The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Using Properties to Reason through Tough Questions Wisconsin Mathematics Annual Conference May 2011 Beth Schefelker, Mathematics Teaching Specialist, MPS Melissa Hedges, Mathematics Teaching Specialist, MTSD Mary Mooney, Mathematics Teaching Speicalist, MPS The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Learning Intention  We Are Learning To… implement the third Standard for Mathematical Practice (Construct viable arguments and critique the reasoning of others) within a chosen Content Standard; strengthen our understanding of division as an unknown factor problem when applied to zero and one. (3.OA.6)

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Success Criteria  We are successful when… we can construct an argument using the properties of numbers and operations to justify what happens when you try to divide by zero.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), CCSS Mathematical Practices #3 Construct viable arguments and critique the reasoning of others. 1. Read Mathematical Practice Standard #3. 2. Discuss the Practice with your table group. 3. Identify key ideas that help define this Practice. 4. Come to an understanding about what teachers need to plan and do to implement this Practice.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Usually we don’t encourage arguments but… Consider the word Argument as it is referred to in the standard. Use the Frayer model to sort out the difference between the everyday use of the word argument and the use of the word argument in academic disciplines.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Frayer Model: Argument

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Argument vs. Confrontation Argument_Clinic.mp4

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Definition: The Academic Use of the word Argument  An argument is a connected series of statements intended to establish a proposition.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Linking to Literacy…  Half the table read CCSS Literacy Standards for grades 3-5 while the other half reads CCSS Literacy Standards for grades  Complete the Venn Diagram in order to discuss the connections between the Literacy Standards and the Mathematical Practice Standard #3

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), What are the connections between literacy and the math practice standards? Literacy Standard Math Practice Standard #3

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Literacy Connections from the CCSS Grade 3 Engage effectively in a range of collaborative discussions with diverse partners build on your own ideas Grade 6 Delineate a speakers’ arguments and specific claims, distinguishing claims that are supported by reasons and evidence from claims that are not.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), CCSS Mathematics Content Focus Cluster Statement and Standards (p.23)  Understand properties of multiplication and the relationship between multiplication and division.  3. OA.5 – Apply properties of operations as strategies to multiply and divide. (note: students need not use formal terms for these properties).  3. OA. 6 – Understand division as an unknown-factor problem. What are some examples you can generate in order to make sense of the standards?

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), What Do You Know?...  Consider the numbers 0 and 1.  Work together with your table group to brainstorm a list of properties for each number.  Be prepared to share an idea from your table with the whole group.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Starting with what we know… 8 friends equally share 24 flowers How many flowers does each friend get? Act out the problem with counters. Use conceptually-based language to describe what you did with the flowers.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Thinking about the context… 8 friends equally share 24 flowers. How many flowers does each friend get? 24 ÷ 8 = 3 What’s another way to reason to get the answer?

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), How many flowers does each friend get? Directions: Apply the reasoning of missing factor to write the division problem and the associated multiplication problem. 8 friends share 16 flowers 8 friends share 8 flowers 8 friends share 0 flowers

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), How many flowers does each friend get? Directions: Apply the reasoning of missing factor to write the division problem and the associated multiplication problem. 8 friends share 24 flowers 4 friends share 24 flowers 3 friends share 24 flowers 0 friends share 24 flowers

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), What’s happening? 8 friends shared 0 flowers 0 friends shared 16 flowers Share your reasoning, one based in context, one based in mathematics, for each of these scenarios.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Seeking Your Advice…. Philomena’s teacher told her that you can’t divide by zero. Is that true? Write a quick note to Philomena outlining an argument that justifies your answer.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), Take Away Message  Students can make sense of why dividing by zero is impossible and support it with an argument based on their understanding of the properties of multiplication and it’s relationship to division.

The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA),