1. Tuesday December 13, 2011 Common Core Leadership in Mathematics (CCLM)
Part 2: Division of Fractions Balancing Procedural and Conceptual Knowledge
Tuesday December 13, 2011
Common Core Leadership in Mathematics (CCLM)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year

2. Deepen conceptual understanding of division of fractions.
Learning Intentions
Deepen conceptual understanding of division of fractions.
Unpack the CCSS standards about division of fractions
Understanding comes from extending your understanding of division of whole numbers
Standard 5NF7 a,b,c
Standard 6NS1
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

3. Success Criteria We will know we are successful when we can
Justify our thinking when dividing fractions using reasoning and models.
Clearly explain and provide examples for specific CCSS-M standards
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

4. Components of Complete Understanding of Division
Estimate the answer
Think about related operations
Draw a diagram
Write an equation
Use a strategy or algorithm
Division
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

5. Let’s Check Our Understanding
Estimate
Greater than 5?
Equal to 5?
Less than 5?
Connection back to the Practices. Sense making…
It’s more than 5 because I can visualize using measurement division
It’s less than 10 because 5 divided by ½ is 10
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

6. CCLM Serving Size: 3/4 cup of popcorn
Task : Popcorn Party #3
Serving Size: 3/4 cup of popcorn
How many servings can be made from:
Individually solve each problem using reasoning and models (don’t forget the tape diagram).
As a group, take turns and share your reasoning
6 cups of popcorn
2 1/4 cups of popcorn
5 cups of popcorn
What is the meaning of the remainder? How can you explain how you find the remainder as a fraction?
We will do 5 cups of popcorn divided by ¾ cup serving together as a group.
You need to understand what the serving size is.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

7. Now It’s Your turn
In pairs, solve each problem using reasoning and models (don’t forget the tape diagram).
How many ¾ cups servings of popcorn are in 4 ¼ cups of popcorn?
A serving is ½ of a cookie. How many servings can I make from 3/8 of a cookie?
Be sure that the teachers use their fraction strips to determine the fraction divided by a fraction.
After this slide, pass out article “Measurement and Fair Sharing models for Dividing Fractions” MTMS May Discuss sequence of problems that lead to understanding of division of fractions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

8. Computational Procedures
What procedure do you use to divide fractions?
Write an example of it on your slate.
Working on 6NS1
Table discussion – whole group discussion
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

9. Two Procedures for Division of Fractions
The common denominator method Invert and Multiply
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

10. The Common Denominator Method
Have you ever used this?
Does it always work?
Make up division problems to decide when you can use this algorithm.
Share problems at the table. Use what you have learned about questioning and probes in these discussions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

11. Two Procedures for Division of Fractions
The common denominator method Invert and Multiply
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

12. Invert and Multiply Method
Have you ever used this?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

13. Why can we “invert and multiply”?
Discuss this question with your shoulder partner. Record your answer on your slate
Share your answer with the whole table.
Possible assignment: Think about this… Convince yourself that the invert and multiply and one of the others always work. Why do we need to know these algorithms? Bring this back next class
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

14. Sample student work CCLM
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

15. Division of Fraction Standard
Examine 6.NS.1
Reread this standard. Do the examples and tasks make more sense to you now?
How have student expectations for division grown in 6th grade? Now extended to dividing fractions by fractions.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

16. Short Readings Homework
Grade 3 2nd narrative p. 21
Grade 4 2nd narrative p. 27
Grade 5 1st narrative p. 33
Grade 6 2nd narrative p. 39
What did you notice? Give some examples of key advances from one grade to the next.
Concludes the study of fractions which began in the summer with addition and subtraction and moved on to multiplication and division
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM

17. Success Criteria We will know we are successful when we can
Justify our thinking when dividing fractions using reasoning and models.
Clearly explain and provide examples for specific CCSS-M standards
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, School Year
CCLM