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 system• Teach unit abbreviations• Provide esteem with easy problems• Gradually increase complexity

5 Steps of Dimensional AnalysisUsing 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 cups x

* Use charts or tables to find relationships

Insert relationship so units cancel.

9.3 cups xcups

*units of known in denominator (bottom) first*** units of unknowns in numerator (top

quart

4

1

Cancel units

9.3 cups xcups

quart

4

1

Do Math

9.3 cups xcups

quart

4

1

• Follow order of operations! • Multiply values in numerator• If necessary multiply values in denominator• Divide.

Do the Math

9.3 cups xcups

quart

4

1

1 x 4=

9.3 x 1

4=

9.3= 2.325 s

Calculator /No Calculator?

• Design problems to practice both.• Show how memory function can speed up

calculations• Modify for special needs students

Sig. 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 km2 is 802 mm2 ?

802 mm2 km2? =

Draw the # of dimensional “jumps”

802 mm2 x

802 mm2 km2? =

x x x x x

Insert Relationships

802 mm2 x

802 mm2 km2? =

x x x x xmm2

cm2

cm2

dm2

dm2

m2

m2

dkm2

dkm2

hm2

hm2

km2

Cancel Units

802 mm2 x x x x x xmm2

cm2

cm2

dm2

dm2

m2

m2

dkm2

dkm2

hm2

hm2

km2

*Units leftover SHOULD be units ofUNKNOWN

Cancel Units

802 mm2 x x x x x xmm2

cm2

cm2

dm2

dm2

m2

m2

dkm2

dkm2

hm2

hm2

km2

*Units leftover SHOULD be units ofUNKNOWN

(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 mm2 x x x x x xmm2

cm2

cm2

dm2

dm2

m2

m2

dkm2

dkm2

hm2

hm2

km2

*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

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