Mathematics 3 – 8Standards for Mathematical Practice

TLQP 2013-14

Tom SweeneyThe Sage Colleges

Sources• http://www.corestandards.org/ • http://www.parcconline.org/ • http://engageny.org/• http://www.illustrativemathematics.org/ • http://www.achievethecore.org/ • http://commoncoretools.me/ • http://insidemathematics.org/• https://www.teachingchannel.org/videos/

Common Core State Standards for Mathematics (CCSSM)

• Standards for Mathematical Practice &(recurring throughout the grades)

(our focus today)

• Standards for Mathematical Content(different at each grade level)

Gain a deeper understanding of the eight Standards for Mathematical Practice (SMP)

Identify evidence of teachers using SMP in their classrooms

Identify evidence of students using SMP in

their work.

Objectives

Video

• The Importance of Mathematical Practices(4:02)

• Mathematical Practices, Focus and Cohere

nce in the Classroom(1:14)

Initial Activity

Newspaper problem

Standards for Mathematical Practice

Compliments of Brenda Lidistri

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Pass out paragraph descriptors assign a stand to each neighboring pair of participants

Standards for Mathematical PracticeACTIVITY (initial)

For your assigned Standard of Mathematical Practice:

What are the verbs that illustrate the student actions for your assigned mathematical practice?

Circle, highlight or underline them.Discuss with a partner:

What stands out?

SMP1: Explain and make conjectures…

SMP2: Make sense of…

SMP3: Understand and use…

SMP4: Apply and interpret…

SMP5: Consider and detect…

SMP6: Communicate precisely to others…

SMP7: Discern and recognize…

SMP8: Notice and pay attention to…

Standards for Mathematical PracticeActivity B

Divide a piece of chart paper in half and on one side label it Student Evidence and on the other side label it Teacher Evidence. Don’t forget to write the number of the MP you selected on your chart paper as well.

ACTIVITY B (cont’d)

Brainstorm with members at your table what students would be doing in the classroom if this MP was being implemented effectively and list evidence on your chart paper.

Next, brainstorm with members at your table what teachers would be doing in the classroom if this MP was being implemented effectively and list evidence on your chart paper.

Standards for Mathematical Practice

ACTIVITY B (cont’d)

Locate all those tables that worked on the same MP as you and come together as one group and share your work. Review the evidence and determine if it should stay on the chart or be deleted. Be prepared to report out.

Standards for Mathematical Practice

MP 1:Make sense of problems and persevere in solving them.

Standards for Mathematical Practice

Standards for Mathematical Practice

MP 2:Reason abstractly and quantitatively.

Standards for Mathematical Practice

MP 3:Construct viable arguments and critique the reasoning of others.

Standards for Mathematical Practice

MP 4:Model with mathematics.

Standards for Mathematical Practice

MP 5:Use appropriate tools strategically.

Standards for Mathematical Practice

MP 6:Attend to precision.

Standards for Mathematical Practice

MP 7:Look for and make use of structure.

Standards for Mathematical Practice

MP 8:Look for and express regularity in repeated reasoning.

Standards for Mathematical Practice

PROBLEM

A rectangle has sides of length 6 in. and 2 in. What is its area ?

Standards for Mathematical Practice

Identify the MPs that align with this problem. Discuss at your tables.

Standards for Mathematical Practice

Pose a different problem that could go deeper but require the same mathematical content knowledge?

Standards for Mathematical Practice

Explain what students might learn from the second question compared to the first question?

Standards for Mathematical Practice

Explain what a teacher might learn from how students answer the first question compared to how students answer the second question?

McDonald’s Claim

Wikipedia reports that 8% of all Americans eat at McDonalds every day.

310 million Americans and 12,800 McDonalds…

Do you believe the Wikipedia report to be true?

Create a mathematical argument tojustify your position.

MCDONALD’S CLAIM PROBLEM

Which mathematical practices are needed to complete the task?

Integrating the Standards for Mathematical Practice

Inside +=x Mathematics

Fran Dickenson (3:53)

Watch the video using the Inside Mathematics link above and collect evidence from the lesson that exemplifies the Standards for Mathematical Practice. Focus on both the students and the teacher.

http://www.insidemathematics.org/index.php/math-standards-together

Guess My Rule from the Video

X Y10 276 158 21

? 5 120

0X

Integrating the Standards for Mathematical Practice

(Continued)Inside +=x

Mathematics Fran Dickenson

Compare your evidence with an elbow partner and then engage in a conversation with members at your table to come to consensus as to which MPs you observed.

Integrating the Standards for Mathematical Practice

(continued)

Inside +=xMathematics

(video)

For a more in-depth study of the Standards for Mathematical Practice, please visithttp://www.insidemathematics.org/index.php/commmon-core-math-intro.

Standards for Mathematical Practice

MP PLACEMAT ACTIVITY

Everyone will need the MP Placemat and the MP Activity Cards. Read through the MP Activity Cards on your own. Once you have read the activity cards, you need to decide where you would put them on your placemat. You have 16 activity cards and 16 boxes on your placemat.

Standards for Mathematical Practice

MP PLACEMAT ACTIVITY (cont’d)

First you will have time to work independently and then in small groups at your table. In the end, your table must come to consensus and a representative needs to come up and post their results on the master placemat.

Instructional Self-assessment• Examine tasks in your instructional

materials:– Higher cognitive demand?– Lower cognitive demand?

• Where are the challenging tasks?• Do all students have the opportunity to

grapple with challenging tasks?• Examine the tasks in your assessments:

– Higher cognitive demand?– Lower cognitive demand?

SMP 3. Construct viable arguments and critique the reasoning of others

• Students make conjectures

• Students justify their conclusions and communicate them

to others

• Students compare the effectiveness of two plausible

arguments

• Students listen and respond to the arguments of others for

sense making and clarity

Thank you!

sweent@sage.edu