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Dimensional Analysis

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.

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Dimensional Analysis

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  1. Dimensional Analysis Why do it? Kat Woodring

  2. 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

  3. 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

  4. 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.

  5. 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

  6. 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.

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

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

  9. 9.3 cups = ? quarts Draw the dimensional “jumps”. 9.3 cups x * Use charts or tables to find relationships

  10. Insert relationship so units cancel. quart 1 9.3 cups x 4 cups *units of known in denominator (bottom) first *** units of unknowns in numerator (top

  11. 1 quart 9.3 cups x 4 cups Cancel units

  12. 1 quart 9.3 cups x 4 cups Do Math • Follow order of operations! • Multiply values in numerator • If necessary multiply values in denominator • Divide.

  13. 9.3 = 4 Do the Math 1 quart 9.3 x 1 9.3 cups x = 4 cups 1 x 4 = 2.325 s

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

  15. 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!

  16. 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

  17. Vocabulary • KNOWN • UNKNOWN • CONVERSION FACTOR • UNITS

  18. Write the KNOWN, identify the UNKNOWN. • EX. How many km2 is 802 mm2 ? 802 mm2 = km2?

  19. 802 mm2 = km2? Draw the # of dimensional “jumps” 802 mm2 x x x x x x

  20. 802 mm2 = km2? Insert Relationships cm2 dm2 m2 dkm2 hm2 km2 802 mm2 x x x x x x mm2 cm2 dm2 m2 dkm2 hm2

  21. cm2 dm2 m2 dkm2 hm2 km2 802 mm2 x x x x x x mm2 cm2 dm2 m2 dkm2 hm2 Cancel Units *Units leftover SHOULD be units of UNKNOWN

  22. cm2 dm2 m2 dkm2 hm2 km2 x x x x x x mm2 cm2 dm2 m2 dkm2 hm2 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

  23. cm2 dm2 m2 dkm2 hm2 km2 x x x x x x mm2 cm2 dm2 m2 dkm2 hm2 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?

  24. 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

  25. Outcomes • Usescience • Thinkscientifically • Communicatetechnical ideas • Teachall students • Bescience conscious not science phobic

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