Constructed Response Assessment October 17th Day 1: Ratios A ratio is a comparison of two quantities using division. Ratios can be written in three different 7 ways: 7 to 5, 7:5, and 5 Order matters when writing a ratio. Find the ratio of boys to girls in Donnelly’s class. 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. 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. Beak Wing 1 2 2 4 3 6 4 8 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 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? Day 3: Equivalent Ratios Ratios that make the same comparison are equivalent ratios. To check whether two ratios are equivalent, you can write both in simplest form. 20 cars : 30 trucks 10 : 15 2 : 3 80 : 120 Check It Out! Example 1 Write the ratio 24 shirts to 9 jeans in simplest form. Write the ratio as a fraction. shirts = 24 jeans 9 = 24 ÷ 3 9÷3 = 8 3 Simplify. The ratio of shirts to jeans is 8 , 8:3, or 8 to 3. 3 Lesson Quiz: Part I Write each ratio in simplest form. 1 1. 22 tigers to 44 lions 2 30 2. 5 feet to 14 inches 7 Find a ratios that is equivalent to each given ratio. 3. 4 15 Possible answer: 8 , 12 30 45 4. 7 21 Possible answer: 1 , 14 3 42 Determining Whether Two Ratios Are Equivalent Simplify to tell whether the ratios are equivalent. A. 3 and 2 27 18 B. 12 and 27 15 36 Lesson Quiz: Part II Simplify to tell whether the ratios are equivalent. 5. 16 and 32 8 = 8; yes 10 20 5 5 6. 36 and 28 24 18 3 14 ; no 2 9 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 and 16 ; yes, both equal 1 64 8 128 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 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? 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. A unit rate compares a quantity to one unit of another quantity. These are all examples of unit rates. 6 tentacles per head 2 eyes per alien 1 tail per body 1 foot per leg 3 windows per spaceship 3 riders per spaceship Rate 150 heartbeats 2 minutes Unit Rate (divide to get it): 150 ÷ 2 = 75 75 heartbeats to 1minute OR 75 heartbeats per minute 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 Try this by yourself! Unit rates are rates in which the second quantity is 1. The ratio 90 can be simplified by dividing: 3 90 = 30 3 1 unit rate: 30 miles, or 30 mi/h 1 hour 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. 90 words ÷ 2 = 45 words 2 minutes ÷ 2 1 minute Divide to find words per minute. Penelope can type 45 words in one minute. 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. Juice is sold in two different sizes. A 48fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy? $2.07 48 fl.oz. $1.64 32 fl.oz. 0.04312 5 0.05125 $0.04 per fl.oz. $0.05 per fl.oz. The 48 fl.oz. bottle is the better value. Additional Example: Finding Unit Prices to Compare Costs 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? price for package = $1.95 = $0.39 Divide the price by the number number of pens 5 of pens. price for package = $6.20 $0.41 number of pens 15 The 5-pack for $1.95 has the lower unit price. 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? price for bottle = $2.19 $0.09 number of ounces 24 Divide the price by the number of ounces. price for bottle = $3.79 $0.11 number of ounces 36 The 24 oz jar for $2.19 has the lower unit price. Day 7: A proportion is an equation stating that two ratios are equal. x3 7 , 21 10 30 Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators. x3 ÷4 No, these ratios do NOT form a proportion, because the ratios are not equal. 8 , 2 9 3 ÷3 A proportion is an equation stating that two ratios are equal. Example: 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? Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline? x8 Unit Rate 25 miles 1 gallon = 8 gallons x8 25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.