Ratios, Rates, and Unit Rates across the Universe

1. Ratios, Rates, and Unit Rates across the Universe What is the difference between a ratio and a rate? 706.2.7 use ratios and proportions to solve problems

2. Definition: A comparison of two numbers: Parts to whole: Or Parts to Parts: Written As: Fraction, with :, and to Examples: 8/35, 8:35, 8 to 35 Ratios Comparing Ratios You can use fraction rules to compare Or You can turn the ratios into decimals Finding Missing Part of Ratio: See how many times it takes to go from one fraction to the other. Do the same thing to the top or bottom. Equivalent Ratios = Equivalent Fractions You can multiply the top and bottom by the same # or reduce to get an Equivalent ratio

3. RATIOS A ratio makes a comparison. There are 3 green aliens and 4 purple aliens. The ratio of green aliens to purple aliens is 3 to 4.

4. RATIOS A ratio makes a comparison. The ratio of green aliens to total aliens is 3 to 7. The ratio of total aliens to purple aliens is 7 to 4.

5. RATIOS A ratio makes a comparison. Ratios can be written in three different ways. 3 to 4 3:4 3 4

6. Ratios • Ratios can be written as a comparison of parts to parts or a comparison of parts to whole. • Ex: 3 boys to 5 girls (not a true fraction) • Ex: 3 boys to 8 students (true fraction)

7. Written As: Fraction, with :, and to (Out of : part to whole only) Examples: 8/35, 8:35, 8 to 35 Definition: A comparison of two numbers: Parts to whole: Or Parts to Parts: Ratios

8. White Board Practice Wins to Losses Wins=17, Losses=14 Write the ratio three different ways: 17:14 17 to 14 17/14 Now write a ratio three different ways for the wins to total games played. 17:31 17 to 31 17/31

9. Definition: A comparison of two numbers: Parts to whole: Or Parts to Parts:

10. Assessment Prompt • What is a ratio? • What are different ways to write a ratio?

12. Definition: A comparison of two numbers: Parts to whole: Or Parts to Parts: Written As: Fraction, with :, and to Examples: 8/35, 8:35, 8 to 35 Ratios Equivalent Ratios = Equivalent Fractions You can multiply the top and bottom by the same # or reduce to get an Equivalent ratio

13. White Board Practice Write the ratio in simplest form and in an equivalent form. For every 6 boys there are 10 girls. 3:5 12 to 20 60 to 100 Why would a fraction not be a good choice for this ratio?

15. Definition: A comparison of two numbers: Parts to whole: Or Parts to Parts: Written As: Fraction, with :, and to Examples: 8/35, 8:35, 8 to 35 Ratios Finding Missing Part of Ratio: See how many times it takes to go from one common part of a fraction to the other. Do the same thing to the top or bottom. Comparing Ratios You can use fraction rules to compare Or You can turn the ratios into decimals Equivalent Ratios = Equivalent Fractions You can multiply the top and bottom by the same # or reduce to get an Equivalent ratio

17. Assessment Prompt • How do you find the missing part of a ratio? 3/5 x/20

18. Real World Uses • Population: Ethnicity, gender, etc. • Sports statistics: ERA, Batting Avg, Free Throw Percent. • Probability: Odds of occurrences • Comparison Shopping: items per package

20. White Board Practice Who has the greater ratio of Rock CD’s to total CD’s? Luis Rae Rock = 9 Rock = 14 Total = 11 Total = 18 Simply turn your fractions into decimals (divide) to see who has the greater amount. Luis has the greater amount .81

21. White Board Practice Who has the greater ratio of Rock CD’s to total CD’s? Luis Rae Rock = 9 Rock = 14 Total = 11 Total = 18 You could also use cross products to see which is larger: 18 * 9 = 162 = Luis 11 * 14 = 154 = Rae, Luis has more.

22. Assessment Prompt • Text a friend and tell them what a ratio is and how we compare them?

23. Definition: A ratio that compares two different Units of measurement 30 pages : 20 minutes Unit Rate: How many per 1 3 corndogs : $1 62 miles per hour Rates Comparing Rates Compare rates like you would a fraction Unit Cost: Money goes on top because you are Trying to find the cost per 1 unit you will turn the denominator into a 1 through division You can also find unit cost by dividing the cost by the number of items. $5 : 15 mini butterfingers = 5 ÷ 15 = $0.33 per 1 mini butterfinger

24. RATES A rate is a ratio that compares quantities that are measured in different units. This spaceship travels at a certain speed. Speed is an example of a rate. Speed can be measured in many different ways. This spaceship can travel 100 miles in 5 seconds. 100 miles in 5 seconds is a rate.

25. Miles Seconds RATES A rate is a ratio that compares quantities that are measured in different units. Rates are often written in fraction form. 100 miles in 5 seconds is a rate. It can be written as…..

26. RATES A rate is a ratio that compares quantities that are measured in different units. One key word that often identifies a rate is PER. Miles per gallon, Points per free throw, slices per pizza, Sticks of gum per pack What other examples of rates can your group think of?

27. Assessment Prompt • What makes a rate different from a ratio? • Is a rate a ratio? Is a ratio a rate?

28. Tic-Tac-Think: Simplifying Radical Expressions: Choose 3 questions that will total at least 5 points 1 1 1 2 2 2 3 3 3

29. End of Lesson

30. Activator • Review: what are ratios and rates? • In math, how much is a unit?

32. Definition: A ratio that compares two different Units of measurement 30 pages : 20 minutes Unit Rate: How many per 1 1 corndog : $0.50 62 miles per hour Rates

35. Definition: A ratio that compares two different Units of measurement 30 pages : 20 minutes Unit Rate: How many per 1 3 corndogs : $1 62 miles per hour Rates Comparing Rates Find the unit rate, the larger unit rate is Bigger. Unit Cost: Money goes on top because you are Trying to find the cost per 1 unit you will turn the denominator into a 1 through division You can also find unit cost by dividing the cost by the number of items. $5 : 15 mini butterfingers = 5 ÷ 15 = $0.33 per 1 mini butterfinger

37. White Board Practice Convert the ratios to a rate 80 miles traveled in 2 hours 40 miles : 1 Hour 24 oranges for $3.00 1 orange for $0.13

38. Assessment Prompt • What is the difference between a rate and a unit rate?

39. Two ways to solve: • Making equivalent ratio to 1. $15 / 3 bags = $? / 1 bag • Divide the numerator by the denominator: $15 / 3 bags = $5 • Key Points: $ should always be on top unless you are finding how much a $1 will buy.

41. Find the Unit Rate: • $350/ 5 nights (solve using equivalent rates) • $1.88 / 20 oz (solve using division) • 90 miles / 3 hours (your choice)

43. Finding a rate from a unit rate • This is real world: You know that 1 bag of dog food costs $5.68. You want to find the rate of 12 bags. You start with a unit rate and work backwards:

44. Finding a rate from a unit rate • This is real world: You can travel 3.8 km per hour. How far could you travel in 4 hours? How far in 270 minutes? You start with a unit rate and work backwards:

45. Using unit rate to find a bargain • You are buying chips for a party. You want to get the most bang for your buck so you want the best price per unit. You have two choices: $8.96 per 40 oz or $9.84 per 48 oz. Which bag of chips should you buy if you want the cheapest unit price?

46. What is the denominator of a unit rate? • Explain the error and correct: $36$1 4 apples .11 apples

47. Worksheet • Turn the camera on and do the worksheet “Is Bigger Always Better?”

48. Homework WORKBOOK: pg. 69-70 all (that is a total of 21 problems if you count # 14 as two separate problems.)