Dimensional Analysis. Why do it?. Kat Woodring. Benefits for students. Consistent problem solving approachReduces errors in algebraReinforces unit conversionSimplifies computationImproves understanding of math applicationsMultiple ways to solve the same problem. Benefits for teachers. Successful problem solving strategy for advanced or special needs studentsVertically aligns with strategies for Chemistry and PhysicsImproves Math scoresEasy to assess and grade.
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2. Dimensional Analysis Why do it?
3. Benefits for students Consistent problem solving approach
Reduces errors in algebra
Reinforces unit conversion
Improves understanding of math applications
Multiple ways to solve the same problem
4. 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. 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.
6. 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
7. 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.
8. Lesson Sequence English to English conversions.
Metric to Metric conversions.
English to Metric conversions.
Metric to English conversions.
9. Write the KNOWN, identify the UNKNOWN. EX. How many quarts is 9.3 cups?
10. Draw the dimensional “jumps”.
11. Insert relationship so units cancel.
12. Cancel units
13. Do Math
14. Do the Math
15. Calculator /No Calculator? Design problems to practice both.
Show how memory function can speed up calculations
Modify for special needs students
16. 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!
17. 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
18. Vocabulary KNOWN
19. Write the KNOWN, identify the UNKNOWN. EX. How many km2 is 802 mm2 ?
20. Draw the # of dimensional “jumps”
21. Insert Relationships
22. Cancel Units
23. Cancel Units
24. Do the Math…
25. 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