Ratios, Rates, Unit Rates

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

2. Ratio • 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? Simplest Form 600 students/30 teachers or 20 students/1 teacher

3. 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: ** 1:2 1 to 2 ALL THREE OF THESE MEAN ~ 1 CHOCOLATE DONUT FOR EVERY 2 DONUTS.

4. 2nd Block start here Equivalent Ratios • __________________ 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!!

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

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

7. 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 Rate

8. Different Types of Ratios

9. Different Types of Ratios

10. Different Types of Ratios

11. Different Types of Ratios

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

13. Practice • Practice Problems: • Glencoe – Rates and Ratios • Page 284 - #1-17

14. Unit Rate • A ____________ is a ratio that is simplified so that it has a denominator of ONE unit. • Examples: • I made $300 for 6 hours of work. Write the unit rate. • 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

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

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

17. Common Unit Rates

18. Common Unit Rates

19. Practice • Practice Problems: • Glencoe – Unit Rates • Page 290 - #7-18

20. Grocery Store Comparison – UNIT RATE! • Four Products: • Find the best price!!

21. 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

22. 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