Integrating Mathematical

Practices K-12Gila 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.

True or False?

Background Information

•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

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45 States + DC Have Adopted the Common Core Math Standards

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

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.

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.203rd = p.27 4th = p.33 5th = p.37 6th = p.44 7th = p.30 8th = p.319th-12th = p.122

Depth and Rigor

Hess’ Cognitive Rigor Matrixdescribes the type of thinking involved, not

whether it will be completed correctlyapplies Webb’s Depth of Knowledge to

Bloom’s Cognitive Process Dimensionsidentifies cognitive levels of student activities

and test questionsInvolves multiple levels (sometimes) in one

activity

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Karin K. Hess, Ed.D., Senior AssociateNational Center for Assessment, Dove, NHkhess@nciea.org

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Karin K. Hess, Ed.D., Senior AssociateNational Center for Assessment, Dove, NHkhess@nciea.org

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)

Skill/ConceptRecallStrategicThinking

ExtendedThinking

Use Extend

MemorizePerform

ProceduresDemonstrate

Understanding

Conjecture,Generalize

Prove

Solve non-routine/ makeconnections

Acquire

Cognitive Demand Sorting Activity

AMemorize Facts,

Definitions, Formulas

ESolve Non-Routine

Problems,Make Connections

BPerform Procedures

CDemonstrate Understanding

of Mathematical Ideas

DConjecture, Analyze,

Generalize, Prove

SEC Math Expectations for Students

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.

Standard Mathematical Practices

Explanations and Examples

Students are expected to:

•5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g. by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result: 2/5 + ½ = 3/7, by observing that 3/7 < ½.Connections: 5.NF.2

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

Examples: Jerry was making two different kinds of cookies. One recipe needed ¾ cup of sugar and the other needed 2/3 cup of sugar. How much sugar did he need to make both recipes?•Mental estimation A student may say that Jerry needs more than one cup of sugar but less than 2 cups of sugar. An explanation may compare both fractions to ½ and state that both fractions are larger than ½ so the total must be more than 1. in addition, both fractions are slightly less than 1 so the sum cannot be more than 2.•Area model

¾ cup of sugar 2/3 cup of sugar

¾ = 9/12 2/3 = 8/12

¾ + 2/3 = 17/12 = 12/12 + 5/ 12 =1 5/12

continued next page

Number and Operations - Fractions (NF)

Use equivalent fractions as a strategy to add and subtract fractions.

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– lowen@gilacountyaz.gov– ggorry@gilacountyaz.gov

• Payson– 112 W. Cedar Ln.– 928-472-5374– lowen@gilacountyaz.gov– ggorry@gilacountyaz.gov