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### Integrating Mathematical Practices K-12

### Background Information

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?

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

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

___The CCSS are a national curriculum.

___ The CCSS represent a modest change from current practice.

___ The CCSS will transform schools.

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

Arizona:

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

Video

- Watch the David Coleman video.
- Listen for the 3 main focuses of the Mathematics Common Core.
- Discuss.

Link: http://usny.nysed.gov/rttt/resources/bringing-the-common-core-to-life.html

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.

Activity

- 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

- 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

- 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

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

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 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.

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 matrix17

Cognitive Demand (Expectations for Student Performance)

Use

Extend

Acquire

Recall

Skill/Concept

Strategic

Thinking

Extended

Thinking

Memorize

Perform

Procedures

Demonstrate

Understanding

Conjecture,

Generalize

Prove

Solve non-

routine/ make

connections

Cognitive Demand Sorting Activity

A

Memorize Facts,

Definitions, Formulas

B

Perform Procedures

E

Solve Non-Routine

Problems,

Make Connections

C

Demonstrate

Understanding

of Mathematical Ideas

D

Conjecture, Analyze,

Generalize, Prove

Mathematical Practices

- Watch the video.
- Note times during the lesson where mathematical practices were being implemented.
- Watch teacher and student behaviors.

Video

Here’s the link to the videos:

http://www.learner.org/resources/series33.html?pop=yes&pid=921# hexominoes – 5th gr geometry

http://www.learner.org/resources/series32.html?pop=yes&pid=879# 2nd gr marshmallows

Video

- Here’s the link to the video:

http://www.learner.org/resources/series33.html?pop=yes&pid=921# rods and rafts – surface area

http://www.learner.org/vod/vod_window.html?pid=925 bungee jumping

Teacher/Student Insights

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

Choose a math standard.

Develop a lesson imbedding mathematical practices.

Write the specific guiding questions.

Share your common core math lesson outline.

Math Standard

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

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

- Questions
- Evaluation
- Now the work begins
- State Resources - http://www.ade.az.gov/standards/CommonCoreStandards/default.asp
- 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

- Globe
- 1400 E Ash St.
- 928-402-8783
- [email protected]
- [email protected]
- Payson
- 112 W. Cedar Ln.
- 928-472-5374
- [email protected]
- [email protected]

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