Standards of Mathematical

Practice

http://thinkmath.blog.monroe.edu/

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 planAnticipate possible solutions

Continuously evaluate progress

Check results

Question sense of solutions

SMP 2: Reason abstractly and quantitatively

DecontextualizeRepresent as symbols, abstract the situation

ContextualizePause as needed to refer back to situation

x x 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 conclusionsRespond to

arguments

Communicate conclusions

Distinguish

correct logic

Explain flaws

Ask clarifying

questions

© Institute for Mathematics & Education 2011

SMP 4: Model with mathematics

Images: http://tandrageemaths.wordpress.com, asiabcs.com, ehow.com, judsonmagnet.org, life123.com, teamuptutors.com, enwikipedia.org, glennsasscer.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: http://forums.xkcd.com/viewtopic.php?f=7&t=66819 © 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. 14 Grade 2: p. 18Grade 3: p. 22 Grade 4: p. 28Grade 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 3rd 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 equations.

• Make an array for the original equation; then change it just enough to match the new equations.

• Write a story for the original equation; then change it just enough to match the new equations.

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

EightSeven boxes with five pieces of jewelry in each box

35 pieces of jewelry+ 5 pieces of jewelry40 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 sixSeven 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

9 x 4 = 36

9 x 5 = 45

10 x 4 = 40

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?

Strategies for Implementing the Practices

Use Rich Tasks

Where to find rich tasks.

http://www.insidemathematics.org/

http://www.rda.aps.edu/mathtaskbank/start.htm

http://www.galileo.org/math/MathProblems.html

http://balancedassessment.concord.org/tasksalpha.html

http://illustrativemathematics.org/

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?