division of fractions balancing procedural and conceptual knowledge tuesday december 6, 2011 common...
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Division of FractionsBalancing Procedural and
Conceptual Knowledge
Tuesday December 6, 2011
Common Core Leadership in Mathematics (CCLM)
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Troubles with Fractions?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Learning Intentions
Deepen conceptual understanding of division of fractions.
Unpack the CCSS standards about division of fractions
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
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, 2011-2012 School Year
Launch: Popcorn Party #1
Serving Size: 1/2 cup of popcornHow many servings can be made from:
1 cup of popcorn 2 cups of popcorn 3 1/2 cups of popcorn
Have we done problems like this in the whole number world?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Explore: Popcorn Party #2
Serving Size: 1/3 cup of popcornHow many servings can be made from:
1 cup of popcorn 2 cups of popcorn 3 2/3 cups of popcorn
Individually solve each problem using reasoning and models
As a group, take turns and share your reasoning
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Explore #2: Juice Party
Serving Size: 1/2 gallon of juiceHow can I divide that among:
2 friends 5 friends
Individually solve each problem using reasoning and models
As a group, take turns and share your reasoning
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Standard 5NF 7
5NF7a… write the story with representation5NF7b… write the story with representation5NF7c… Solving problems, write equations
Divide your slate in half. On one side, rephrase these standard and on the other side, provide an example.
Share with your partner. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee,
2011-2012 School Year
Break
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
An Important Cluster in 6thGrade
Apply and Extend Previous Understanding of Multiplication and Division to Divide Fractions by Fractions
Identify 3-4 previous understandings from 3rd - 5th grade around multiplication and division that students would be expected to apply.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Division of Fraction Standard
Examine 6.NS.1
In a group of 3, on your slates, draw a visual model for each example given in the standard in italics. (For example) Then write the equation for each example to solve the problem.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Task : Popcorn Party #3
Serving Size: 3/4 cup of popcornHow 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
2 1/4 cups of popcorn 5 cups of popcorn 4 cups of popcorn
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Let’s Check Our Understanding
Estimate
Greater than 5? Equal to 5? Less than 5?
4
35
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Computational Procedures
What procedure do you use to divide fractions?
Write an example of it on your slate.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Several Procedures for Division of Fractions
The common denominator method
Dividing component parts.
Invert and Multiply
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
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.
2
3
4
4
4
24
3
2
1
4
3
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Several Procedures for Division of Fractions
The common denominator method
Dividing component parts.
Invert and Multiply
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Dividing Component Parts Method
Have you ever used this?
Does it always work?Make up division problems to decide
when you can use this algorithm.
2
11
2
3
24
13
2
1
4
3
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Several Procedures for Division of Fractions
The common denominator method
Dividing component parts.
Invert and Multiply
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Invert and Multiply Method
Have you ever used this?
8
71
8
15
2
5
4
3
5
2
4
3
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Why can we “invert and multiply”?
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
Discuss this question with your shoulder partner. Record your answer on your slate
Share your answer with the whole table.
Short Readings Homework
Grade 3 2nd narrative p. 21Grade 4 2nd narrative p. 27Grade 5 1st narrative p. 33Grade 6 2nd narrative p. 39
What did you notice? Give some examples of key advances from one grade to the next.
Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year
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, 2011-2012 School Year