Dimensional Analysis

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Dimensional Analysis

• Why do it?

Kat Woodring
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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

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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

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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.

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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

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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.

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Lesson Sequence

• English to English conversions.
• Metric to Metric conversions.
• English to Metric conversions.
• Metric to English conversions.
• Complex conversions
• Word problems

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Write the KNOWN, identify the UNKNOWN.

• EX. How many quarts is 9.3 cups?

9.3 cups
? quarts

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Draw the dimensional jumps.
9.3 cups
x
Use charts or tables to find relationships
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Insert relationship so units cancel.
quart
1
9.3 cups
x
cups
4
units of known in denominator (bottom) first
units of unknowns in numerator (top
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Cancel units
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Do Math

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

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Do the Math
quart
1
9.3 x 1
9.3 cups
x

cups
4
1 x 4

2.325
s
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Calculator /No Calculator?

• Design problems to practice both.
• Show how memory function can speed up
  calculations
• Modify for special needs students

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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!

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Show ALL Work

• Dont 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

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Vocabulary

• KNOWN
• UNKNOWN
• CONVERSION FACTOR
• UNITS

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Write the KNOWN, identify the UNKNOWN.

• EX. How many km2 is 802 mm2 ?

802 mm2
km2?

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Draw the of dimensional jumps
802 mm2
x
x
x
x
x
x
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Insert Relationships
cm2
dm2
m2
dkm2
hm2
km2
802 mm2
x
x
x
x
x
x
mm2
cm2
dm2
m2
dkm2
hm2
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Cancel Units
Units leftover SHOULD be units of UNKNOWN
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Cancel Units
(1)2
(1)2
(1)2
(1)2
(1)2
(1)2
802 mm2
(10)2
(10)2
(10)2
(10)2
(10)2
(10)2
Units leftover SHOULD be units of UNKNOWN
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Do the Math
(1)2
(1)2
(1)2
(1)2
(1)2
(1)2
802 mm2
(10)2
(10)2
(10)2
(10)2
(10)2
(10)2
What kind of calculator is BEST?
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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

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Outcomes

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

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