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# Teaching for Understanding Division with Fractions - PowerPoint PPT Presentation

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 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.

• Deepen conceptual understanding of division with fractions.

• Examine “why” we can invert and multiply.

Popcorn PartyServing Size: 2 cups

How many servings from:

• 8 cups of popcorn

• 5 cups of popcorn

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

• Identify the meaning of each number in the equations.

12

SummarizeHow many 2–cup servings?

8 ÷ 2 = 4

cups cup servings

serving

5 ÷ 2 = 2

cups cup

serving

servings

12

What does the represent?

• One-half of a cup of popcorn?

• One-half of a serving?

• Are you sure?

12

12

Popcorn PartyServing Size: cup

How many servings from:

• 1 cup of popcorn

• 4 cups

• 2 cups

12

12

SummarizeHow many 2–cup servings?

cup

serving

1 ÷ = 2

cup servings

4 ÷ = 8

cups

servings

cup

serving

TaskPopcorn Parties #1 &#2

• Facilitator

• Paper Strip Demonstrator

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.

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

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

34

Popcorn PartyServing Size: cup

How many servings from 4 cups?

34

SummarizeHow many 2–cup servings?

cup

serving

4 ÷ =

cups

### Discussion

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

Fraction Division Algorithm Photo Sequence from Session

7 X = 1

?

a X = 1

?

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

1a

Is this true for any number?

What about zero?

a X = 1

a ≠ 0

34

?

X = 1

7 ÷ 8 =

12

1224

?

• =

?

12

1224

112

112

• =

Greater than 5?

Equal to 5?

Less than 5?

34

5 ÷ =

34

SummarizeHow many 2–cup servings?

How else can we write this?

5 ÷ =

34

5

• =

1

34

92

• =

1

cd

ab

• =

1