 15 tulip bulbs and 10 of them grow into flowers that bloom. If you plant 21 more tulip bulbs, predict how many of them would bloom. 2. Park rangers in Yosemite estimated the number of raccoons in one hiking area. The rangers tagged 15 raccoons in the hiking area. The following week they captured 40 raccoons. If the park rangers estimated there were 75 raccoons in the area, how many of the captured raccoons were tagged? 3. Bill surveyed 20 students. He asked for their favorite type of music. Their responses are below. Music Type Hip-Hop Rock Classical Country Number of Students 4 8 6 2 a. Find the experimental probability a student will pick each of the four types of music. Write as a simplified fraction. Music Type Hip-Hop Rock Classical Country Experimental Probability b. Use the probability in part a to predict how many students out of 55 students would choose rock as their favorite type of music. 4. Tim randomly asked 30 students who they planned to vote for in the upcoming class election. 2 From his results, he determined about 66 3 % planned to vote for Kelly. Based on his prediction, how many of the 30 students he interviewed planned to vote for Kelly? 5. a. Complete the chart to the right showing the sum of two number cubes. b. If Haley rolls the number cubes 18 times, estimate the number of times you would expect her to roll a sum of 3. c. If Haley rolls the number cubes 18 times, estimate the number of times you would expect her to roll a sum of 7. d. How many times would Haley have to roll the number cubes in order for you to expect her to roll a sum of 2? + 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6
Lesson 15C ~ Probabilities and Data Displays 1. Bryan randomly asked several students which type of animal they had at home as a pet. The results are in the pie chart below. a. What percent of the students had dogs? b. What percent of the students had birds? c. How many total students did Bryan interview? Cats 30% Birds 20 Dogs 3 5 2. Marvin was in charge of ordering sodas for the class fundraiser. He made a circle graph to show the number of each size of soda. However, he accidently put his work in the graph showing the degree measures he used to make the chart instead of the number of sodas he needed and he threw away his original paper showing the number of each. Help him figure out how many of each size of soda he needs to order by answering the questions below. a. Fill in the chart to show the percent of each size of soda Marvin needs to order. Size Small Medium Large Extra Large Medium Large Percent of Students 135 120 b. If there are 96 students ordering sodas next week, how many of each size soda does Marvin need to order? Size Small Medium Large Extra Large Number of Students 60 Small X-Large 3. The histogram to the right shows the number of students in a PE class with their mile running times. a. How many students are in the PE class? b. Which interval would have the time 8 minutes? c. In which interval of time did most students finish? d. Find the probability a random student chosen ran with a time between 6 and 7 minutes. e. The teacher teaches a total of 120 students in all PE classes. Predict how many students will run between 6 and 7 minutes. Number of Stud ents 15 10 5 Student Mile Times 1 6 5 8 10 5 6 7 8 9 10 Time (minutes)
Lesson 16C ~ Solving Percents Using Proportions Identify the percent of unit squares that are shaded. If necessary, use a proportion to find the percent. 1. 2. Use a proportion to solve the problems on the left. Solve the equations on the right. Match the solutions to the equations with the solutions to the percent problems. 3. What is 10% of 1? A. 3x + x 10 = 5x 40 4. Five is 20% of what number? B. 10(x + 3) = 31 5. Eighteen is 150% of what number? C. 30 3x = 31 x 6. What is 15% of 60? D. 2(x + 7) = 3x 2 7. Peggy went to dinner with friends. The bill was $82.50. Peggy left a 20% tip. How much money did Peggy leave for the tip? 8. Carl bought a jacket. It was originally $65. He bought the jacket for 30% off the original price. a. What was the discount on the price of the jacket? b. What did Carl actually pay for the jacket? 9. At the end of the day, Mandy sold the rest of her hot dogs at her hot dog stand for half price. She sold 24 hot dogs at half price which meant she sold all of her hot dogs that day. If she sold 30% of her hot dogs at half price, how many hot dogs did she sell at full price that day? 10. Kay planted flower seeds in her garden. The package said about 85% of the seeds would grow into flowers. Kay had 119 flowers that bloomed. About how many seeds did not bloom?
Lesson 17C ~ Solving Percents Using Equations For each problem: a. Use the percent equation to solve. b. Write a different percent problem that has the same answer as part a. 1. What is 25% of 60? 2. Eight is 5% of what number? 3. What percent of 64 is 96? 4. What is 0.2% of 3,000? 5. Eighteen is 90% of what number? 6. What percent of 54 is 18? A 7. Use the rectangle to the right. a. Sketch a rectangle that has side lengths 25% of those in ABCD. Label the vertices EFGH 12 m and write the measurements for the new side lengths. C 20 m B D b. What is the scale factor of ABCD to EFGH? 8. Two similar figures have a scale factor 2 : 3. a. If the smaller figure has a side with a length of 16 inches, what is the corresponding length on the larger figure? b. How much longer is each side on the second figure than the first using a percent? 9. A cube has a side length of 25 centimeters. Another cube has side lengths that are 40% of those on the first cube. a. What are the side lengths on the second cube? b. What is the surface area of the second cube? c. What is the volume of the second cube? 25 cm 10. Tiffany went to dinner with friends. The bill was $54. She paid for the dinner and the 15% tip. How much did Tiffany spend altogether?
Lesson 18C ~ Percent of Change Identify the percent of change as an increase or a decrease. Find the percent of change. 1. 60 to 75 2. 96 to 48 3. 120 to 80 Identify the new number given the original number and the percent of increase or decrease. 4. 40 to 5. 15 to 6. 35 to percent increase: 20% 1 percent increase: 33 3 % percent decrease: 40% 7. 100 to 8. 24 to 9. 50 to percent decrease: 25% percent increase: 50% percent decrease: 2% 10. Brandon needed to pick blueberries from 60 bushes. He has picked blueberries from 6 of them. Find the percent decrease in the number of blueberry bushes from which he still needs to pick berries. 11. George bought a house for $210,000. Now, it has increased in value by 8%. a. How much more is the house worth now? b. What is the total value of the house now? 12. Lance bought a car last year for $18,000. It has decreased in value by 15%. How much is the car worth now? 13. You are planning a fundraiser for next year. This year you sold $650 worth of plants. You would like to increase your sales by 30% next year. How much money do you hope to raise next year?
Lesson 19C ~ Percent Applications A store buys an item for the original price listed. It then charges customers the original price paid plus an additional percent of markup. If the item does not sell, the store tries to sell the item on sale at a discounted price. For each problem: a. Find the selling price once the store applies its percent of markup. b. Find the sale price for the item using the percent of discount from your answer to part a. Round to the nearest tenth, if necessary. 1. original: $42.50 2. original: $63.10 percent of markup: 6% percent of markup: 20% percent of discount: 5% percent of discount: 10% 3. original: $24.50 4. original: $45.90 percent of markup: 40% percent of markup: 50% percent of discount: 20% percent of discount: 25% 5. Nancy went to breakfast with her friend. The waitress brought the bill which was $21.20. They decided to leave a 15% tip and split the total cost. How much did Nancy pay? 6. Kevin went to dinner with two friends. The bill was $42.00. They decided to leave a 15% tip and then split the total cost. How much did Kevin pay? 7. Tanya bought a pair of roller skates in California. The skates cost $32 before the 8% sales tax was applied. How much did Tanya pay for the roller skates after taxes were included in the cost? 8. Megan found a pair of shoes that were originally $65.00. They had been on sale for 20% off and they were now an additional 10% off the sale price. a. What was the actual price of the shoes? b. Megan s friend insisted the shoes were 30% off the original price. Was this true? 9. Fadia bought a new computer in Tennessee. The computer was originally $400. It was on sale for 15% off the original price. Tennessee has a 7% sales tax. How much did Fadia spend on the new computer? 2010
Lesson 20C ~ The Coordinate Plane Graph the ordered pairs for each figure. Connect the points in the order given and connect the last point to the first. The two figures are similar. a. Write the scale factor of Figure 1 to Figure 2. b. Write the ratio of their perimeters. c. Write the ratio of their areas. 1. Figure 1: (4, 0) (4, 6) (0, 6) (0, 0) 2. Figure 1: ( 3, 0) ( 3, 4) (0, 0) Figure 2: ( 5, 8) ( 5, 2) (4, 2) (4, 8) Figure 2: (0, 0) (6, 0) (6, 8) Graph the points in each table. If the pattern continued, what would be the next point? 3. x 3 1 1 3 5 4. x 8 4 0 4 8 y 5 2 1 4 7 y 9 6 3 0 3 5. x 2 1 0 1 2 6. y 3 1 1 3 5 x 7 4 1 2 5 y 7 4 1 2 5
Lesson 21C ~ Making Sense of Graphs 1. Viviana walked for one hour at a constant speed. Sketch a graph that shows her speed over time. Sketch a second graph that shows her total distance travelled over time for the one hour. Speed Distance 1 hour 1 hour 2. Tyrone was at a movie. He drove home afterward and then went to a friend s house. On his way to his friend s house, he stopped to get gas. The graph below shows his distance from home (miles) over time (hours). Tyrone s Trip a. How far away was the movie theater from Tyrone s house? b. Find Tyrone s rate of speed in miles per hour for the trip home from the movie theater. c. Find Tyrone s rate of speed in miles per hour for the trip from home to the gas station. d. How long was Tyrone at the gas station? e. How long did it take Tyrone to get from his house to his friend s house? Distance from home (miles) (1.75, 4) Time (hours) 3. Timba drove from her home to the desert. The graph below shows her speed in miles per hour over time in minutes. a. What was Timba s fastest speed? Timba s Trip (10, 57) b. How long did Timba drive at her fastest speed? c. What distance did Timba travel while at her fastest speed? d. What does the point (60, 0) mean on the graph? Speed (miles) Time (minutes) 4. Cannon walked to his aunt s house. He walked at a rate of 4 miles per hour. He walked for one-half hour to get to his aunt s house. He stayed for two hours before returning home walking at a rate of 5 miles per hour. Graph Cannon s trip using the coordinate plane at the right. Be sure to include all ordered pairs when line segments change direction. Time (hours) Distance (miles)
Lesson 22C ~ Direct Variation Tables and Graphs Each table below represents direct variation. Graph each scatter plot. Find the rate by which each graph increases. 1. x y 2. x y 3. x y 2 2 0 0 6 2 1 1 2 1 3 1 0 0 4 2 0 0 1 1 6 3 3 1 2 2 8 4 6 2 Determine whether the table models direct variation. Explain why or why not. If it does, give the rate. 4. x y 5. x y 6. 0 0 4 1 2 4 0 0 4 5 4 1 6 6 8 2 8 7 12 3 x y 2 1.5 4 3 6 4.5 8 6 10 7.5 7. a. Draw an example of a direct variation graph. b. Write the ordered pairs for at least two points on your graph. c. Identify the rate of your direct variation graph. d. Write a story that fits your direct variation graph. 8. a. Draw a graph that does NOT show direct variation. b. Write the ordered pairs for at least two points on your graph. c. Explain why your graph is NOT a direct variation graph.
Lesson 23C ~ Direct Variation Equations The tables below show ordered pairs which model direct variation. Write an equation relating the x and y coordinates. 1. x y 2. x y 0 0 3 1 3. 2 6 0 0 4 12 3 1 6 18 6 2 8 24 9 3 x y 5 2 0 0 5 2 10 4 15 5 4. A novel weighs 4 3 pound. Philip is putting the books into boxes and wants to know how much the novels inside will weigh. a. Write an equation that shows the weight of the novels in the box (y) as a function of the number of books (x) inside the box. b. Explain why the weight of the total novels based on the number of novels can be modeled by a direct variation function. c. If a box holds two dozen books, how much will the novels weigh? d. Make a graph of your equation in part b for Philip. Does it make sense to connect the points on the graph? Why or why not? Weight of Novels Number of Novels 5. A truck driver drives for 5 hours at a constant speed of 55 miles per hour. a. Write an equation that shows the total distance traveled (y) depending on the hours spent driving (x). b. Explain why the distance traveled by the truck driver over the 5 hours can be modeled by a direct variation function. Distance (miles) c. After 3.5 hours, how far had the truck driver traveled? Time (Hours) d. Make a graph of your equation in part b. Does it make sense to connect the points on the graph? Why or why not? Speed e. Draw a graph of the speed of the truck over the 5 hours. Does the graph show a direct variation function? Why or why not? Time (Hours)
Lesson 24C ~ Recognizing Direct Variation 1. Sketch an example of a direct variation graph. 2. Sketch an example of a graph that does not show a direct variation equation. Tell whether or not each equation is a direct variation equation. If it is direct variation, identify the slope. If it is not direct variation, explain. x 3. y = 4. y 4 3 = x 5. y = 4x 5 5 Tell whether or not each table shows ordered pairs that model a direct variation equation. If the ordered pairs show direct variation, write the direct variation equation. If the ordered pairs do not show direct variation, explain. 6. x y 7. x y 8. 2 4 4 3 1 2 4 3 0 0 8 6 1 2 12 9 2 4 16 12 x y 5 3 0 0 5 3 10 5 15 8 9. Pierre runs one lap around the track in 1.75 minutes. a. Complete the table below to show the minutes it takes Pierre to run the given number of laps. Number of Laps 0 1 2 3 4 5 6 7 Minutes 0 1.75 b. Does the table model a direct variation equation? If so, write the equation. If not, explain why not. 10. a. Complete the table below and write the perimeter of a square with the given side length. Length of Side 0 1 2 3 4 5 6 7 Perimeter 0 4 b. Does the table model a direct variation equation? If so, write the equation. If not, explain why not.
Lesson 25C ~ Writing Linear Equations Sometimes it is important to know where two linear equations intersect. Suppose you have a choice of buying a pizza pass for $15 that entitles you to buy large pizzas for $5. Without the pass, a large pizza costs $8. Follow the directions below to determine how many pizzas you will have to buy for the two total costs to equal one another. 1. Fill in the table showing the total cost given the number of pizzas purchased. Number of Pizzas 0 1 2 3 4 5 6 7 Cost with Pizza Pass Cost with NO Pass 2. Write an equation that models the total amount of money spent (y) for x number of pizzas with the pizza pass. 3. Write an equation that models the total amount of money spent (y) for x number of pizzas without the pizza pass. Cost 4. Graph the equations from #2 and #3 on the same grid. At which point do they intersect? 5. How many pizzas would you have to buy in order for the pass to be a better deal? Number of Pizzas Graph the two equations given. Write the ordered pair for the point where the two lines intersect. 6. y = 2x +1 7. y = x + 5 y = 3x 1 y = 21 x 1