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Integrating Mathematical Practices K-12. Gila County Teacher Institute Gail Gorry & Deb Leverance June 1, 2012. Agenda. Background of Common Core Explore the Mathematical Practices Discover Level of Knowledge Develop a Mathematical Practice Integrated Lesson. Where Are You Now?.

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Integrating mathematical practices k 12

Integrating Mathematical Practices K-12

Gila County Teacher Institute

Gail Gorry & Deb Leverance

June 1, 2012


Background of Common Core

Explore the Mathematical Practices

Discover Level of Knowledge

Develop a Mathematical Practice Integrated Lesson

Where are you now
Where Are You Now?

How comfortable do you feel implementing the 2010 Arizona Mathematics Standards?

How knowledgeable are you about the components and how to access them?

Integrating mathematical practices k 12

True or False?

___The CCSS are a national curriculum.

___ The CCSS represent a modest change from current practice.

___ The CCSS will transform schools.

Background information

Background Information

The Partnership for Assessment of Readiness for College and Careers (PARCC)


Is a PARCC Governing State

Will be Pilot State for Assessment Development

Starts Computer/Performance based testing in 2014/2015

Follows the 2008 Math Standards format


  • Watch the David Coleman video.

  • Listen for the 3 main focuses of the Mathematics Common Core.

  • Discuss.


Standards of mathematical practice
Standards of 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.


  • Jigsaw with your table one of the Standards of Mathematical Practice.

  • Share your thoughts about what this practice means with your table group.

  • Record key ideas on easel paper.

  • Post your paper.

  • Gallery walk.

Mathematical practices take home
Mathematical Practices Take Home

  • How are the mathematical practices reflected in your daily instruction?

  • Move into integrated grade level groups.

  • Compare and contrast the grade level mathematical practices.

  • Share findings.

Grade level documents
Grade Level Documents

  • Find a person who shares your grade level.

  • Locate the mathematical practices from the standards documents.

  • Any changes from

    your earlier discussion?

    K = p.21 1st = p.21 2nd = p.20

    3rd = p.27 4th = p.33 5th = p.37

    6th = p.44 7th = p.30 8th = p.31

    9th-12th = p.122

Depth and rigor
Depth and Rigor

Hess’ Cognitive Rigor Matrix

describes the type of thinking involved, not whether it will be completed correctly

applies Webb’s Depth of Knowledge to Bloom’s Cognitive Process Dimensions

identifies cognitive levels of student activities and test questions

Involves multiple levels (sometimes) in one activity

Integrating mathematical practices k 12


Karin K. Hess, Ed.D., Senior Associate

National Center for Assessment, Dove, NH

Integrating mathematical practices k 12


Karin K. Hess, Ed.D., Senior Associate

National Center for Assessment, Dove, NH

Identify the dok level
Identify the DOK Level

Analyze the following chart entitled, “The Speed of Indy 500 Cars per Lap” and be ready to share your conclusions.

Retrieve information from a table or graph.

Identify the dok level1
Identify the DOK Level

Gather information about the speed of vehicles in your neighborhood. Analyze and evaluate the information in a presentation of your choice to the class.

Compare and contrast the data from 1985 to 2010 from the following table.

Design activities to fill the matrix

Your team will be assigned a verb from Bloom’s Revised Taxonomy. Design activities that will fill the matrix (Levels 1-4) for your assigned verb.

Make a chart and be ready to share with the entire group.

Design activities to fill the matrix


Integrating mathematical practices k 12

Cognitive Demand (Expectations for Student Performance)


















Solve non-

routine/ make


Cognitive demand sorting activity
Cognitive Demand Sorting Activity (Expectations for Student Performance


Memorize Facts,

Definitions, Formulas


Perform Procedures


Solve Non-Routine


Make Connections




of Mathematical Ideas


Conjecture, Analyze,

Generalize, Prove

Sec math expectations for students
SEC Math Expectations for Students (Expectations for Student Performance

Mathematical practices
Mathematical Practices (Expectations for Student Performance

  • Watch the video.

  • Note times during the lesson where mathematical practices were being implemented.

  • Watch teacher and student behaviors.

Video (Expectations for Student Performance

Here’s the link to the videos: hexominoes – 5th gr geometry 2nd gr marshmallows

Video (Expectations for Student Performance

  • Here’s the link to the video: rods and rafts – surface area bungee jumping

Teacher student insights
Teacher/Student Insights (Expectations for Student Performance

Note mathematical practices.

Discuss teacher/student actions and words.

What DOK levels were illustrated?

How do these activities compare to the learning activities in your classroom?

Activity (Expectations for Student Performance

Choose a math standard.

Develop a lesson imbedding mathematical practices.

Write the specific guiding questions.

Share your common core math lesson outline.

Math standard
Math Standard (Expectations for Student Performance

7 NS 3 Solve real-world and mathematical problems involving the four operations with rational numbers, (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

Session review
Session Review (Expectations for Student Performance

Discover level of knowledge

Investigate the format of the 2010 Math Standards

Explore and use the Mathematical Practices

Develop a “math practices” focused lesson

Closing remarks
Closing Remarks (Expectations for Student Performance

  • Questions

  • Evaluation

  • Now the work begins

  • State Resources -

  • County Resources

    • Coaching

    • County Curriculum Specialist

    • Teacher Resource Library

    • Professional Development workshops

      • Differentiated Instruction

      • STEM Education and Training

      • Intel Math Training

      • Common Core

Gila county education service agency
Gila County Education Service Agency (Expectations for Student Performance

  • Globe

    • 1400 E Ash St.

    • 928-402-8783



  • Payson

    • 112 W. Cedar Ln.

    • 928-472-5374