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Teaching for Understanding Division with Fractions

Teaching for Understanding Division with Fractions. Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner University of Wisconsin-Milwaukee Math Teacher Leader (MTL) Seminar Milwaukee Public Schools June 2005.

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Teaching for Understanding Division with Fractions

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  1. Teaching for UnderstandingDivision with Fractions Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner University of Wisconsin-Milwaukee Math Teacher Leader (MTL) Seminar Milwaukee Public Schools June 2005 • This material is based upon work supported by the National Science Foundation Grant No. EHR-0314898.

  2. Session Goals • Deepen conceptual understanding of division with fractions. • Examine “why” we can invert and multiply.

  3. Popcorn PartyServing Size: 2 cups How many servings from: • 8 cups of popcorn • 5 cups of popcorn

  4. Summarize • Write the equation for each situation (8 cups; 5 cups). • Identify the meaning of each number in the equations.

  5. 12 SummarizeHow many 2–cup servings? 8 ÷ 2 = 4 cups cup servings serving 5 ÷ 2 = 2 cups cup serving servings

  6. 12 What does the represent? • One-half of a cup of popcorn? • One-half of a serving? • Are you sure?

  7. 12 12 Popcorn PartyServing Size: cup How many servings from: • 1 cup of popcorn • 4 cups • 2 cups

  8. 12 12 SummarizeHow many 2–cup servings? cup serving 1 ÷ = 2 cup servings 4 ÷ = 8 cups servings cup serving

  9. TaskPopcorn Parties #1 &#2 • Facilitator • Paper Strip Demonstrator

  10. Algorithm

  11. TaskPopcorn Parties #1 &#2 • Facilitator poses one problem at a time. • Each individual silently solves it. • On facilitator’s cue: State answer. • Demonstrator models with paper strips. • Take turns to justify your reasoning.

  12. 1 4 Popcorn Party #1 Serving Size: cup of popcorn How many servings can be made from: • 1 cup of popcorn • 2 cups of popcorn • 3 1/2 cups of popcorn

  13. Popcorn Party #2 Serving Size: cup of popcorn How many servings can be made from: • 3/4 cup of popcorn • 6 cups of popcorn • 2 1/4 cups of popcorn • 4 1/2 cups of popcorn 3 4

  14. 34 Popcorn PartyServing Size: cup How many servings from 4 cups?

  15. 34 SummarizeHow many 2–cup servings? cup serving 4 ÷ = cups

  16. Discussion In reviewing these division situations and your solutions, what are you noticing?

  17. Fraction Division Algorithm Photo Sequence from Session

  18. 7 X = 1 ?

  19. a X = 1 ? Multiply by the inverse, which is also called the reciprocal.

  20. 1a Is this true for any number? What about zero? a X = 1 a ≠ 0

  21. 1 34 ? X = 1

  22. How else can we write this? 7 ÷ 8 =

  23. 12 1224 ? • = ?

  24. 12 1224 112 112 • =

  25. Estimate Greater than 5? Equal to 5? Less than 5? 34 5 ÷ =

  26. 34 SummarizeHow many 2–cup servings? How else can we write this? 5 ÷ =

  27. 34 5 • = 1

  28. 34 92 • = 1

  29. cd ab • = 1

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