Standards of Mathematical Practice

Today’s Goals To explore the mathematical standards for Content and Practice To discuss and learn strategies for getting students engaged in the Standards of Mathematical Practice To explore how we can use existing resources to focus on the Practices

Common Core State Standards Mathematics Standards for Content Standards for Practice

Standards for Mathematical Practice Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning © Institute for Mathematics & Education 2011

SMP 1: Make sense of problems and persevere in solving them. © Institute for Mathematics & Education 2011 Gather Information Make a plan Anticipate possible solutions Continuously evaluate progress Check results Question sense of solutions

SMP 2: Reason abstractly and quantitatively Decontextualize Represent as symbols, abstract the situation Contextualize Pause as needed to refer back to situation x x P 5 ½ Mathematical Problem © Institute for Mathematics & Education 2011

SMP 3: Construct viable arguments and critique the reasoning of others Use assumptions, definitions, and previous results Make a conjecture Build a logical progression of statements to explore the conjecture Analyze situations by breaking them into cases Recognize and use counter examples Justify conclusions Respond to arguments Communicate conclusions Distinguish correct logic Explain flaws Ask clarifying questions © Institute for Mathematics & Education 2011

SMP 4: Model with mathematics Images: asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org, glennsasscer.comhttp://tandrageemaths.wordpress.com Problems in everyday life… …reasoned using mathematical methods © Institute for Mathematics & Education 2011

SMP 5: Use appropriate tools strategically © Institute for Mathematics & Education 2011

SMP 6: Attend to precision Comic: © Institute for Mathematics & Education 2011

SMP 7: Look for and make use of structure © Institute for Mathematics & Education 2011

SMP 8: Look for and express regularity in repeated reasoning © Institute for Mathematics & Education 2011

Over emphasis on computation obscures understanding of the operations. Focus on behavior of the operations supports computational fluency. Deborah Schifter

Content Goals These standards of practice will be examined in the context of the following content standard: Understand properties of the operations. Grade 1: p. 14Grade 2: p. 18 Grade 3: p. 22Grade 4: p. 28 Grade 5: p. 33 (paragraph #2)

What generalization is suggested by these problems?

Video 1 – Will it always work? CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003 Ms. Kaye’s 3 rd Grade

Video 2 – Will it always work?

Video 3 – Will it always work?

What Standards for Mathematical Practice were focused on in this task?

Adding 1 to a Factor Writing prompt: In a multiplication problem, if you add 1 to a factor, I think this will happen to the product…

Students’ Articulation of the Claim “The number that is not increased is the number that the answer goes up by.” “The number that is staying and not going up, increases by however many it is.” “I think that the factor you increase, it goes up by the other factor.”

Sample task Draw a picture for the original equation; then change it just enough to match the new equation. Make an array for the original equation; then change it just enough to match the new equation. Write a story for the original equation; then change it just enough to match the new equation. Example: Original equation 7 x 5 = 35 New equations 7 x 6 = 42 8 x 5 = 40

Frannie’s Story Context There are 7 jewelry boxes and each box has 5 pieces of jewelry. There are 35 pieces of jewelry altogether.

Jewelry Boxes 7 x 5 Seven boxes with five pieces of jewelry in each box 35 pieces of jewelry

7 x 5  8 x 5 Eight Seven boxes with five pieces of jewelry in each box 35 pieces of jewelry + 5 pieces of jewelry 40 pieces of jewelry Jewelry Boxes

7 x 5 Seven boxes with five pieces of jewelry in each box 35 pieces of jewelry Jewelry Boxes

7 x 5  7 x 6 six Seven boxes with five pieces of jewelry in each box 35 pieces of jewelry + 7 pieces of jewelry 42 pieces of jewelry Jewelry Boxes

Other Stories Baskets of bouncy balls Tanks with salmon eggs Baskets of mozzarella sticks Rows of chairs

Explain how the array changes from 7 x 5 to 8 x 5 and from 7 x 5 to 7 x 6. Making Sense of Multiplication

What Standards for Mathematical Practice were focused on in this task?

Work Backwards

What Standards for Mathematical Practice were focused on in this task?

What is 3 x 14?

What is ?

What is 32 x 17?

Strategies for Implementing the Practices

Use Rich Tasks

Where to find rich tasks

Rich Problems Worksheet Read through the tasks on the Rich Problems worksheet With a partner discuss what similarities you see in these problems

Creating Open Ended Questions

Creating open ended questions With a partner choose an upcoming topic you will be teaching. Create 3 open ended questions to engage your students? For each questions what Math Practices would you expect your students to be engaged in?

Additional Strategies

Where do I find these opportunities in my resources?

With a partner, pick an upcoming lesson and discuss how you are going to integrate the standards of Mathematical Practice. Focus on 1 or 2 Practices What will you see the students doing if they are engaging in the Practices? How will you facilitate the Practices?