Dimensional Analysis Why do it? Kat Woodring

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

Benefits for teachers Successful problem solving strategy for advanced or special needs students Vertically aligns with strategies for Chemistry and Physics Improves Math scores Easy to assess and grade

5 Steps of Problem Solving Identify what you are asked. Write down what is given or known. Look for relationships between knowns and unknowns (use charts, equations). Rearrange the equation to solve for the unknown. Do the computations, cancel the units, check for reasonable answers.

Teaching Opportunities with Metric System Beginning of year Review math operations Assess student abilities Re-teach English and SI systemSI system Teach unit abbreviations Provide esteem with easy problems Gradually increase complexity

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.

Lesson Sequence English to English conversions. Metric to Metric conversions. English to Metric conversions. Metric to English conversions. Complex conversions Word problems

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

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

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

Cancel units 9.3 cupsx cups quart 4 1

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

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

Calculator /No Calculator? Design problems to practice both. Show how memory function can speed up calculations Modify for special needs students

Sig. FigSig. Fig./Sci. Not.? Allow rounded values at first. Try NOT to introduce too many rules Apply these rules LATER or leave SOMETHING for Chem teachers!

Show ALL Work Don’t allow shortcuts Use proper abbreviations Box answers and units are part of answer Give partial credit for each step Later, allow step reduction If answer is correct, full credit but full point loss

Vocabulary KNOWN UNKNOWN CONVERSION FACTOR UNITS

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

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

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

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

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

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

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

Outcomes Use science Think scientifically Communicate technical ideas Teach all students Be science conscious not science phobic