Dimensional Analysis

Dimensional Analysis PowerPoint PPT Presentation


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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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Dimensional Analysis

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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 Simplifies computation 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. Complex conversions Word problems

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 UNKNOWN CONVERSION FACTOR UNITS

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

26. Outcomes

27. www.cpo.com 800-932-5227

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