1. 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
This material is based upon work supported by the National Science Foundation Grant No. EHR

2. Session Goals
Deepen conceptual understanding of division with fractions.
Examine “why” we can invert and multiply.
Goals for the MTL Content Strand
To deepen your knowledge of mathematics so that you can use this knowledge in your work with students and in your work as a Math Teacher Leader.

3. Popcorn Party Serving 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. Summarize How many 2–cup servings?
÷ =
cups cup servings
serving
÷ = 2
cups cup
1 2
servings

6. What does the represent?
1 2
One-half of a cup of popcorn?
One-half of a serving?
Are you sure?

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

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

9. Task Popcorn Parties #1 & #2
Facilitator
Paper Strip Demonstrator

10. Algorithm

11. 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.

12. Popcorn Party #1 1 Serving Size: cup of popcorn 4
How many servings can be made from:
1 cup of popcorn
2 cups of popcorn
3 1/2 cups of popcorn 1 4

13. Popcorn Party #2 3 Serving Size: cup of popcorn 4
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. Popcorn Party Serving Size: cup
3 4
How many servings from 4 cups?

15. Summarize How many 2–cup servings?
÷ =
cups
3 4
cup
serving

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. Is this true for any number?
What about zero?
1 a
a X = 1
a ≠ 0

21. 1 ?
3 4
X = 1

22. How else can we write this?
7 ÷ 8 =

23. ?
12 24
1 2
• = ?

24. 1 12
12 24
1 2
• =
1 12

26. Estimate
Greater than 5?
Equal to 5?
Less than 5?
5 ÷ =
3 4

27. Summarize How many 2–cup servings?
How else can we write this?
5 ÷ =
3 4

28. 5
• =
3 4 1

30. 9 2
• =
3 4 1

32. a b
• =
c d 1