part 2: division of fractions balancing procedural and conceptual knowledge

Part 2: Division of FractionsBalancing Procedural and

Conceptual Knowledge

Tuesday December 13, 2011Common Core Leadership in

Mathematics (CCLM)

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

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

Let’s Check Our Understanding

Estimate

Greater than 5? Equal to 5? Less than 5?

435

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

6 cups of popcorn 2 1/4 cups of popcorn 5 cups of popcorn

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

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?

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

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

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.

123

124

41

31

121234

31134

134

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

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

Invert and Multiply Method

Have you ever used this?

871

815

25

43

52

43

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.

Sample student work

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

Division of Fraction Standard

Examine 6.NS.1

Reread this standard. Do the examples and tasks make more sense to you now?

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

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