2. Constructed Response Assessment October 17th

3. A ratio is a comparison of two quantities using division. Ratios can be written in three different ways: 7 to 5, 7:5, and Order matters when writing a ratio. 7575 Day 1: Ratios Find the ratio of boys to girls in Donnelly’s class.

4. Lucky Ladd Farms has: 16 cows, 8 sheep, and 6 pigs  cows to sheep  pigs to total animals  sheep to pigs Always simplify your ratio to the lowest term.

5.  The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.  For every vote candidate A received, candidate C received nearly three votes. Make a table or model to represent one of the above situations. BeakWing 12 24 36 48

6. Remember, a ratio makes a comparison. The ratio of green aliens to total aliens is 3 to 7. ****Make sure you write the ratio just like they ask for it!**** The ratio of total aliens to purple aliens is 7 to 4. Not 4 to 7

7.  1. What is the ratio of blue balloons to red balloons?  2. What is the ratio of total balloons to orange balloons?  3. What is the ratio of yellow balloons to total balloons?  4. What is the ratio of green balloons to purple balloons?

8. Ratios that make the same comparison are equivalent ratios. To check whether two ratios are equivalent, you can write both in simplest form. Day 3: Equivalent Ratios 20 cars : 30 trucks 10 : 152 : 3 80 : 120

9. Check It Out! Example 1 Write the ratio 24 shirts to 9 jeans in simplest form. 24 9 8383 The ratio of shirts to jeans is, 8:3, or 8 to 3. = shirts jeans 24 ÷ 3 9 ÷ 3 Write the ratio as a fraction. = = Simplify. 8383

10. Lesson Quiz: Part I Write each ratio in simplest form. 1. 22 tigers to 44 lions 2. 5 feet to 14 inches 4 15 3. 7 21 4. 8 30 12 45 Possible answer:, 1313 14 42 Possible answer:, Find a ratios that is equivalent to each given ratio. 1212 30 7

11. Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent. 12 15 B. and 27 36 3 27 A. and 2 18

12. Lesson Quiz: Part II 7. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. Are the ratios of poured juice to starting amount of juice equivalent? 8 64 16 128 and ; yes, both equal 1818 8585 8585 =; yes 16 10 5. 36 24 6. Simplify to tell whether the ratios are equivalent. and 32 20 and 28 18 3232 14 9  ; no

13. 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. This spaceship can travel 100 miles in 5 seconds is a rate. It can be written 100 miles 5 seconds

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

15.  Remember: A rate is a ratio that compares two quantities measured in different units (miles, inches, feet, hours, minutes, seconds).  The unit rate is the rate for one unit of a given quantity. Unit rates have a denominator of 1.

16. A unit rate compares a quantity to one unit of another quantity. These are all examples of unit rates. 2 eyes per alien 1 foot per leg 6 tentacles per head 1 tail per body 3 windows per spaceship 3 riders per spaceship

17. 150 heartbeats 2 minutes Unit Rate (divide to get it): 150 ÷ 2 = 75 75 heartbeats to 1minute OR 75 heartbeats per minute Rate

18. Amy can read 88 pages in 4 hours (rate). What is the unit rate? (How many pages can she read per hour?) 88 pages 4 hours 22 pages / hour

19. Unit rates are rates in which the second quantity is 1. unit rate: 30 miles, 1 hour or 30 mi/h The ratio 90 3 can be simplified by dividing: 90 3 = 30 1 Try this by yourself!

20. Check It Out! Can you solve? Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute? 90 words 2 minutes Write a rate. = Penelope can type 45 words in one minute. 90 words ÷ 2 2 minutes ÷ 2 Divide to find words per minute. 45 words 1 minute

21.  Unit price is a unit rate used to compare price per item.  Use division to find the unit prices of the two products in question.  The unit rate that is smaller (costs less) is the better value.

22. Juice is sold in two different sizes. A 48- fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy? $2.07 48 fl.oz. 0.04312 5 $0.04 per fl.oz. $1.64 32 fl.oz. 0.05125 $0.05 per fl.oz. The 48 fl.oz. bottle is the better value.

23. Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which pack has the lower unit price? Additional Example: Finding Unit Prices to Compare Costs Divide the price by the number of pens. price for package number of pens = $1.95 5 =$0.39 price for package number of pens = $6.20 15  $0.41 The 5-pack for $1.95 has the lower unit price.

24. Try this by yourself John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price?  $2.19 24 = $0.09 = $3.79 36  $0.11 The 24 oz jar for $2.19 has the lower unit price. price for bottle number of ounces price for bottle number of ounces Divide the price by the number of ounces.

25. 7 10, 21 30 x 3 Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators. 8 9, 2 3 ÷ 4 ÷ 3 No, these ratios do NOT form a proportion, because the ratios are not equal. Day 7: A proportion is an equation stating that two ratios are equal.

26.  A proportion is an equation stating that two ratios are equal. Example: A piglet can gain 3 pounds in 36 hours. If this rate continues, the pig will reach 18 pounds in _________ hours. Jessica drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles?

27. Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline? 25 miles 1 gallon Unit Rate = 8 gallons x 8 25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.