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Teaching for Understanding Division with Fractions

Dive deep into division with fractions at the MTL seminar by Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner. Explore the concept of inverting and multiplying. Practice applying fractions in real-life scenarios like the Popcorn Party. Understand the meaning of numbers in equations and develop new problem-solving strategies. Enhance your fraction division skills and gain confidence in mathematical concepts through interactive sessions. Discover the division algorithm and learn to simplify and interpret solutions. Sharpen your mathematical reasoning and problem-solving abilities with this comprehensive workshop.

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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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