Daily Questions:

1. Daily Questions: Think-Pair-Share: How are common fractions, decimals, percents, and ratios alike? How are they different?

2. Click on the topic to go to that section Table of Contents Writing Ratios Equivalent Ratios Rates Proportions Direct & Indirect Relationships in Tables & Graphs Constant of Proportionality Writing Equations for Proportions Understanding Graphs of Proportions Problem Solving Scale Drawings Similar Figures Common Core: 7.RP.1, 7.RP.2, 7.G.1

3. Ratios and Proportions I can define unit rate. I can compute unit rates, including those with fractions.

4. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Ratios × Ratio - A comparison of two numbers by division Ratios can be written three different ways: a to b a : b a b Each is read, "the ratio of a to b." Each ratio should be in simplest form. Find the ratio of boys to girls in this class

5. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are 48 animals in the field. Twenty are cows and the rest are horses. Write the ratio in three ways: The number of cows to the number of horses The number of horses to the number of animals in the field Remember to write your ratios in simplest form!

6. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are 27 cupcakes. Nine are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of vanilla cupcakes to strawberry cupcakes? A 7 : 9 7 27 B 7 11 C 1 : 3 D

7. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are 27 cupcakes. Nine are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of chocolate cupcakes to total cupcakes? 7 9 A 7 27 B 9 27 C 1 3 D

8. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are 27 cupcakes. Nine are chocolate, 7 are vanilla and the rest are strawberry. What is the ratio of total cupcakes to vanilla cupcakes? 27 to 9 A B 7 to 27 27 to 7 C D 11 to 27

9. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Equivalent Ratios Return to Table of Contents

10. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Equivalent ratios have the same value 3 : 2 is equivalent to 6: 4 1 to 3 is equivalent to 9 to 27 5 35 6 is equivalent to 42

11. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ There are two ways to determine if ratios are equivalent. 1. Common Factor = 4 12 5 15 x 3 = 4 12 5 15 x 3 Since the numerator and denominator were multiplied by the same value, the ratios are equivalent

12. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 2. Cross Products = 4 12 5 15 Since the cross products are equal, the ratios are equivalent. 4 x 15 = 5 x 12 60 = 60

13. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 4 is equivalent to 8 ? 9 18 True False

14. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 5is equivalent to 30 ? 9 54 True False

15. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 18:12 is equivalent to 9,which is equivalent to 36 ? 24 6 True False

16. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 2is equivalent to 10, which is equivalent to 40 ? 24 120 480 True False

17. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ 1:7 is equivalent to 10,which is equivalent to 5 to 65? 70 True False

18. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Rates Return to Table of Contents

19. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Rates Rate: a ratio of two quantities measured in different units Examples of rates: 4 participants/2 teams 5 gallons/3 rooms 8 burgers/2 tomatoes

20. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Unit Rates Unit rate: Rate with a denominator of one Often expressed with the word "per" Examples of unit rates: 34 miles/gallon 2 cookies per person 62 words/minute

21. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Finding a Unit Rate Six friends have pizza together. The bill is $63. What is the cost per person? Hint: Since the question asks for cost per person, the cost should be first, or in the numerator. $63 6 people Since unit rates always have a denominator of one, rewrite the rate so that the denominator is one. $63 6 6 people 6 $10.50 1 person ÷ ÷ = The cost of pizza is $10.50 per person

22. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ John's car can travel 94.5 miles on 3 gallons of gas. How many miles per gallon can the car travel?

23. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ The snake can slither 240 feet in half a day. How many feet can the snake move in an hour?

24. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ The recipe calls for 6 cups of flour for every four eggs. How many cups of flour are needed for one egg?

25. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Sarah rode her bike miles in hour. What is Sarah's unit rate in miles per hour?

26. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Tahira and Brendan going running at the track. Tahira runs 3.5 miles in 28 minutes and Brendan runs 4 miles in 36 minutes. Who runs at a faster pace (miles per hour)? Show your work! Tahira A B Brendan

27. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Fruity Oats is $2.40 for a 12 oz. box. Snappy Rice is $3.52 for a 16 oz. box. Which cereal is cheaper per ounce? Show your work! Fruity Oats A B Snappy Rice

28. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Two families drive to their vacation spot. The Jones family drives 432 miles and used 16 gallons of gas. The Alverez family drives 319 miles and uses 11 gallons of gas. Which family got more miles per gallon of gas? Show your work! A Jones Family B Alverez Family

29. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Mariella typed 123 words in 3 minutes. Enrique typed 155 words in 5 minutes. Who typed more words per minute? Show your work! A Mariella B Enrique

30. I can define unit rate.I can compute unit rates, including those involving fractions.______________________________________________________________________________________________________________________________________________ Textbook Practice Pages 276-277 #5-8, 12-14, 23-27

31. Ratios and Proportions I can define unit rate. I can compute unit rates, including those with fractions. I can determine if two quantities have a proportional relationship.

32. Daily Questions Equivalent ratios? 10:4 and 5/2 4 to 15 and 30:8 What is the unit rate? 650 miles using 32 gallons of gas $56 for 18 bagels What is the missing variable? _x_ = _9_ 3 5

33. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Proportions Return to Table of Contents

34. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Proportions A proportion is an equation that states that two ratios are equivalent. Example: 2 12 3 18 = = 5 15 9 27

35. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Cross out all of the ratios that are not equivalent.

36. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ If one of the numbers in a proportion is unknown, mental math can be used to find an equivalent ratio. Example 1: = 2 6 3 x x 3 = 2 6 3 x Hint: To find the value of x, multiply 3 by 3 also. = 2 6 3 9 x 3

37. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ If one of the numbers in a proportion is unknown, mental math can be used to find an equivalent ratio. Example : = 28 7 32 x ÷ 4 = Hint: To find the value of x, divide 32 by 4 also. 28 7 32 x = 28 7 328 ÷ 4

38. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Solve the proportion using equivalent ratios?

39. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ In a proportion, the cross products are equal. = 530 2 12 = 5 12 2 30 60 60 =

40. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Proportions can also be solved using cross products. = 4 12 5 x Cross multiply Solve for x 4x = 5 12 4x = 60 x = 15 Example 2 = 7 x 8 48 7 48 = 8x 336 = 8x 42 = x Cross multiply Solve for x

41. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Use cross products to solve the proportion?

42. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ Textbook Practice Page 285 #1-8, 29-30, 39-45

43. Ratios and Proportions I can define unit rate. I can compute unit rates, including those with fractions. I can determine if two quantities have a proportional relationship.

44. Daily Questions The Crayola crayon company can make 2400 crayons in 4 minutes. How many crayons can they make in 15 minutes? A typist can type 120 words in 100 seconds. At that rate, how many seconds would it take her to type 258 words? A can of tomato paste weighs 16 ounces and/or 452 grams. This depends on whether you use English measurement or SI.  Find the number of ounces in a kilogram (1000 grams).

45. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000? • Mixing 4 ml of red paint and 15 ml of yellow paint makes orange paint. How much red would be needed if you use 100 ml of yellow paint?  • A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed? • Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she practice in 5 weeks? • In the year 2000, there were 8.7 deaths per 1000 residents in the United States. If there were 281,421,906 residents in the U.S. during 2000, how many people died that year? • In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1000? • A piece of cable 8.5 cm long weighs 52 grams. What will a 10-cm length of the same cable weigh? • Mary can read 22 pages in 30 minutes. How long would it take her to read a 100 page book? Write your answer in hours and minutes and round to the nearest minute, if needed.

46. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000?

47. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 2.) Mixing 4 ml of red paint and 15 ml of yellow paint makes orange paint. How much red would be needed if you use 100 ml of yellow paint? 

48. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 3.) A fast typist can type 120 words in 100 seconds. In 180 seconds, how many words could be typed?

49. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 4.) Carol spends 17 hours in a 2-week period practicing her culinary skills. How many hours does she practice in 5 weeks?

50. I can compute unit rates, including those involving fractions. I can determine if two quantities have a proportional relationship.______________________________________________________________________________________________________________________________________________ • 5.) In the year 2000, there were 8.7 deaths per 1000 residents in the United States. If there were 281,421,906 residents in the U.S. during 2000, how many people died that year?