Alicia HoltzclawJune 20, 2012

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Welcome! Introductions Overview of Common Core Project 2010 Mathematics Standards Treasure

Hunt Unwrapping the Standards Cognitive Demand Mathematical Practices 3-2-1 Summary Sheet

Purpose:Examine and understand structure of

new standards and supporting documents

Explore elements of effective instruction and Model Content Frameworks

Consider implications for implementation of the new standards and impact on instruction

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In 2009, initial work began… Council of Chief State School Officers

(CCSSO) National Governor’s Associate for Best

Practice In partnership with:

◦ ACT◦ College Boards◦ Achieve, Inc.

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A national set of standards - written by experts, teachers, and administrators that are:

• Designed for college and career readiness• Mastery focused vs. exposure• Optional for state-adoption• Evidence/Research-based• Internationally benchmarked

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Emphasis on both concepts and skills

(learning progressions):

• Fewer standards• Clear, focused outcomes• Higher–order thinking skills

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◦Consistency among states promotes:

• common high-quality assessments• sensible instructional materials• clear, focused professional development

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◦Common Core Consortium considered:

• teacher input (NEA, AFT, NCTM, NCTE)• built from strengths and lessons learned◦ by current state standards• the avoidance of duplicity or repetition• the end goal for student mastery of◦ concepts and skills

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*Minnesota adopted the CCSS in ELA/literacy only

ANCHORED IN COLLEGE AND CAREER READINESS

• More demanding standards and new topics

• New assessments measuring more complex reasoning

• Urgency to address performance gaps• Need to reform professional

development

Common Core State Standards are critical, but they are just the first step

Common assessments aligned to the Common Core will help ensure the new standards truly reach every classroom

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1. Create high-quality assessments

2. Build a pathway to college and career readiness for all students

3. Support educators in the classroom

4. Develop 21st century, technology-based assessments

5. Advance accountability at all levels

End-of-Year Assessment

• Innovative, computer-based items

Performance-BasedAssessment (PBA)

•Extended tasks•Applications of concepts and skills

Summative,Required assessment

Non-summative, optional assessment

Diagnostic Assessment• Early indicator of student knowledge and skills to inform instruction, supports, and PD

Speaking And

Listening

Flexible

Mid-Year Assessment•Performance-based•Emphasis on hard-to-measure standards•Potentially summative

English Language Arts/Literacy and Mathematics, Grades 3-11

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Sept. 2011

Development phase begins

Sept. 2012

First year field testing and

related research and

data collection begins

Sept. 2013

Second year field testing begins and

related research and

data collection continues

Sept. 2014

Full administration

of PARCC assessments

begins

Oct. 2010

Launch and design phase

begins

Summer 2015

Set achievement

levels, including

college-ready performance

levels

For more information see, www.PARCCConsortium.org/Timeline

PROFESSIONAL DEVELOPMENT MODULES

• Common Assessment 101-103: PD focused on implementation of the new assessments• Common Assessment 201-204: PD focused on how to interpret and use the assessment results

INSTRUCTIONAL TOOLS TO SUPPORT

IMPLEMENTATION

•Content frameworks (released)• Additional sample assessment tasks•Model instructional units

EDUCATOR-LED TRAINING TO SUPPORT “PEER-TO-PEER”

TRAINING•Training for cadres of K-12 educators around the instructional tools AND around training their peers to use the instructional tools

TIMELY STUDENT ACHIEVEMENT DATA

• Aligned performance-based assessments given throughout year • Data reports will be available, designed with teacher use in mind

K-12 Educator

2.MD.1

Grade 2 Standard 1

Domain: Measurement and Data

Operations and Algebraic Thinking (OA)Use the four operations with whole numbers to solve problems.Standards Mathematical Practices Explanations and ExamplesStudents are expected to:4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Connections: 4.OA.3; 4.SL.1d; ET04-S1C2-01; ET04-S1C2-02

4.MP.2. Reason abstractly and quantitatively.4.MP.4. Model with mathematics.

A multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity (e.g., “a is n times as much as b”). Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times.

4.OA.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (see Table 2)

Connections: 4.RI.7; ET04-S1C2-01; ET04-S1C2-02

4.MP.2. Reason abstractly and quantitatively.4.MP.4. Model with mathematics.4.MP.5. Use appropriate tools strategically.4.MP.7. Look for and make use of structure.

Students need many opportunities to solve contextual problems. Table 2 in the glossary includes the following multiplication problem: “A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost?”

In solving this problem, the student should identify $6 as the quantity that is being multiplied by 3. The student should write the problem using a symbol to represent the unknown.

($6 x 3 = )

Table 2 in the glossary includes the following division problem:A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?

In solving this problem, the student should identify $18 as the quantity being divided into shares of $6.

Continued on next page

DomainDomainClusterCluster

StandardStandard

Operations and Algebraic Thinking (OA)Use the four operations with whole numbers to solve problems.Standards Mathematical Practices Explanations and ExamplesStudents are expected to:4.OA.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Connections: 4.OA.3; 4.SL.1d; ET04-S1C2-01; ET04-S1C2-02

4.MP.2. Reason abstractly and quantitatively.4.MP.4. Model with mathematics.

A multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity (e.g., “a is n times as much as b”). Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times.

4.OA.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (see Table 2)

Connections: 4.RI.7; ET04-S1C2-01; ET04-S1C2-02

4.MP.2. Reason abstractly and quantitatively.4.MP.4. Model with mathematics.4.MP.5. Use appropriate tools strategically.4.MP.7. Look for and make use of structure.

Students need many opportunities to solve contextual problems. Table 2 in the glossary includes the following multiplication problem: “A blue hat costs $6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost?”

In solving this problem, the student should identify $6 as the quantity that is being multiplied by 3. The student should write the problem using a symbol to represent the unknown.

($6 x 3 = )

Table 2 in the glossary includes the following division problem:A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?

In solving this problem, the student should identify $18 as the quantity being divided into shares of $6.

Continued on next page

Mathematical Mathematical PracticesPractices

Flamingo DialogueA flamingo dialogue is a short, interactive conversation lasting approximately as long

as the speaker can stand on one foot.

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Photo by graur razan ionut

1. Nouns2. Verbs3. Major Idea

in 5-7 words

Teachers understand◦ Cognitive demand◦ Necessary knowledge and skills

Teachers are more prepared to design assessment & instruction that is aligned with the standards◦ Prerequisite skills◦ Vocabulary◦ Enrichment and intervention◦ Assessment

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• Standards• What we want students to know and be

able to do (knowledge and skills)• Nouns: define the WHAT• Verbs: define the ACTION• Rigor is defined by both

• Level of complexity of the content• Cognitive Demand

Students use the same basic skills but in a more sophisticated way.

Same rules, higher level game….

How might you best determine the rigor of

a standard?

Cognitive Demand (Expectations for Student Performance)

Skill/ConceptRecallStrategicThinking

ExtendedThinking

Use Extend

MemorizePerform

ProceduresDemonstrate

Understanding

Conjecture,Generalize

Prove

Solve non-routine/ makeconnections

Acquire

AMemorize Facts,

Definitions, Formulas

ESolve Non-Routine

Problems,Make Connections

BPerform Procedures

CDemonstrate Understanding

of Mathematical Ideas

DConjecture, Analyze,

Generalize, Prove

Exploring Cognitive DemandEngage:CgD Immersion Activity

• Each Group w/ CgD Pie• Each Person w/ 1 set of the Cgd Descriptors

Step 1: Read each card silently and place CgD cards on Pie Slices face down

Step 2: Once everyone’s card are down, turn cards over: ID agreements

e.g. 2 cards w/ same descriptor in same sliceif Group Agrees ... discuss key wordsif not … Discuss …

4.OA.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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Crosswalk from 2010 to 2008 Summary of Changes

◦ Removed ◦Moved to a different grade level (New term: Redistributed)

◦Moved from another grade level to this one

◦ New to the standards

CROSSWALK: Grade 4 - Operations and Algebraic Thinking – (OA)CLUSTER 2010

STANDARDITEM DESCRIPTION 2008 PO ITEM DESCRIPTION

Use the four operations with whole numbers to solve problems.

4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

*

4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (see glossary Table 2)

*

4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

M04-S1C2-04 Use multiple strategies to divide whole numbers.

M04-S1C3-02 Make estimates appropriate to a given situation or computation with whole numbers and fractions.(Includes estimating)

M04-S3C3-01 Use a symbol to represent an unknown quantity in a simple algebraic expression involving all operations.

M04-S3C3-02 Create and solve one-step equations that can be solved using addition, subtraction, multiplication, and division of whole numbers. (Includes one-step equations only)

SUMMARY OF CHANGES: GRADE 4

Removed Moved to a Different Grade Level

Moved from another Grade Level

New Standards

M04-S1C1-05 (2008) Use simple ratios to describe problems in context.

M04-S1C1-03 (2008) Express fractions as fair sharing, parts of a whole, parts of a set, and locations on a real number line. MOVED TO 3.NF.2a (2010) & 3.NF.2b (2010)

M03-S1C1-02 (2008) MOVED TO 4.NBT.2 (2010) Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

4.OA.1 (2010) Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

M04-S2C1-01 (2008) Collect, record, organize, and display data using double bar graphs, single line graphs, or circle graphs.

M04-S2C2-01 (2008) Describe elements of theoretical probability by listing or drawing all possible outcomes of a given event and predicting the outcome using word and number benchmarks. MOVED TO 7.SP.5 (2010)

M03-S2C3-01 (2008) MOVED TO AZ.4.OA.3.1a (2010) Solve a variety of problems based on the multiplication principle of counting.a.Represent a variety of counting problems using arrays, charts, and systematic lists, e.g., tree diagram.

4.OA.2 (2010) Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (see glossary Table 2)

M04-S2C1-03 (2008) Use median, mode, and range to describe the distribution of a given data set.

M04-S3C1-01 (2008) Recognize, describe, create, extend, and find missing terms in a numerical sequence involving whole numbers using all four basic operations. MOVED TO 5.OA.3 (2010)

M03-S2C3-02 (2008) MOVED TO AZ.4.OA.3.1 (2010) Solve a variety of problems based on the multiplication principle of counting.

4.NBT.1 (2010) Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 70 = 10 by applying concepts of place value and division.

Key advances in the standards between grade levels

Fluency expectations and major within-grade dependencies

Connections among standards, clusters, or domains

Opportunities for In-Depth Focus Opportunities for Connecting Mathematical

Content and Mathematical Practices

Using the content frameworks with the standards to sketch out potential model instructional unit plans

Use the frameworks to support increased focus and coherence in instructional programs

Recognizing the shifts in the standards from grade to grade and using these shifts as grade level curricula are developed and as materials are purchased to align with the curricula

Frameworks are available on www.parcconline.org/parcc-content-frameworks

Frameworks are intended to be dynamic and responsive to evidence and on-going input

◦ In Summer 2012, once educators have used the frameworks, PARCC will collect feedback and refine frameworks as necessary

PARCC will develop additional model instructional tools and supports that build on the frameworks◦ Model Instructional Units◦ Educator Leader Cadres◦ Item specifications◦ Item and task prototypes 42

Implementation & Next Steps

How can we ensure that instruction supports the 2010 Mathematics Standards? What should effective instruction look like?

Looks Like

Sounds Like

Feels Like

Number off 1-8 Read assigned Mathematical Practice (MP) View video - Bungee Jump Record evidence of assigned MP (what you

see teachers/students doing and what you hear teachers/students saying) on your graphic organizer

Meet at numbered posters with Expert Group to discuss evidence

By Mathematical Practice Group Share

Return to original groupShare (round robin) evidence of your assigned Mathematical Practice

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“Not all tasks are created equal, and different tasks will provoke different levels and

kinds of student thinking.”

Stein, Smith, Henningsen, & Silver, 2000

“The level and kind of thinking in which students engage determines what they

will learn.”Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray,

Oliver, & Human, 1997

What are the essential features of mathematical tasks that engage students in the Mathematical Practices?

Do all students have the opportunity to engage in mathematical tasks thatpromote students’ attainment of the mathematical practices on a regular basis?

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Standards are only the foundation Successful implementation is key Implementation and buy-in is a long-

term process:1. Awareness (Familiarity) - 2011-20122. Knowledge - Understanding –

2011-2012 (Kindergarten must begin full implementation in 2011-2012)

3. Internalization and Incorporation – 2011-2013

4. Full Implementation at ALL grade levels (2013-2014)

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Implementation Challenges

Transitioning to the new standards and assessments at the classroom level

Transitioning the High School Competency Exam system

Significant Shift in Instructional Focus

Higher Education Engagement

Budgetary planning

Policy Challenges

Accountability

◦Break in Trend

College admissions/ placement

Use of NRT

Perceptions about what these assessments can do

Technical Challenges

• Transitioning to a computer-based assessment system

Communication

Challenges

• Student expectations

• Parent Engagement

• Multiple Stakeholders

• Common Message

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http://www.ade.gov Updated information, links, and resources for implementation and

transition to the 2010 standards and PARCC assessment.

http://www.achieve.org/ Achieve website.  Achieve is the project management partner for PARCC.

http://www.parcconline.org/ PARCC website.  PARCC is the assessment consortium that Arizona is part

of.  Arizona is a governing state within the consortium.

http://www.cehd.umn.edu/NCEO/ Here you will find the NCEO briefs and additional information related to

assessing our current AIMS-A students (1%). 

http://www.corestandards.org/ This site will give you background and additional information about the

standards.  Much of this same information can be found on the new Arizona Department of Education website.

http://www.ccsso.org/ Council of Chief State School Officers website. Excellent link to Hunt

Institute and CCSSO Common Core Implementation Video Series.

Purpose:Examine and understand structure of new standards and supporting documents

Explore elements of effective instruction and Model Content Frameworks

Consider implications for implementation of the new standards and impact on instruction

What’s running around in YOUR head right now?

Share your thoughts with us on a round post-it.