02.24.12 Transitioning to the Common Core Trinity County Office of Education August 15, 2012 Mathematics

02.2

4.12

Transitioning to the Common Core Trinity County Office of Education

August 15, 2012

Mathematics

Agenda•

Welcome and Agenda Review•W

arm-Up Activity•I

ntroduction - CCSS•C

CSS Math – Standards Design•C

CSS Math – Practice and Instruction•C

CSS Math – Materials and Alignment•A

ssessment •P

lanning for Implementation2

Binder Resources•C

ISC Math Powerpoint•S

tandards for Mathematical Practice •F

acilitating Mathematical Thinking with Effective Questions •Q

uestions for Planning and Observation•S

BAC Powerpoint•S

ample SBAC Assessment Items•A

rticle: “Teaching in Grades 3 and 4: How is each Common Core State Standard different from each old objective?”

•Article: “10 Practical Tips for Making Fractions Come Alive and Make Sense”

•California Common Core State Standards – Math 3

Handouts•S

tandards for Mathematical Practice (laminated)•F

acilitating Mathematical Thinking with Effective Questions (laminated)

•Activity Worksheets: Table Pattern Task, Grade Level Tasks, Next Steps

•CCSS Standards Implementation Worksheet

4

English Learners and the

Common Core State Standards• The toolkit is an introduction and guide to initial

implementation.• Additional intentional support for English

learners is critical.• Work grounded in the revised English Language

Development (ELD) standards will be necessary.

5

KWL ChartWhat I already KNOW about the Common Core State Standards

What I WOULD like to learn about the Common Core State Standards

What I LEARNED about the Common Core State Standards

2011 © CA County Superintendents Educational Services Association

6

States that Adopted

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7

Why?T

o ensure that our students are…•m

eeting college and career expectations (Text Complexity needs to be increased K-12);

•provided a vision of what it means to be an academically literate person in the twenty-first century;

•prepared to succeed in our global economy and society; and

•provided with rigorous content and applications of higher knowledge through higher order thinking skills. 2011 © CA County Superintendents Educational Services Association8

Benefits•I

nternationally benchmarked•E

vidence and research-based•E

xpectations clear to students, parents, teachers, and the general public

•Consistent expectations for all

2011 © CA County Superintendents Educational Services Association9

ELA

•College and Career Readiness Anchor Standards

Mathematics

•Standards for Mathematical Practice

Heart and Soul


Lexile Framework © for Reading Study Summary of

Text Lexile Measures

600

800

1000

1400

1600

1200

Text

Lex

ile M

easu

re (L

)

HighSchool

Literature

CollegeLiterature

HighSchool

Textbooks

CollegeTextbooks

Military PersonalUse

Entry-LevelOccupations

SAT 1,ACT,AP*

* Source of National Test Data: MetaMetrics

Interquartile Ranges Shown (25% - 75%)

11

5th Grade

Collaborative Conversations•E

ngage effectively in collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners, building on others’ ideas and expressing one’s own clearly.

•Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.

•Follow agreed-upon rules for discussions and carry out assigned roles.

•Pose and respond to specific questions by making comments that contribute to the discussion and elaborate on the remarks of others.

•Review the key ideas expressed and draw conclusions in light of information and knowledge gained from discussions.


Integrating Media SourcesR

eading Standards for Informational Text, Grade 67

. Integrate information presented in different media or formats (e.g., visually, quantitatively) as well as in words to develop a coherent understanding of a topic or issue.

Writing Standards, Grade 6

6. Use technology, including the Internet, to produce and publish writing as well as to interact and collaborate with others; demonstrate sufficient command of keyboarding skills to type a minimum of three pages in a single sitting.


Standards for

Mathematical Practice“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.”

National Governors Association Center for Best Practices and Council of Chief State School Officers (2010)Common Core State Standards for Mathematics

14

Underlying FrameworksNational Council of Teachers of Mathematics

Five Process Standards

•Problem Solving

•Reasoning and Proof

•Communication

•Connections

•Representations

National Council of Teachers of Mathematics (2000)Principles and Standards for School Mathematics

15

Underlying FrameworksStrands of Mathematical Proficiency

National Research Council (2001)Adding It Up

Strategic Competence

Adaptive Reasoning

Conceptual Understanding Productive

Disposition

Procedural Fluency

16

Part 1: Standards for

Mathematical Practice1. Make sense of problems and persevere in

solving them…start by explaining the meaning of a problem and looking for entry points to its solution

2. Reason abstractly and quantitatively…make sense of quantities and their relationships to problem situations

3. Construct viable arguments and critique the reasoning of others…understand and use stated assumptions, definitions, and previously established results in constructing arguments

4. Model with mathematics…can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace


Part 2: Standards for

Mathematical Practice5. Use appropriate tools strategically

…consider the available tools when solving a mathematical problem

6. Attend to precision…communicate precisely using clear definitions and calculate accurately and efficiently

7. Look for and make use of structure…look closely to discern a pattern or structure

8. Look for and express regularity in repeated reasoning…notice if calculations are repeated, and look for both general methods and for shortcuts


Standards for

Mathematical PracticeLocate the CCSS for Mathematics and read the first three words for each mathematical practice and notice the similarities.

What do they begin with?

Mathematically proficient students…Briars & Mitchell (2010)

Getting Started with the Common Core State Standards

19

Standards for

Mathematical Practice•L

ocate and read the handout, Standards for Mathematical Practice.

•Discuss the importance of the verbs in the practices and how they define the habits of mind demonstrated by a mathematically proficient student.

20

Standards for

Mathematical PracticeThe Eight Standards for Mathematical Practice place an emphasis on student demonstrations of learning that describe the thinking processes, habits of mind, and dispositions that students need to develop.

adapted from Briars & Mitchell (2010)Getting Started with the Common Core State Standards

21

Domains Distribution (K-8)

Findell & Foughty (2011)College and Career-Readiness through the Common Core State Standards for Mathematics

22

Focusing Attention Within

Number and Operations

Briars & Mitchell (2010)Getting Started with the Common Core State Standards

Operations and Algebraic Thinking

Operations and Algebraic Thinking

Number and Operations - Base Ten

Number and Operations - Base Ten

Number and Operations -

Fractions

Number and Operations -

Fractions

Expressions and Equations

Expressions and Equations

The NumberSystem

The NumberSystem

AlgebraAlgebra

K-5 6-8 High School

23

California Grade 8 OptionsG

oal for 8th grade students is Algebra 1.•T

wo sets of standards for 8th grade– Standards for Algebra 1 (CA addition to the CCSS)• 8th grade Common Core Standards for Mathematics

– 8th grade Common Core• Finalize preparation for students in high school.


Mathematics Standards

for High SchoolArranged by conceptual categories (not by course):

•Number and Quantity (p. 49)•Algebra (p. 52)•Functions (p. 56)•Modeling (p. 60)•Geometry (p. 62)•Statistics and Probability (p. 67)

adapted from Foster (2011)Assessment for Learning

25

High School

Two Mathematics Pathways

TRADITIONAL Pathway (Typical in U.S.)

2 Algebra courses, 1 Geometry course, with Probability and

Statistics interwoven

INTEGRATED Pathway(Typical outside of U.S.)

3 courses that attend to Algebra, Geometry, and Probability and

Statistics each year

HS Algebra IHS Algebra I Mathematics IMathematics I

GeometryGeometry Mathematics IIMathematics II

Algebra IIAlgebra II Mathematics IIIMathematics III

Courses in higher level mathematics: Precalculus, Calculus*, Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or courses designed for career

technical programs of study.

Courses in higher level mathematics: Precalculus, Calculus*, Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or courses designed for career

technical programs of study.

adapted from 2011 © CA County Superintendents Educational Services Association26

Getting to Calculus Sooner:

Two Compacted Pathways•T

raditional Compacted Pathway: complete content of 7th, 8th, and HS Algebra I in grades 7 (Compacted 7th Grade) and 8 (8th Grade Algebra I) enabling them to finish Algebra II by the end of the sophomore year.

•Integrated Compacted Pathway: complete content of 7th, 8th, and Mathematics I in grades 7 (Compacted 7th Grade) and 8 (8th Grade Mathematics I), enabling them to complete Mathematics III by the end of the sophomore year

Both prepare students for Precalculus in their junior year and Calculus in their senior year.27

Format of the Overview

Domains:Overarching

ideas that connect topics

across the grades

Clusters:Illustrate the

progression of increasing

complexity from grade to grade

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. 28

Format of the Standards

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

29

Format of the Standards

California’s 15% Addition

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

California’s 15% Addition

30

Assessment: What We Know•A

ssessments will begin in 2014-15.•C

alifornia is a governing state in the SMARTER Balanced Assessment Consortium.

•Assessments will include:– Computer Adaptive Assessments

(interim & summative)– Performance Assessments (interim & summative)

• Selected Response• Constructed Response• Extended Performance Assessments31

Common Core State Standards

Implementation Considerations•A

ll Teachers – Scaffold comprehension of increasingly complex texts– Integrate media sources into instructional activities– Support/monitor informal talk

•ELA Teachers – Teach more informational text– Teach how a wide variety of forms fall into three overarching modes of

writing: Argument, Expository, and Narrative•S

cience and History Teachers – Teach Reading and Writing skills in their content

areas explicitly•M

athematics Teachers – Teach the habits of mind that students need to develop a deep, flexible,

and enduring understanding of mathematics32

Reflection•L

ocate the KWL chart you began earlier in the training.

•Complete the third column.

•Discuss with a partner.

33

Toolkit Modules•M

odule 1: Overview (3 hours)•M

odule 2: Content and Curriculum (90 minutes each)– ELA, K-12

– Additional Mini-Modules (60 minutes): Informational Text; Writing; Text Complexity; Collaboration, Research, and Use of Media

– Mathematics, K-8 – Mathematics, 6-12

•Module 3: Instruction (3 hours each)– ELA and Mathematics, K-5

– ELA only: Additional Mini-Modules (60 minutes): Informational Text; Writing; Text Complexity; Collaboration, Research, and Use of Media

– ELA, 6-12 – Mathematics, 6-12

•Module 4: Instructional Materials (3 hours each)– ELA and Mathematics, K-5– ELA, 6-12 (3 hours)– Mathematics, 6-12

34

Effective Instruction“A long line of students has established that the single most important school influence on student learning is the quality of the teacher.”

as presented by Linda Darling-Hammond (2007)

How would you describe a classroom where effective instruction and learning is

taking place?

35

California Standards

for the Teaching Profession •E

ngaging and supporting all students– Connect to students’ prior knowledge– Use a variety of instructional strategies– Promote autonomy, interaction, and choice– Engage students in critical thinking/problem solving– Engage students in reflecting on their learning

•Understanding and organizing content– Organize curriculum to support understanding– Interrelate ideas and information36

California Standards

for the Teaching Profession •P

lanning instruction– Establish clear goals for student learning– Design short- and long-term plans– Modify plans according to student needs

•Assessing student learning– Collect and use multiple sources of information– Use results to guide instruction– Involve students in assessing their own learning

37

Learning Pyramid

38adapted from Ntl Institute for Applied Behavioral Science (n.d.)

ActiveLearning

PassiveLearning

Rigor/Relevance Framework®

Inte

rnat

iona

l Cen

ter f

or L

eade

rshi

p in

Edu

catio

n (n

.d.)

39

3

Apply knowledge across

disciplines

4

Apply to real-world predictable

situation

5

Apply to real-world

unpredictable situation

Application3

Analysis4

Evaluation 6

DAdaptation

Quadrant D: Adaptation

Inte

rnat

iona

l Cen

ter f

or L

eade

rshi

p in

Edu

catio

n (n

.d.)

Synthesis 5

Students think in complex ways and

apply acquired knowledge

and skills, even when confronted with perplexing

unknowns,to find creative

solutions and take action that further

develops their skills and

knowledge.

40

Quadrant DV

erbse

valuatev

alidatej

ustifyr

ater

efereei

nferr

ankd

ramatizea

rguec

onclude

Products

evaluation

newspaper

estimation

trial

editorial

radio program

Play

collage

machine

adaptation

poem

debate

invention

41

1

Knowledge in one discipline

2

Apply Knowledge in one discipline

Application3

Analysis4

Evaluation 6

CAssimilation

Quadrant C: Assimilation

Inte

rnat

iona

l Cen

ter f

or L

eade

rshi

p in

Edu

catio

n (n

.d.)

Synthesis 5 Students extend and refine their

knowledge so that they can use it

automatically and routinely to analyze and solve problems

and create solutions.

42

Quadrant CV

erbss

equencea

nnotatee

xaminer

eportc

riticizep

araphrasec

alculatee

xpands

ummarizec

lassifyd

iagram

Products

essay

abstract

blueprint

inventory

report

plan

chart

questionnaire

classification

diagram

discussion

collection

annotation

43

3

Apply knowledge across

disciplines

4

Apply to real-world predictable

situation

5

Apply to real-world

unpredictable situation

Awareness 1

Comprehension 2

BApplication

Quadrant B: Application

Inte

rnat

iona

l Cen

ter f

or L

eade

rshi

p in

Edu

catio

n (n

.d.)

Application 3

Students use acquired

knowledge to solve problems,

design solutions, and complete work.

44

Quadrant BV

erbsa

pplys

equenced

emonstratei

nterviewc

onstructs

olvec

alculated

ramatizei

nterpreti

llustrate

Products

scrapbook

summary

interpretation

collection

annotation

explanation

solution

demonstration

outline

45

1

Knowledge in one discipline

2

Apply knowledge in

discipline

AAcquisition

Quadrant A: Acquisition

Inte

rnat

iona

l Cen

ter f

or L

eade

rshi

p in

Edu

catio

n (n

.d.)

Students gather and

store bits of knowledge/information and are

expected to remember or

understand this acquired

knowledge.

Awareness 1

Comprehension 2

Application 3

46

Quadrant AV

erbsn

amel

abeld

efines

electi

dentifyl

istm

emorizer

ecitel

ocater

ecord

Products

definition

worksheet

list

quiz

test

workbook

true-false

reproduction

recitation47

Rigor/Relevance Framework®

Teacher/Student Roles

48

StudentThink

CC

BBAA

DDStudentThink & Work

TeacherWork

StudentWork

RELEVANCE

Low High

RIGOR Low

High

Inte

rnat

iona

l Cen

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eade

rshi

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The Gradual Release of Responsibility

Structure for Successful Instruction

TEACHER RESPONSIBILITY

Focus Lesson

Guided Instruction

“I do it”

“We do it”

“You do it together”Collaborative

Independent “You do it alone”

Fisher & Frey (2008)Better Learning Through Structured Teaching

STUDENT RESPONSIBILITY

49

The “Sudden” Release of Responsibility


Focus Lesson “I do it”



50


The “Good Enough” Release of Responsibility


Focus Lesson

Guided Instruction

“I do it”

“We do it”



51


A Model for Student Success The Gradual Release of Responsibility


Focus Lesson

Guided Instruction

“I do it”

“We do it”

“You do it together”Collaborative



52


CCSS for Mathematics•P

rovide focus and coherence•O

rganized around mathematical principles•S

tress conceptual understanding of key ideas as well as skills

•Prepare students for college and career

What are the implications for instruction?53

“…teachers themselves need to understand the standards. Teachers must have deep and appropriate content knowledge to reach that understanding; they must be adaptable, with enough mastery to teach students with a range of abilities; and they must have the ability to inspire at least some of their students to the highest levels of mathematical achievement.”

Ewing (n.d.) The Common Core Math Standards

“…teachers themselves need to understand the standards. Teachers must have deep and appropriate content knowledge to reach that understanding; they must be adaptable, with enough mastery to teach students with a range of abilities; and they must have the ability to inspire at least some of their students to the highest levels of mathematical achievement.”

Ewing (n.d.) The Common Core Math Standards

Influence on Student Learning

54

Strands of Math Proficiency

•Adaptive Reasoning

•Strategic Competence

•Conceptual Understanding

•Procedural Fluency

•Productive Disposition

Strands of Math Proficiency• Adaptive Reasoning• Strategic Competence• Conceptual Understanding• Procedural Fluency• Productive Disposition

Standards for Mathematical Practice

Seek to Develop in Students N

CTM Process Standards•P

roblem Solving•R

easoning and Proof•C

ommunication•R

epresentation•C

onnections55

Standards for

Mathematical Practice

56

adapted from McCallum (2011)Standards for Mathematical Practice

Overarching habits of mind of a productive mathematical thinker

Reasoning and explaining

Modeling and using tools

Seeing structure and generalizing

1. M

ake

sens

e of

pro

blem

and

per

seve

re

in s

olvin

g th

em.

6. A

ttend

to p

recis

ion.

1. M

ake

sens

e of

pro

blem

and

per

seve

re

in s

olvin

g th

em.

6. A

ttend

to p

recis

ion.

2. Reason abstractly and quantitatively.3. Construct viable arguments and

critique the reasoning of others.

2. Reason abstractly and quantitatively.3. Construct viable arguments and

critique the reasoning of others.

4. Model with mathematics.5. Use appropriate tools strategically.4. Model with mathematics.5. Use appropriate tools strategically.

7. Look for and make use of structure.8. Look for and express regularity in

repeated reasoning

7. Look for and make use of structure.8. Look for and express regularity in

repeated reasoning

Create a Frayer Model PosterEssential Characteristics

Teaching Methods

Examples of What Students Will Be Doing

Non-examples of What

Students Will Be Doing

Standards for Mathematical

Practice

• Work with a table group on one of the Standards for Mathematical Practice.

• Create a Frayer Model Poster connecting student actions and teacher actions.

57

Frayer Model Poster Carousel•D

isplay your poster.•E

xamine the poster to the right of your group’s poster.

•Look for evidence of the “processes and proficiencies.”

•Rotate to the right and continue until you have finished examining all posters.

•Be ready to share out any questions or “ahas.”58

Research-Informed

Best Practices•A

ccess prior knowledge and address students’ misconceptions

•Provide routines and structures that help struggling learners organize critical content

•Engage students with challenging tasks that involve active meaning making

•Use formative assessment and provide timely, specific feedback

•Provide on-going cumulative distributed practice

•Promote learners’ beliefs about their own intelligence (growth mindset vs. fixed mindset)

adapted from Briars (2011) Intensified Algebra

59

• Access prior knowledge and address students’ misconceptions

• Provide routines and structures that help struggling learners organize critical content

• Engage students with challenging tasks that involve active meaning making

• Use formative assessment and provide timely, specific feedback

• Provide on-going cumulative distributed practice• Promote learners’ beliefs about their own

intelligence (growth mindset vs. fixed mindset)adapted from Briars (2011)

Intensified Algebra

Cognitively-Guided

Instruction ProcessStart the study of a new

concept with a rich problem or hypothesis

Start the study of a new concept with a rich problem

or hypothesis

Question, justify, and critique thinking


Use your understanding of student thinking to guide

further instruction

Use your understanding of student thinking to guide

further instruction

Communicate multiple representations of

solutions.

Communicate multiple representations of

solutions.

Invite your students to engage in the problemInvite your students to engage in the problem

60

Gendron (2011)So, What’s New in the Common Core State Standards?

Table Pattern TaskA catering manager wants to know how many people can sit around the tables he uses for parties. The number of people who can sit around the tables will depend on the shape of the table and the number that are put together. How can the manager determine how many people can sit around any number of tables of any shape?

61

Table Pattern TaskFind an algebraic rule to describe the relationship between the number of tables, n, and the number of people, p, for tables with any number of sides, s. Explain your thinking.

62

Debrief the CGI ProcessStart the study of a new

concept with a rich problem or hypothesis

Start the study of a new concept with a rich

problem or hypothesis



Use your understanding of student thinking to

guide further instruction

Use your understanding of student thinking to

guide further instruction

Communicate multiple representations of solutions.

Communicate multiple representations of solutions.

Invite your students to engage in the problemInvite your students to engage in the problem

Table Pattern

Task

Asked questions to unpack

the problem

Asked questions about strategies and relationships

Asked questions to check for understanding during and after the task

Use results to plan

next steps

63

Gendron (2011)So, What’s New in the Common Core State Standards?

Table Pattern Task and Standards for

Mathematical PracticeStandard for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.•How did the teacher facilitate the task to support Standard 3?•As a student, what did you do to demonstrate proficiency of Standard 3?•What other Standards for Mathematical Practice were addressed by this task?

64

How might we vary the task for different grade levels?

Using the CCSS for Mathematics handout, work with grade-level partners to provide some examples.

Modifying the

Table Pattern Task

65

Students’ Beliefs

About Their Intelligence•F

ixed Mindset– Avoid learning situations if they might make mistakes– Try to hide, rather than fix, mistakes or deficiencies

•Growth Mindset– Work to correct mistakes and deficiencies– View effort as positive; increase effort when

challenged

66

Briars (2011)Implementing the More Challenging Aspects of Common Core State Standards

Students Can

Develop Growth Mindsets•E

xplicit instruction about the brain, its function, and that intellectual development is the result of effort and learning has increased students’ achievement in middle school mathematics.

•Teacher praise influences mindsets:– Fixed: Praise refers to intelligence– Growth: Praise refers to effort,

engagement, perseverance67

Briars (2011)Implementing the More Challenging Aspects of Common Core State Standards

Expectancy: Can I Do This?•A

ttribute successes to high effort or effective strategy

•Attribute failures to low effort or ineffective strategy

•Avoid saying, “You’re smart”

•Discuss the different views of intelligence

•Be explicit about what sorts of effort lead to success

•Design instruction to support successful learning experiences

Dweck (2006)Presentation on Intelligence Theory

Dweck (2006)Presentation on Intelligence Theory

68

Value: Is This Important?

69

“How many of us have used the “it’s on the test” to emphasize the importance of a skill or assignment?”

Value: Is This Important?•C

onnect classroom activities to personal short-term goals.

•Connect classroom activities to personal long-term goals.

•Place classroom activities in personally meaningful contexts.

70

Growth Mindset and

Productive Disposition“Just as students must develop a productive disposition toward’s mathematics such that they believe that mathematics makes sense and that they can figure it out, so too must teachers develop a similar productive disposition.”


“Just as students must develop a productive disposition towards mathematics such that they believe that mathematics makes sense and that they can figure it out, so too must teachers develop a similar productive disposition.”


71

Best Practices for the

Common Core•E

ngage students with challenging tasks that involve active meaning making– Quadrant B, C, and D learning opportunities– Cognitively-Guided Instruction with a focus on the

Standards for Mathematical Practice– Questioning to facilitate thinking and learning

•Promote learners’ beliefs about their own intelligence (growth mindset vs. fixed mindset)– Design instruction to support student success– Explicitly reinforce high effort and students’ use of

effective strategies– Repackage content using real-world connections,

puzzles, and games– Model a productive disposition72

Reflection• Think about what you learned today.• Decide on one thing you will do differently

to start transitioning to the Common Core State Standards.• Share your ideas with a partner.

73

Effective Instruction“A long line of students has established that the single most important school influence on student learning is the quality of the teacher.”

as presented by Linda Darling-Hammond (2007)

How would you describe a classroom where effective instruction and learning is

taking place?

74

Update Supplemental

Instructional MaterialsRecent legislation (SB 140) authorizes the CDE to approve supplemental instructional materials to provide a bridge between the common core academic content standards and the instructional materials currently being used.

75

Step 1: Select a Standard

Concept 1997 Standard CCSS

Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle)

Grade 2 Kindergarten

Introduction of fractions as numbers Grade 2 Grade 3

Add and subtract simple fractions Grade 3 Grade 4

Introduction of Integers Grade 4 Grade 6

Dividing fractions by fractions Grade 5 Grade 6

adapted from © 2001 California County Superintendents Educational Services Associations, Mathematics General

Examples of Grade Level Shifts

76

Step 1: Select a Standard

Model•C

oncept: Add and Subtract Fractions•D

omain: Number and Operations – Fractions 4.NF– Standard: 3b. Decompose a fraction into a sum of

fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples:

3/8 = 1/8 + 1/8 + 1/83/8 = 1/8 + 2/82 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/877

Step 2: Align the Standard

Model•L

ook for instruction and resources that align to the standard.

•Determine the resources with which you will start.

•Analyze the instruction, identify the alignment in the instructional design, rigor, and/or focus of the materials.

78

Step 3: Identify Next Steps•W

ith your group, identify the next steps necessary to analyze the alignment between the CCSS and current instructional materials.

•Record the next steps on chart paper.

•Be prepared to share with the whole group.

79

Part 1: Connecting to Standards for Mathematical Practice

Instructional Materials•W

ith your table group, locate and read the Questions for Planning and Observation handout.

•Discuss how these questions might support the effective implementation of these practices and what, if any, additional questions you might add.

80


Instructional Materials•F

ollow along as the instructor models the Task Analysis Templates and Samples.

•With a partner, look through your instructional materials and locate places that could be used to support the effective implementation of the Standards for Mathematical Practice. Consider:– Lesson Sections– Sample Problems/Tasks– Assessment Items– Other Ancillary Materials81


Instructional Materials•U

sing the Task Analysis Template, “Finding and Enhancing Tasks Already Aligned to CCSS Standards for Mathematical Practice in the Text,” find a specific problem/task that reflects a CCSS mathematical practice.

•Describe the expected student behaviors.


82


Instructional Materials•W

ith a partner, identify a “routine” problem from a lesson in your instructional materials using the Task/Practice Sample, “Extending a Textbook Problem to Access a Mathematical Practice.”

•Using the Standards for Mathematical Practice, describe how you might extend the problem to better access a SPECIFIC practice.

83


Instructional Materials•U

sing the same problem, discuss how you would extend it again to access a DIFFERENT Standards for Mathematical Practice.

•Be ready to share out both problems.

84

Reflection•H

ow might the information from this activity change the way you utilize instructional materials to effectively incorporate Standards for Mathematical Practice in your instruction?

•Which problems/tasks will you choose to implement and why?

•Which Standards for Mathematical Practice are addressed in these tasks? 85

Alignment ProcessAligning Current Instructional Materials to the Common Core State Standards

1.Select the Standard2.Align the Standard3.Identify Next Steps

86

Step 1: Select a Standard•S

tart with– Standards that are completely new to a grade– Standards that are significantly different in rigor

or complexity

•Decide on a comprehensive approach– Review one of these standards from each strand OR – Review one whole strand at a time

87

Step 2: Aligning the Standard to Your

Current Instructional Materials•L

ook for instructional materials and resources in your current adoption that align to the standard.

•Brainstorm which materials and resources you will start with.

•“Dig in” to identify alignment or gaps in the instructional design, rigor, and/or focus of the materials.

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Step 3: Identify Next Steps•W

ith your group, identify the next steps necessary to analyze the alignment between the CCSS and current instructional materials.

•Record the next steps on chart paper.


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Reflect, Discuss, Share•E

xamine standards that will clearly require collaboration.

•Develop ideas for ways in which teachers will work together across content areas.

•Consider ways that collaboration can be sustained in planning, teaching, and assessment of student work.

•Share out main ideas and where to start.

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Connecting to Current PracticeT

hink-Pair-Share•H

ow do the new standards correspond to what you already include in your curriculum?

•Think back to the last informational text passage, writing, or speaking assignment you gave your students. What might you do differently next time to help students transition to the CCSS?

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Next Steps• What can be done as an individual teacher,

a department, a site, and/or a district to support the transition to teaching the CCSS?

• Choose a perspective and write down three ideas:1.

2.

3. 92

For Further Investigation•C

alifornia’s Common Core State Standardshttp://www.cde.ca.gov/ci/cc/

•Common Core State Standards Initiativehttp://www.corestandards.org

•Illustrativemathematics.org

•commoncoretools.me

•map.mathshell.org

•ime.math.arizona.edu/progressions

•www.smarterbalanced.org•www.dpi.state.nc.us•www.corestandards.org

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http://www.cde.ca.gov/ci/cc/

http://www.corestandards.org/

http://www.smarterbalanced.org/























http://www.dpi.state.nc.us/








































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Math Standards Summary (key concepts/skills) of Standard:

1

2

3

4

5

6

7

8

9

10

Documents

02.24.12 Transitioning to the Common Core Trinity County Office of Education August 15, 2012 Mathematics