Teaching for UnderstandingDivision with Fractions

Dr. DeAnn Huinker, Dr. Kevin McLeod, Dr. Henry Kepner University of Wisconsin-Milwaukee

Math Teacher Leader (MTL) SeminarMilwaukee Public Schools

June 2005This material is based upon work supported by the National Science Foundation Grant No. EHR-0314898.

Session Goals

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

Summarize

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

Identify the meaning of each number in the equations.

SummarizeHow many 2–cup servings?

8 ÷ 2 = 4 cups cup servings

serving

5 ÷ 2 = 2 cups cup

serving

12

servings

What does the represent?

One-half of a cup of popcorn?

One-half of a serving?

Are you sure?

12

Popcorn PartyServing Size: cup

How many servings from:

1 cup of popcorn

4 cups

2 cups

12

12

SummarizeHow many 2–cup servings?

1 ÷ = 2 cup servings

4 ÷ = 8 cups servings

12

cupservin

g12

cupservin

g

TaskPopcorn Parties #1 & #2

Facilitator

Paper Strip Demonstrator

Algorithm

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

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

14

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

34

Popcorn PartyServing Size: cup

How many servings from 4 cups?

34

SummarizeHow many 2–cup servings?

4 ÷ = cups

34

cupservin

g

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.

a X = 1

a ≠ 0

Is this true for any number?

What about zero?

1a

34 X = 1

1

?

7 ÷ 8 =

How else can we write this?

1224 • =

?

?12

1224 • =

1121

12

12

5 ÷ =

34

Estimate

Greater than 5? Equal to 5? Less than 5?

SummarizeHow many 2–cup servings?

5 ÷ = 3

4

How else can we write this?

5• =3

41

• =34

1

92

• =cd

1

ab