Measurement Class 4

1. Measurement Class 4 OB: Learning the rules and operations of unit conversion math, AKA DIMENSIONAL ANALYSIS

2. In our lives, and in our studies, we will have to convert our math units from one form to another all the time. Each time you put on your two sneakers in the morning, or your pair of sneakers, you put on the same number of sneakers, but you think it, or say it differently. 2 Sneakers 1 pair of sneakers Same thing, right?

3. No matter if you are playing 52-Pickup or watching a magician, you know that there are 52 cards in the deck of cards. A deck of cards has 52 cards. A deck of cards EQUALS 52 cards. If your brother ripped the ace of diamonds in half during a minor fit of insanity, you no longer have a deck of cards (although if he’s under eight years old he might not notice). =

4. If I said how many cards are in 2 decks of cards, or how many shoes are in three pairs of shoes, could you tell me? (104 + 6) To figure these problems out, you would probably just “do it in your head”, but in fact you are doing dimensional analysis computations. X • = 6 shoes 3 pairs of shoes1 2 shoes 1 pair of shoes This is how your “mind” converted from pairs to shoes in units. You didn’t even realize (probably) that 2 shoes = 1 pair of shoes is called an Equality, which can be changed into 2 different CONVERSION FACTORS.

5. Conversion factors are used to convert one unit to another. • All conversion factor numerators must = their denominators. • They MUST have units top and bottom. MUST. • They will always equal “1” - right side up or upside down. Every equality can make 2 different conversion factors, and conversion factors equal 1. 12 inches = 1 foot An Equality TwoConversionFactors From one equality = • 1 foot12 inches 12 inches1 foot

6. Let’s convert your teachers mass (220 pounds) into ounces. Do you know of an equality with pounds & ounces. 1 pound = 16 ounces

7. Let’s convert your teachers mass (220 pounds) into ounces. Do you know of an equality with pounds & ounces. = 220 pounds1 • 16 ounces1 pound X ounces 3520 ounces. But, WHOA! What about SF? How many SF in the math? How many SF are supposed to be in the answer? What’s the real answer? 3500 ounces has 2 SF, which is as close as we can measure.

8. Let’s try a few one step unit conversion problems in a row. Set it up correctly, with our “starting point” over 1, use units, cancel units, talk to each other and check to see if your neighbor has the same answer as you do. Convert 1.2 kilograms into grams (1 kg = 1000 g). Convert 56,750 mL into liters (l L = 1000 mL).

9. Convert 1.2 kilograms into grams (1 kg = 1000 g). = X 1.2 kg1 • 1000 g1 kg 1200 g Convert 56,750 mL into liters (l L = 1000 mL). • X • 1 L1000 mL • 56,750 mL1 = 56.75 L Starting point ◊ watch units ◊ watch SF ◊ BANG!

10. Multiple step unit conversions… You can sometimes get a problem that you can’t simply convert from one unit to another because you don’t know a conversion factor. But you know other ones, so you can go in steps. Convert your age (you are 15.4 years old right now) into minutes. How many minutes are in one year? There is an answer to that, and if you know it, you can make this a one step conversion problem. Since you don’t let’s think. All conversion factors must equal 1. If you multiply 15.4 x a conversion factor = 15.4 If you multiply 15.4 x a conversion factor x another one = 15.4 You can multiply any number by 1 as many times as you like, it’s ok.

11. Convert 15.4 years into minutes.

12. Convert 15.4 years into minutes. 15.4 yr1 • 24 hours1 day • 365 days1 yr • 60 minutes1 hour • = • X X • X 15.4 yr1 • 24 hours1 day • 365 days1 yr • 60 minutes1 hour • = • X X • X Be sure to see how you started OVER 1, and ALL of the units cancel, and the last unit left (minutes) is the one that the answer needs to have! Do the math, and consider your ANSWER’S SF BEFORE you multiply. How many SF does your answer NEED to have? 8,094,240 min., but with just 3 SF: 8,090,000 min.

13. No exits in sight!

14. Convert the 400. meter race into yards so the football players can easily compare that length to their field. 1 inch = 2.54 centimeters

15. Convert the 400. meter race into yards so the football players can easily compare that length to their field. 1 inch = 2.54 centimeters 400. m1 • 1 inch2.54 cm • 100 cm1 m • 1 yard36 inches • = • X X • X 400. m1 • 1 inch2.54 cm • 100 cm1 m • 1 yard36 inches • = • X X • X How many SF in the answer?! Do the math across the top and write your answer, then CLEAR your calculators. Do the math across the bottom, write your answer, then clear again. Then do the division. 40,00091.44 = 437.445319 changes to 437 yards with 3 SF

16. I live in a make believe world (sometimes) and in my world there are special magical ways that will allow me to convert from unusual units to even more unusual units. Sometimes I bring silly problems back to Earth, just to help my students think abstractly. As long as you have equalities, you can make conversion factors. Ergo, you can convert units easily. A YOWZA is what a student yells when she earns an all correct on her quiz.1 Yowza feels the same as 3.4 hoo-hoo’s 1 hoo-hoo is the same as hollaring 8.2 ka-ching’s 1 ka-ching is equal to 2.3 hmmmm’s It takes 5.9 hmmmm’s to match up with 1.6 unh’s. So, tell me quick! How many unh’s are the same as 7.00 Yowza’s? (units are units, and they are there just to be crossed out) Watch your starting point, and how many SF in your answer? Homework Tonight: Measurement HW _____

17. 1.6 unh5.9 hmm • 2.3 hmm1 ka-ch • 8.2 ka-ch1 Hoo 7.00 Y1 • 3.4 Hoo1 Y = X X X X Set it up, watch the unit placement, cancel the units out, is your LAST UNIT the one that you need in the answer? Do the math across the top, hit equal and write that down. Do the same on the bottom. Divide and check SF. 718.1888 5.9 = 121.7269… with 3 SF rounds to 122 unh’s! Do your homework tonight, I will collect it tomorrow.