Today’s Lesson Dimensional Analysis

1. Chemistry Today’s LessonDimensional Analysis

2. Materials needed for today’s session: • Notepaper • Pen/pencil • calculator • Your thinking cap on

3. Learning Objectives we are covering today: • Use base and derived metric units to solve problems. • Converting/Changing from 1 unit to another • Meets: Common Core Math Standard-Algebra • SSE – Seeing Structure in Expressions • Write expressions in equivalent forms to solve problems

4. What is “Dimensional Analysis”? Examples: How many wheels are on 350 Ford pick-up trucks? How many seconds are in a day? If you are going 50 miles per hour, how many feet per second are you traveling? 186,282 miles per second into how many meters per second?

5. First watch a video to get started Pick one of these: http://www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-165s.html http://www.youtube.com/watch?v=lAan6L9UjsE

6. Let’s Begin! Using what’s called Dimensional Analysis or the Factor-Label Method – You can convert from one unit of measurement to another • You use the relationship of one unit to another • For Example: 12 inches = 1 foot in length • These 2 values are equivalent to each other. • For every 12 inches = you get 1 foot or for every 1 foot – there are 12 inches.

7. Tips Step 1: Strategize – find your conversion factor. Step 2: Set up the problem, write it out fully Step 3: Muliply/Divide, and simplify Step 3: Solve Step 4: Check your work

8. Example 1: • The problem: How many feet are in 2 miles?

9. Strategize & The Setup: The problem: How many feet are in 2 miles? 1. Strategize: given that 5,280 feet are in 1 mile I used this website to help find out how many feet are in 1 mile: http://quizzes.cc/metric-conversion-charts.php 2. The Setup: Picket Fence– draw a Fence on your paper

10. Strategize & The Setup: The problem: How many feet are in 2 miles? 1. Strategize: Start with what you are given in the problem and put your amount in the first fence on the top And put multiplication signs in-between each fence picket 2. The Setup: 2 miles x

11. The Setup: Next – fill in the next Track with a conversion, (how many feet are in every 1 mile?) putting miles in the denominator. 5,280 feet are found in every 1 mile. I used this website to help find out how many feet are in 1 mile: http://quizzes.cc/metric-conversion-charts.php This way like units are diagonal from each other (in this case, miles) and can cancel out when we solve the problem 5,280 ft 2 miles x 1 mile

12. Let’s Solve The unit miles cancels out since miles are diagonal from each other – one in the numerator and in the denominator. This is the same method for multiplying fractions; such as 1 2 -- x ---- = 1/5 2 5 5,280 ft 2 miles x 1 mile

13. Strategize & The Setup: Strategize: How many feet are in 2 miles? • Multiply across the top: 2 x 5,280 = 10,560 • Multiply across the bottom: 1= 1 10,560 5,280 ft 2 miles x = 1 1 mile

14. Solve Strategize: How many feet are in 2 miles? • Finally – divide 10,560 / 1 = 10,560 feet is your answer 10,560 feet 10,560 ft 5,280 ft 2 miles x = = 1 1 mile

15. Example 2: a multi-step problem Convert : 1100 feet per second into miles per hour We are given 1100 feet per second And want – miles per hour in the final answer

16. Setup your Problem Setup your problem with the Picket Fence – putting your given in the first fence – top & bottom. Feet per second Given 1100 feet per second = 1100 feet / 1 second 1100 feet x = = 1 second

17. Setup the next Fence Strategize: Setup your problem with the Picket Fence Given 1100 feet per second = 1100 feet / 1 second Want – miles per hour in the final answer • Let’s work on changing feet into miles and then seconds into hours How many feet are in 1 mile? How many seconds are in 1 hour? 1100 feet x = = 1 second

18. Find your Conversions How many feet are in 1 mile? = 5280 Found from the conversion website: http://quizzes.cc/metric-conversion-charts.php How many seconds are in 1 hour? 60 seconds in 1 minute 60 minutes are in 1 hour

19. Setup the next Fence Given 1100 feet per second = 1100 feet / 1 second Want – miles per hour in the final answer How many feet are in 1 mile? 5280 ** Feet are across from each other in the fence so they will cancel out – we want to end up with miles and hours in final answer 1100 feet 1 mile x = = 5280 ft 1 second * We are not done yet – need miles and hours in the final answer – not miles and seconds

20. Setup the next Fence Given 1100 feet per second = 1100 feet / 1 second Want – miles per hour in the final answer How seconds are in 1 hour? = 60 seconds in 1 minute 1100 feet 1 mile 60 seconds We are so close! Seconds has been cancelled out – but answer needs hours not minutes. One more Fence needed… x = = 5280 ft 1 minute 1 second

21. Setup the next Fence Given 1100 feet per second = 1100 feet / 1 second Want – miles per hour in the final answer How seconds are in 1 hour? = 60 seconds in 1 minute 60 minutes in 1 hour ** Cross out like units that are diagonal from each other = now units in feet, seconds, and minutes have cancelled 60 seconds 60 minutes 1100 feet 1 mile x = = = 5280 ft 1 minute 1 hour 1 second

22. Multiply across top & bottom Given 1100 feet per second = how many miles per hour is this? 60 seconds 60 minutes 1100 feet 1 mile 3960000 miles x x x = ____________ 5280 ft 1 minute 1 hour 1 second 5280 hours

23. Divide & Solve for your Final Answer Given 1100 feet per second = how many miles per hour is this? 60 seconds 60 minutes 1100 feet 1 mile 3960000 miles x x x = ____________ 5280 ft 1 minute 1 hour 1 second 5280 hours = 750 Miles per Hour

24. Assignment time – 1. Unit Conversion Practice Problems Convert the following quantities. Show ALL your work – all steps to get the answer: 1. 2678 cm into feet 2. 165 pounds into kilograms 3. 43 miles into feet 4. 60 miles per hour into meters per second 5. 130 meters per second into miles per hour * Type these up on a Document with your name. Save your document & send to class dropbox called “Unit Conversions Practice” *You can also hand write on paper – then scan or take a clear digital picture of your paper and send that to me in the class dropbox called “Unit Conversion Practice” Conversions to Use: 1 hour = 3600 seconds 1 mile = 5280 feet 1 yard = 3 feet 1 meter = 3.28 feet 1 km = 0.62 miles 1 kg = 2.2 lbs 1 lb = 0.45 kg 1 quart = 0.946 liters 1 m/s = 2.2 miles/hour 1 foot = 12 inches 1 inch = 2.54 cm

25. 2. Create your Own Dimensional Analysis Problem • Post to the class discussion board titled, Dimensional Analysis • You may create a 1 step (like Example 1) or 2-3 step problem (like Example 2) • Here is a helpful website for conversion factors you can use in your problem: • http://quizzes.cc/metric-conversion-charts.php • Also remember time conversions that you can use: 60 seconds in 1 minute, 60 minutes in 1 hour, 24 hours in 1 day

26. To turn into Class by Friday: 1. Your completed Unit Conversion Practice Problems 5 problems; 5 points each = 25 points total possible Turn it into the class dropbox titled “Unit Conversions Practice” 2. Your own created Dimensional Analysis Problem posted to the class discussion board titled, Dimensional Analysis. Then your reply / answer/comment on at least 2 of your classmate’s postings – due in 1 week

27. Remember these items are due Friday: 1. Unit Conversion Practice problems, 1-5 calculated out on a computer document or written neatly by hand – and submitted to the class dropbox 2. Your dimensional analysis problem posted to the discussion board

28. Practice Your Conversions 1. Helpful Website for Dimensional Analysis Practice • http://www.alysion.org/dimensional/fun.htm • Work through the given 10 examples

29. Questions – Concerns? Contact me for any questions about the class lessons, help, and to stay informed! • Kmail • Office Phone: 360-329-6867