2. Dimensional Analysis Why do it? Kat Woodring

3. Benefits for students Consistent problem solving approach Reduces errors in algebra Reinforces unit conversion Simplifies computation Improves understanding of math applications Multiple ways to solve the same problem

4. 5 Steps of Dimensional Analysis Using the Metric Conversion Start with what value is known, proceed to the unknown. Draw the dimensional lines (count the “jumps”). Insert the unit relationships. Cancel the units. Do the math, include units in answer.

5. Write the KNOWN, identify the UNKNOWN. EX. How many quarts is 9.3 cups? 9.3 cups? quarts=

6. Draw the dimensional “jumps”. 9.3 cups? quarts= 9.3 cupsx * Use charts or tables to find relationships

7. Insert relationship so units cancel. 9.3 cupsx cups *units of known in denominator (bottom) first *** units of unknowns in numerator (top quart 4 1

8. Cancel units 9.3 cupsx cups quart 4 1

9. Do Math 9.3 cupsx cups quart 4 1 Follow order of operations! Multiply values in numerator If necessary multiply values in denominator Divide.

10. Do the Math 9.3 cupsx cups quart 4 1 1 x 4 = 9.3 x 1 4 = 9.3 =2.325s

11. Vocabulary KNOWN UNKNOWN CONVERSION FACTOR UNITS

12. LecturePLUS Timberlake12 Initial and Final Units 1. A person has a height of 2.0 meters. What is that height in inches? Initial unit = mFinal unit = _______ 2) Blood has a density of 0.05 g/mL. If a person lost 0.30 pints of blood at 18°C, how many ounces of blood would that be? Initial = pintsFinal unit = _______

13. LecturePLUS Timberlake13 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)

14. LecturePLUS Timberlake14 Learning Check An adult human has 4650 mL of blood. How many gallons of blood is that? Unit plan: mL qt gallon Equalities:1 quart = 946 mL 1 gallon = 4 quarts Your Setup:

15. LecturePLUS Timberlake15 Solution Unit plan: mL qt gallon Setup: 4650 mL x 1 qt x 1 gal = 1.23 gal 946 mL 4 qt 3 SF 3 SF exact 3 SF

16. Write the KNOWN, identify the UNKNOWN. EX. How many km 2 is 802 mm 2 ? 802 mm 2 km 2 ?=

17. Draw the # of dimensional “jumps” 802 mm 2 x km 2 ?= xxxxx

18. Insert Relationships 802 mm 2 x km 2 ?= xxxxx mm 2 cm 2 dm 2 m2m2 m2m2 dkm 2 hm 2 km 2

19. Cancel Units 802 mm 2 xxxxxx mm 2 cm 2 dm 2 m2m2 m2m2 dkm 2 hm 2 km 2 *Units leftover SHOULD be units of UNKNOWN

20. Cancel Units 802 mm 2 xxxxxx mm 2 cm 2 dm 2 m2m2 m2m2 dkm 2 hm 2 km 2 *Units leftover SHOULD be units of UNKNOWN (10) 2 (1) 2 (10) 2 (1) 2 (10) 2 (1) 2 (10) 2 (1) 2 (10) 2 (1) 2 (10) 2 (1) 2

21. Do the Math… 802 mm 2 xxxxxx mm 2 cm 2 dm 2 m2m2 m2m2 dkm 2 hm 2 km 2 *What kind of calculator is BEST? (10) 2 (1) 2 (10) 2 (1) 2 (10) 2 (1) 2 (10) 2 (1) 2 (10) 2 (1) 2 (10) 2 (1) 2

22. Differences from other math approaches Solve for variables in equation first, then substitute values Open ended application No memorized short-cuts No memorized formulas Reference tables, conversion factors encouraged