Warm-Up #2

1. 9 5 45 p __ __ __ __ 5 x 36 6 Warm-Up #2 Use the table to write each ratio. 1. tulips to daffodils 2. crocuses to total number of bulbs 3. total bulbs to lilies 9:17 20:51 51:5 Find the missing value in each proportion. 4. = 5. = x = 25 p = 30

2. Ratio Versus RateRate Versus Unit Rate What’s the difference?

3. Ratio, Rate, and Unit Rate What am I Learning Today? How will I show that I learned it? Compare and contrast ratios and rates. Express rates in a per unit form, where the denominator is one. Determine which form of a rational number is most appropriate in a given situation.

4. Vocabulary • Rate: A ratio that compares two quantities measured in different units • Unit rate: A rate in which the second quantity in the comparison is ONE unit

5. Questions Notes Questions Answers • Ratiothat compares two quantities with different units and expressed in a “per unit” form • Miles per hour • Words per minute What is a rate and how is it expressed? Unit rateis when the comparison is for ONE unit -Used for comparison shopping and finding the better deal What is unit rate and how is it used? -Can be solved by using proportion -Simply take the rate and divide the numerator by the denominator (“how much” by “how many”) -But since units of measurement are different, both must be kept as part of the final answer. How do you determine unit rate? EXAMPLE: The fastest running bird is the ostrich. An ostrich can run 240 miles in 6 hours. How far can an ostrich run in an hour? 240 miles 6 hours 40 miles or 40mph 1 hour What is its rate? What is its unit rate?

6. RATIO RATE both • Compares similar units • Can be written 3 different ways • Read it using the word “to” • Compares different units • Read it using the word “per” • Allows you to calculate the “better deal” • Written as fractions • Reduce to lowest form

7. Unit Rate Example: Doughnuts a) 3 for $1.00 OR b) $.45 each $1.00 = $0.3333… 3 about 33 cents each To find unit rate…. divide the total rate by total # of items $.45 = $0.45 1 45 cents each What is the better deal??

8. Now let's take a look at a problem that involves finding the best buy. Find the unit price, or the cost per ounce, of each box. Divide the price by the number of ounces. 12-ounce box $2.64  12 ounces = $0.22 per ounce 20-ounce box $3.80  20 ounces = $0.19 per ounce 32-ounce box $5.44  32 ounces = $0.17 per ounce 48-ounce box $8.64  48 ounces = $0.18 per ounce The 32-ounce box costs the least per ounce. Is bigger better? The costs of different sizes of boxes of cereal are shown. Which box costs the least per ounce?

9. Now let's take a look at a problem that involves unit price and total cost. • "A sign in a store says: 3 Pens for $2.70. How much would 10 pens cost?" To solve the problem, find the unit price of the pens, then multiply by 10. 2.70 = x 3 1 2.70 = 3x $2.70 ÷ 3 = $0.90 $0.90 x 10 = $9.00 • Finding the cost of one unit first makes it easy to find the total cost of multiple units.

10. Holiday Shopping Challenge: Unit Rate & Total Cost 1) Put name and title on your paper. 2) Number your paper from 1-4. 3) Choose the BEST BUY—the one with the lowest unit rate… Not the lowest TOTAL cost. 4) Slide will automatically transition after 4 minutes! 5) At the end we will tabulate your score and see who is the best shopper! Get Ready…. What’s the better buy? How much do I owe?

11. #1: Present for your little sister a) 2 Webkinz for $15.50 OR b) 3 Webkinz for $20.99 Which is the better buy?

12. #2: Present for your Mom or Grandma a) $36.00 for 3.6 oz at Macy’s OR b) $17.00 for 1.7 oz at Wal-mart Where is the better buy?

13. #3: Present for your BFF a) 2 board game $15.99 OR b) 3 board games for $49.99 Which is the better buy?

14. #4: Goodies for the Entire Family a) This chest full of candy: 1 chocolate everyday for a year for $60 OR b) $24.99 for a 100-count bag of chocolate Which is the better buy?

15. TIME IS UP ! Give yourself 10 points for each correct answer.

16. #1: Present for your little sister a) 2 Webkinz for $15.50 $15.50/2 = $7.75 per Webkinz OR b) 3 Webkinz for $20.99 $20.99/3=$6.996=$7 per Webkinz Which is the better buy?b) unit rate for 1 Webkinz ~$7.00

17. #2: Present for your Mom or Grandma a) $36.99 for 3.6 oz at Macy’s $36.99/3.6 = $10.275 per ounce OR b) $17.49 for 1.7 oz at Wal-mart $17.49/1.7= $10.288 per ounce Where is the better buy? a) Macy’s. The unit rate is $10.28 per ounce

18. #3: Present for your BFF a) 2 board games for $25.99 $25.99/2 = $12.995 =$13 per game OR b) 3 board games for $49.99 $49.99/3 = $16.663 per game What is the better buy? a) unit cost $13.00 per game

19. #4: Goodies for the Entire Family a) 1 chocolate everyday for a year for $60 $60/365 = ~$0.164 per candy OR b) $24.99 for a 100-count bag of chocolate $24.99/100 = ~$0.245 per candy What is the better buy? a) unit cost per candy ~$0.16

20. Find Your Total CostYou found such a deal that you stocked up • 2 Webkinz at a unit rate of $7.00 per Webkinz • 25 chocolates at $0.16 cents each • 3 board games at a unit rate of $13 per game • 1/4 gallon of Lovely at a unit rate of $10.28 per ounce (psst… there are 128 ounces in a gallon) 1) Find the total cost of each type of gift and the subtotal. 2) Add 6% sales tax. 3) How much did you spend? You had $500. How much do you have left?

21. Find Your Total Cost • 2 Webkinz at a unit rate of $7 per Webkinz • 25 chocolates at $0.16 cents each • 3 board games, unit rate $13 per game • 1/4 gallon of Lovely at a unit rate of $10.28 per ounce (psst… there are 128 ounces in a gallon) (128 divided by 4 = 32) • Find the subtotal. • Add 6% sales tax. • Find the total. • You had $500. How much money do you have left? 2 x $7.00 = 14.00 + 25 x $0.16 = 4.00 + 4 x $13 = 52.00 + 32 x $10.28 = 328.96 __________ $398.96 tax 23.94 ________________ $422.90 500.00 - 422.90 $77.10

22. Thanks for playing…now go home and SAVE your money.