2. Ratios, Rates, Unit Rates 7 th Grade Math November, 2012

3.  A ___________ is a comparison of two numbers by division.  A ratio must be expressed in __________.  Example #1: There are approximately 600 students at Lewisburg School. There are 30 teachers. What is the student to teacher ratio at Lewisburg School? 600 students/30 teachers or 20 students/1 teacher

4. 3 ways to write a RATIO!  There were 6 chocolate donuts in the box of 12 donuts.  Part to Whole = = ** This can be expressed as: ** 1:21 to 2 ALL THREE OF THESE MEAN ~ 1 CHOCOLATE DONUT FOR EVERY 2 DONUTS.

5.  __________________ shows 2 ratios have the same value.  Reduce to lowest terms.  Same methods as “Equivalent Fractions”  Example – Are these two ratios equivalent?:  $4 for every 16 ounces$4/16 oz  $10 for every 40 ounces$10/40 oz  These two ratios are equivalent!! 2 nd Block start here

6. Grab Bag!!  Bag of various items.  Create ratios on whiteboards (include units)  Time Frame = 15 minutes

7. Choose a partner and take turns taking your pulse for 2 minutes. 1. Count the number of beats for each of you. 2. Write the ratio beats to minutes as a fraction.

8.  A ___________ is a ratio that compares two different kinds of units.  Example:  Heartbeat example  Two Units = heartbeats and minutes  Gasoline example  Two Units = miles and gallons  Money example  Two Units = price and pounds

9. Different Types of Ratios

10. Ratios Comparing Same Units Part/Whole (Fraction) Part/Part Comparing Different Units Rate

11. Different Types of Ratios Part/Whole Examples Ratio Part/Part Examples RatioRate ExamplesRate 6 red roses to 24 flowers in bouquet 6 red roses to 18 yellow roses 12 roses per 3 bouquets 5 footballs to 25 balls in gym supply 5 footballs to 8 soccer balls 5 footballs per class 80 points earned to 100 points possible 80 points earned to 20 points not earned 1400 points earned per 20 students 14 girls to 22 students in class 14 girls to 8 boys in class 110 students per 5 teachers

12. Different Types of Ratios Part/Whole Examples Ratio Part/Part Examples RatioRate ExamplesRate 6 red roses to 24 flowers in bouquet 6/246 red roses to 18 yellow roses 6 to 1812 roses per 3 bouquets 12:3 5 footballs to 25 balls in gym supply 5/255 footballs to 8 soccer balls 5 to 85 footballs per class 5:1 80 points earned to 100 points possible 80/10080 points earned to 20 points not earned 80 to 201400 points earned per 20 students 1400:20 14 girls to 22 students in class 14/2214 girls to 8 boys in class 14 to 8110 students per 5 teachers 22:1

13. Let’s try together: http://math.rice.edu/~lanius/proportions/rate.html Take out since we did the grab bag!

14. Practice  Practice Problems:  Glencoe – Rates and Ratios  Page 284 - #1-17

15.  A ____________ is a ratio that is simplified so that it has a denominator of ONE unit.  Examples: 1. I made $300 for 6 hours of work. Write the unit rate. 2. We drove 220 miles on 8 gallons of gas. Write the unit rate $300/6 hours = $50/1 hour 220 miles/8 gallons = 27.5 miles/1 gallon

16. How to calculate unit rate?  Easiest way is to divide BOTH the numerator AND the denominator by the denominator.  Example #1:

17. How to calculate unit rate?  Easiest way is to divide BOTH the numerator AND the denominator by the denominator.  Example #2:

18. Common Unit Rates My Ideas Rate Unit Rate Class Ideas Rate Unit Rate

19. Common Unit Rates RateUnit Rate Number of Miles 1 hour Miles per hour Number of Miles 1 gallon Miles per gallon Number of Dollars 1 pound Price per pound Number of Dollars 1 hour Dollars per hour

20. Practice  Practice Problems:  Glencoe – Unit Rates  Page 290 - #7-18

21. Grocery Store Comparison – UNIT RATE!  Four Products:  Find the best price!!

22. Practice  Small Group:  Use the grid provided to answer the question on each card  Deck of cards  MUST INCLUDE THE UNITS FOR RATIOS!!  LEVEL 1: INDIVIDUAL  Deal out cards evenly to each player  Answer that problem on your paper  Place your card in a “common pile” so partners can find what they need  Continue until you’ve answered all cards

23. Practice  Parent Participation:  Using what you know about unit rate, ask your parents/grandparents to give you 3 examples of when they have compared unit rates.  Write them down and be prepared to share them with the class  Example: Mr. Northern