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

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

Popcorn Party Serving 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.

Summarize How many 2–cup servings? 8 ÷ 2 = 4 cups cup servings serving 5 ÷ 2 = 2 cups cup serving 1212 servings

What does the represent?  One-half of a cup of popcorn?  One-half of a serving?  Are you sure? 1212

Popcorn Party Serving Size: cup How many servings from:  1 cup of popcorn  4 cups  2 cups

Summarize How many 2–cup servings? 1 ÷ = 2 cup servings 4 ÷ = 8 cups servings 1212 cup serving 1212 cup serving

Task Popcorn Parties # 1 & # 2 æFacilitator æPaper Strip Demonstrator

Algorithm

Task Popcorn 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 1414

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 3434

Popcorn Party Serving Size: cup How many servings from 4 cups? 3434

Summarize How many 2–cup servings? 4 ÷ = cups 3434 cup serving

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

3434 X = 1 ?

7 ÷ 8 =

12 24 =

Summarize How many 2–cup servings? 5 ÷ = 3434

5 =

=

=