2. CCGPS Coordinate Algebra Day 2 (8-14-12) UNIT QUESTION: Why is it important to understand the relationship between quantities? Standard: MCC9-12.N.Q.1-3, MCC9-12.A.SSE.1, MCC9-12.A.CED.1-4 Today’s Question: How are unit conversions performed, and why is it important? Standard: MCC9-12.N.Q.1 and N.Q.2

3. Measurement Words

4. How would you measure this?

5. Measurement Conversion Graphic Organizer

6. Quantity- an exact amount or measurement

8. A ratio is a comparison of two quantitites (numbers or measures). A ratio can be written three ways: 3:53/5 3 to 5 BACK

9. Ratios are often expressed as fractions in simplest or as a decimal. BACK

10. A ratio is the comparison of two numbers with the same units by division. A ratio may be written in three ways. What ratios can we form from the tiles above? 12 to 8 BACK

11. Create as many ratios as possible. Write each ratio three different ways. BACK

12. Simplest Form Write the ratio 50 to 300 in simplest form. BACK

13. Simplest Form Write the ratio 60¢ per dozen in simplest form. BACK

14. Look over the ratios you have written. Is there another way that you can write those ratios? The ratio illustrated here is four filled cells to ten total cells. The ratio shown here is two filled cells to five total cells. What do you know about these two ratios? How can you prove your answer? BACK

15. Proportion An equation that sets two ratios equal to one another BACK

16. Unit Rate A comparison of two measurements in which the second term has a value of 1 “How much for just 1?” BACK

17. If it costs $78 for 13 sandwiches, What is the unit rate? Unit Rate BACK

18. The cost of a 12-ounce box of Cheerios is $3.29. Publix brand Cheerios cost $4.89 for an 18- ounce box. Find the unit rate to find the better buy. BACK

19. Mile per Gallon M.P.G. stands for miles per gallon and is usually used for gas mileage in cars. BACK

20. Unit Rate If it takes 11 gallons to drive 250 miles, What is the unit rate or m.p.g.? BACK

21. Solving Word Problems Write problem as proportions: Solve using cross multiplication. BACK

22. Measurements Problem Solving Using Conversion Factors

23. Example 1 1. Bob studied for 2.5 hrs. How many minutes did he study for? Initial unit = hr.Final unit = _______ Multiply by: What you want What you have

24. How many minutes are in 2.5 hours ? Initial unit 2.5 hr Conversion Final factor unit 2.5 hr x 60 min = 150 min 1 hr cancel Answer (2 SF)

25. Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? 1) 2440 cm 2)244 cm 3)24.4 cm

26. Solution A rattlesnake is 2.44 m long. How long is the snake in cm? 2)244 cm 2.44 m x 100 cm = 244 cm 1 m

27. LecturePLUS Timberlake26 Example 2 How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x ?? 1 day

28. Unit plan: days hr min seconds 1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min = 120,000 sec Solution

29. Learning Check If the ski pole is 3.0 feet in length, how long is the ski pole in mm?

30. Solution 3.0 ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm = 214.4 mm.

31. John Isner serves 140 miles per hour. How fast is that feet per second? Example 3

32. Solution 140 miles x 5,280 ft. x 1 hr x 1 min = 1 hr 1 mile 60 min 60 sec. = 205.3 ft/sec.

33. Why are unit conversions important?