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, 2011-2012 School Year

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, 2011-2012 School Year CCLM

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 CCLM

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, 2011-2012 School Year CCLM

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, 2011-2012 School Year CCLM

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, 2011-2012 School Year CCLM

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 2007. Discuss sequence of problems that lead to understanding of division of fractions. Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year CCLM

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, 2011-2012 School Year CCLM

Two Procedures for Division of Fractions The common denominator method Invert and Multiply Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year CCLM

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, 2011-2012 School Year CCLM

Two Procedures for Division of Fractions The common denominator method Invert and Multiply Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year CCLM

Invert and Multiply Method Have you ever used this? Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year CCLM

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, 2011-2012 School Year CCLM

Sample student work CCLM Common Core Leadership in Mathematics Project, University of Wisconsin-Milwaukee, 2011-2012 School Year CCLM

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, 2011-2012 School Year CCLM

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, 2011-2012 School Year CCLM

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 CCLM