2. Ratios 7 th Grade Math February, 2011

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? 600/30 or 20/1

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. Equivalent Ratios  Two ratios are the same when put in simplest form.  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!!

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

7.  A ___________ is a ratio that compares two different kinds of units.  Example:  Heartbeat example  Two Units = heartbeats and minutes

8.  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 = 50/1 220/8 = 27.5/1

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

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

11. Common Unit Rates RateUnit Rate

12. 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

13. Different Types of Ratios

14. Ratios Comparing Same Measures Part/Whole (Fraction) Part/Part Comparing Different Type of Measures Rate

15. Different Types of Ratios Part/Whole Examples Ratio Part/Part Examples RatioRate ExamplesRate Number of red roses to number of flowers in bouquet Number of red roses to number of yellow roses Number of roses per bouquet Number of footballs to number of balls in gym supply Number of footballs to number of soccer balls Number of footballs per class Number of points earned to number of points possible Number of points earned to the number of points not earned Number of points earned per pupil Number of girls to number of student in class Number of girls to number of boys in class Number of students per teacher

16. Different Types of Ratios Part/Whole Examples Ratio Part/Part Examples RatioRate ExamplesRate Number of red roses to number of flowers in bouquet 6/24Number of red roses to number of yellow roses 6 to 18Number of roses per bouquet 12:1 Number of footballs to number of balls in gym supply 5/25Number of footballs to number of soccer balls 5 to 8Number of footballs per class 5:5 Number of points earned to number of points possible 80/100Number of points earned to the number of points not earned 80 to 20Number of points earned per pupil 1140:15 or 76:1 Number of girls to number of student in class 14/22Number of girls to number of boys in class 14 to 8Number of students per teacher 22:1

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

18. Let’s try together: http://math.rice.edu/~lanius/proportions/rate.html

19. Practice  Small Group:  Number your paper from 1-12  Deck of cards  LEVEL 0: INDIVIDUAL  Deal out cards evenly to each player  Answer that problem on your paper  Rotate the card (clockwise) to your partner  Continue until you’ve answered all cards  LEVEL 1: PARTNERS  Check your answers with your partners

20. Practice  Practice Problems:  Glencoe – Rates and Ratios  Rotate Problems through groups (5-10 minutes) each