6 th Grade Math- Focus 1 Ratios, Rates and Proportions

1. 6th Grade Math- Focus 1Ratios, Rates and Proportions Standards: 6.RP.1, 6.RP.3a, 6.RP3d, M06.S5C2.09 Resource: Van De Walle pages 154-159

2. Welcome to Our Math Class! Let’s look around the room and see what partsmake up our whole class! • How many students make up the whole class? • How many girls make up part of our class? • How many girls are in our class compared to our whole class? • Write the number of girls (part) compared to the class (whole) as a FRACTION.

3. How many boys make up part of our class? • How many boys in our class compared to our whole class? • Write the number of boys (part) compared to the class (whole) as a FRACTION.

4. Types of RATIOS Vocabulary Definition: A ratio is a comparison of any two quantities. When you are comparing two of the SAME measures, you are using these two types of ratios. • Part to Whole Ratios • Part to Part Ratios

5. What is a Part to Whole RATIO? • PART to WHOLE RATIOScan be written in THREE different ways. • Did you know? Every FRACTION is a Part to Whole Ratio! • Did you know? Every PERCENT is a Part to Whole Ratio! • Did you know? Every DECIMAL is a Part to Whole Ratio! Student Practice- Write your answers in your math journal/workbook. 1. Using all the three different ways to write Part to Whole Ratios, represent the part to whole comparisons of the girls and boys in our whole math class.

6. In your own words, answer the following in your workbook. What is your definition of a FRACTION?

7. What is a Part to Part Ratio? Let’s compare the number of girls to the number of boys in our class. • How many girls (part) are in our class? • How many boys (part) are in our class? • PART to PART RATIOS are be written in TWO different ways. Student Practice- Write your answers in your math journal/workbook. 2. Why can’t fractions be PART to PART Ratios? 3. Using the two different ways to write Part to Part Ratios, represent the part to partcomparisons of the girls to boys in our whole math class. 4. Using the two different ways to write Part to Part Ratios, represent the part to part comparison of the boys to girls in our class.

8. 6th Grade Math Homework My Life in Numbers! YOU MAY WRITE ON THE WORKSHEET. You will be turning in it on THURSDAY.

9. BrainPOP Video: Ratio • http://www.brainpop.com/math/ratioproportionandpercent/ratios/

10. Types of RATIOS Vocabulary Definition: A ratio is a comparison of any two quantities. When you are comparing two DIFFERENT measures, you are using this types of ratio. • Rate-comparing two DIFFERENT measures

11. What is a RATE? A RATE RATIO (or justRATE)- compares measures of two different types. For example, these are all rates. • miles per hour • dollars per item • cents per pound • passengers per busload

12. Measurement Relationships as Rates • Relationships between two units of measure are also rates. For example, these are all rates. • Inches per foot • Milliliters per liter • Centimeters per inch

13. Can you tell what type of Ratios it is?Part to Whole, Part to Part, or Rate Student Practice- Write your answers in your math journal/workbook. 5. Number of red roses to number of yellow roses 6. Number of points earned to number of possible points 7. Number of footballs per PE class 8. Number of roses per flower arrangement 9. Number of heads on a penny after ten tosses 10. Number of footballs to number of balls in the PE supply 11. Number of footballs to number of soccer balls 12. Number of points earned per student 13. Number of points earned to number of points not earned 14. Number of red roses to number of flowers in bouquet 15. Probability of getting a head with one coin toss 16. Odds of getting a head with one coin toss

14. Can you tell what type of Ratios it is?Part to Whole, Part to Part, or Rate CHECK your answers in your math journal/workbook. 5. Part to Part 6. Part to Whole 7. Rate 8. Rate 9. Rate 10. Part to Whole 11. Part to Part 12. Rate 13. Part to Part 14. Part to Whole 15. Part to Whole 16. Part to Part

15. Now that we know about Ratios…What are Proportions? Vocabulary Definition: A proportion is a statement of equality between two ratios. For example, This might be read “3 is to 9 as 4 is to 12.” Or it might be read “3 and 9 are in the same ratio as 4 and 12.”

16. Include the Units of Measure with Rates A ratio that is RATE usually includes the units of measure when written. For example, This might be read “$12.50 per gallon compared to $37.50 for 3 gallons.” The dollar signs and the words, gallon/gallons, are the UNITS for these numeric values. • Did you notice? $12.50 X 3 = $37.50 and 1 gal X 3 = 3 gals Big Concept Idea! Proportional Reasoning involves Multiplication or Division to maintain EQUAL ratios!

17. Which Has More? (Van de Walle, Activity 6.1) Student Practice- Write your answers in your math journal/workbook. Situation 1: Which class team has more girls? (Which class team has a larger proportion of girls?) Situation 2: Which fish tank has more goldfish? (Which fish tank has a larger proportion of goldfish?)

18. Which Has More? (Van de Walle, Activity 6.1) Student Practice- Write your answers in your math journal/workbook. Situation 3: Which figure has more circles? Situation 4: Did Ollie or Sandy grow more?

19. Which Has More? (Van de Walle, Activity 6.1) Class Discussion about Situations 1 & 2 Class Discussion about Situations 3 & 4 Which class team has more girls? Which fish tank has more goldfish? Which figure has more circles? Did Ollie or Sandy grow more?

20. Ticket Out the Door! • What is the definition of a RATIO? • What is ONE type of ratio? • What is ANOTHER type of ratio? • What is a comparison of two same measures called? • What is a comparison of two different measures called? • What type of ratio is a fraction or percent? • What is a comparison of two ratios called? Did we follow the Sabercat Way today? CMS ROARS! 