Unit 2 ~ Comparing Bits & Pieces

Transcription

1 Unit 2 ~ Comparing Bits & Pieces Investigation 1: Making Comparisons I can use rates, ratios, and percents to solve problems. Directions: Please complete the necessary problems to earn the maximum number of points according to the chart below. Show all of your work clearly and neatly for credit- which will be earned based on completion rather than correctness.. Lesson Practice problems Options Maximum Points Points Earned Lesson 1: Creating Ratios points Lesson 2: Equivalent Ratios points Lesson 3: Understanding Rates points Lesson 4: Unit Rates points /40 points

2 1. Write the ratio of frogs to turtles: 2. Write the ratio of basketballs to soccer balls: 3. Write the ratio of calculators to pencils: out of 28 students in a class own a dog. What is the ratio of students who own a dog to students who do not? 5. Name two things that you would like to have in a ratio of 6:1, but not in a ratio of 1:6. Explain your reasoning.

3 6. Describe a real-life relationship that can be represented by the ratio 5 to A math club has 25 members. 11 are males and the rest are females. What is the ratio of males to all club members? 8. A group of preschoolers has 8 boys and 24 girls. What is the ratio of girls to ALL children? 9. A herd of 52 horses has 12 white and the rest are brown. What is the ratio of white horses to brown horses? 10. Describe a real-life relationship that can be represented by the ratio of 7: During a given month, the ratio of sunny days to rainy days is 4:1. Interpret (describe) what the ratio means in terms of sunny days and rainy days. 12. The ratio of left-handed students to right-handed students is 23:5. What is the ratio of righthanded students to total students?

4 13. A bowl has oranges and apples in a ratio of 1:1. If there are 3 apples in the jar, how many oranges are there? 14. Gavin has nickels, dimes, and quarters in the ratio of 8:1:2 (in that order). If Gavin has 6 quarters, how many nickels does he have? 15. A ratio of girls to boys in a swimming club was 2:4. There were 14 girls. How many boys were in the club? How many kids TOTAL were in the club? 16. Your friend uses this reasoning to describe why she thinks that the ratios 4:8 and 8:12 are equivalent. Is she correct? Explain your reasoning. 17. You are downloading songs to your tablet. The ratio of pop songs to rock songs is 5:4. You download 40 pop songs. How many rock songs did you download?

5 18. Are the following ratios equivalent? Show why or why not. 6:10 and 12: Are the following ratios equivalent? Show why or why not. 2:3 and 4:5 20. Are the following ratios equivalent? Show why or why not. 24:100 and 6: Write a ratio that is equivalent to the ratio 3:5. Show why they are equivalent. 22. Write a ratio that is equivalent to the ratio 8:10. Show why they are equivalent. 23. Fill in the blank so that the ratios are equivalent: :5 and 6: Fill in the blank so that the ratios are equivalent: 4:6 and 12:

6 25. Write the following rate as a fraction with labels: Sarah can run 3 miles in 30 minutes. 26. Write the following rate as a fraction with labels: Freddy bought two pounds of apples which cost $ Write the following rate as a fraction with labels: Nancy can text 80 words in two minutes. 28. Write the following rate as a fraction with labels: Jack is traveling 50 miles per hour. For questions 29-33, use the following chart. Students are volunteering at an animal shelter. They are making posters: 29. What is Andrea s rate for making posters? 30. What is Enrique s rate for making posters? 31. Who is the fastest at making posters out of all 4 students? Why?

7 32. Who is the slowest at making posters out of all 4 students? Why? 33. At Andrea s rate, how long would it take her to make 15 posters? 34. Chrissy takes a train to a destination that is 180 miles away. It takes her 3 hours to get there. What is her rate as a fraction? 35. Use the rate from question 34. How long did it take Chrissy to travel just 60 miles? 36. Use the rate from question 34. If Chrissy stayed on the train and traveled a total of 6 hours, how many miles would she travel? 37. Write a unit rate for: 24 animals in 2 square miles. 38. Write a unit rate for: $100 for every 5 guests.

8 39. Write a unit rate for: 880 calories in 8 servings. 40. Write a unit rate for: $12.50 for 5 ounces. 41. Lightning strikes Earth 1000 times in 10 seconds. Find the unit rate, and then find how many times lightning strikes in 12 seconds. 42. You earn $35 for washing 7 cars. Find the unit rate, and then find out how much you earn for washing 4 cars. 43. Decide whether the two rates below are equivalent and explain why. 24 laps in 6 minutes 72 laps in 18 minutes 44. Decide whether the two rates below are equivalent and explain why. $16 for 4 pounds $1 for 1 pound 45. Decide whether the two rates below are equivalent and explain why. 15 breaths for every 36 seconds 90 breaths for every 3 minutes 46. Decide whether the two rates below are equivalent and explain why. 120 points for 3 games 200 points for 5 games

9 47. You job 2 kilometers in 12 minutes. Your friend jogs 3 kilometers in 16 minutes. Who jogs faster? Show how you got your answer. 48. A runner completed a 13 mile race in 105 minutes. Calculate the unit rate, in miles per minutes. Then calculate a different unit rate, in minutes per mile. Exit Ticket After finishing this investigation you should be comfortable doing the following: -Creating ratios. -Determining if two ratios are equivalent. -Understanding rates. -Using unit rates in story problems. Level of Understanding (Circle one)