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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 l.jpg

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.


Session goals l.jpg
Session Goals

  • Deepen conceptual understanding of division with fractions.

  • Examine “why” we can invert and multiply.


Popcorn party serving size 2 cups l.jpg
Popcorn PartyServing Size: 2 cups

How many servings from:

  • 8 cups of popcorn

  • 5 cups of popcorn


Summarize l.jpg
Summarize

  • Write the equation for each situation (8 cups; 5 cups).

  • Identify the meaning of each number in the equations.


Summarize how many 2 cup servings l.jpg

12

SummarizeHow many 2–cup servings?

8 ÷ 2 = 4

cups cup servings

serving

5 ÷ 2 = 2

cups cup

serving

servings


What does the represent l.jpg

12

What does the represent?

  • One-half of a cup of popcorn?

  • One-half of a serving?

  • Are you sure?


Popcorn party serving size cup l.jpg

12

12

Popcorn PartyServing Size: cup

How many servings from:

  • 1 cup of popcorn

  • 4 cups

  • 2 cups


Summarize how many 2 cup servings8 l.jpg

12

12

SummarizeHow many 2–cup servings?

cup

serving

1 ÷ = 2

cup servings

4 ÷ = 8

cups

servings

cup

serving


Task popcorn parties 1 2 l.jpg
TaskPopcorn Parties #1 &#2

  • Facilitator

  • Paper Strip Demonstrator



Task popcorn parties 1 211 l.jpg
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.


Popcorn party 1 l.jpg

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


Popcorn party 2 l.jpg
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


Popcorn party serving size cup14 l.jpg

34

Popcorn PartyServing Size: cup

How many servings from 4 cups?


Summarize how many 2 cup servings15 l.jpg

34

SummarizeHow many 2–cup servings?

cup

serving

4 ÷ =

cups


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Discussion

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


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Fraction Division Algorithm Photo Sequence from Session


Slide18 l.jpg

7 X = 1

?


Slide19 l.jpg

a X = 1

?

Multiply by the inverse, which is also called the reciprocal.


Slide20 l.jpg

1a

Is this true for any number?

What about zero?

a X = 1

a ≠ 0


Slide21 l.jpg

1

34

?

X = 1



Slide23 l.jpg

12

1224

?

• =

?


Slide24 l.jpg

12

1224

112

112

• =


Slide26 l.jpg

Estimate

Greater than 5?

Equal to 5?

Less than 5?

34

5 ÷ =


Summarize how many 2 cup servings27 l.jpg

34

SummarizeHow many 2–cup servings?

How else can we write this?

5 ÷ =


Slide28 l.jpg

34

5

• =

1


Slide30 l.jpg

34

92

• =

1


Slide32 l.jpg

cd

ab

• =

1


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