Katy Thomas, K-12 Instructional CoachCurriculum/Professional Learning

Kim Bemis, Teacher LeaderJoseph Sims Elementary

Terri Mills, Teacher LeaderDavid Reese Elementary

5th Grade MathematicsCommon Core Standards

Preparing Students for College and Career Readiness

2013

Welcome and Introductions

Introduce yourself to the group. Please tell us: Your name Your school site The number of years you have been teaching

How many years?How many years of collective teaching

experience are in the room right now?

Turn to the person next to you and explain how you made sense of the problem and how you solved it.

Compare your strategy to that of your partner.

NormsBe invested.

Collaborate with colleagues.

Avoid sidebar conversations.

Turn your cell phone to silent. Please step outside if you have an emergency and need

to text.

OverviewDay 1: Teachers will gain an understanding of

the relationships between CCSS math rationale, content standards, and Standards for Mathematical Practice.

Overview

Day 2: Teachers will become familiar with the components of “Go Math,” be able to use the program as a tool to teach CCSS, and understand how to design a CCSS math lesson.

Day 3: Teachers will take a look at assessment options, parents and CCSS-M, and continue with lesson design.

Today’s Outcomes

Build an understanding of:• Background and rationale of the

CCSS• Content standards• Standards for Mathematical Practice• Smarter Balanced assessments• Instructional shifts

Do You Have Additional Questions?

Engagement Strategy: Appointment Clock

9

Please make appointments for 12:00, 3:00, 6:00 and 9:00

Getting to Know the CCSS Mathematics Standards

“These standards are not intended to be new names for old ways of doing business. They are a case to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that these standards are not just promises to our children, but promises we intend to keep.”

NGA & CCSSO, 2010, pg. 5

Rationale for the Common Core

Meet with your 3:00 appointment to discuss your reactions to the video and

the quote.

One aspect of the video that resonated with me is _______.

I am wondering about _____.

Try to do these problems mentally.What mathematics do students need to know to understand what they are doing?

8

797

300200 8

31

3897

1010310102

4106

8

797

8

1107or

9 1097 + 3 + 35

45 States Have Adopted the CCSS-M

CA Adopts

August 2, 2010

Background and Rationale of the Common Core State Standards

• Were developed by states as a collaborative initiative

• Are informed by other top performing countries, so that all students are prepared to succeed in our global economy and society

Background and Rationale of the Common Core State Standards

• Are aligned with college and career expectations

• Are clear, understandable and consistent

• Include rigorous application of knowledge through high-order skills

A+ Countries United States

Mastery Learning

Spirals

Common Fractions taught in 3rd – 6th grades Common Fractions taught in 1st – forever!

17

A Topical Comparison: Coherence

A+ Countries United States

18

A Topical Comparison: Focus

Mastery Learning

Spirals

Focus on learning a few topics in depth Many topics per grade, revisited year after year

CCSS Mathematics K – 8Domain Progressions

Two Types of Standards

• Content Standards– Vary at each grade level– Grade span concept bands– Bolded, underlined standards specific to California

• Standards for Mathematical Practice (SMP)– Consistent K-8

Content Standards Structure K - 8Standards define what students should understand and be able to do.Clusters summarize groups of related standards. Note that standards from different clusters may be closely related, because mathematics is a connected subject.

Domains are larger groups of related standards. Standards from different domains may sometimes be closely related.

DomainDomain NotationNotation

StandardStandardCluster of StandardsCluster of Standards

Standard (CA Addition)

Standard (CA Addition)

CCSS Mathematics K – 8Domain Progressions

C

11 Clusters

11 Clusters

5 Domains

5 Domains

Grade

5Grade

5

Examining Content Standards

You will need your Grade Level Content Standards.

1. With your partner, examine the domains emphasized at your grade level.

2. Determine which clusters are included in each domain at your grade level.

3. Read the standards that make up each cluster.

4. What are the big differences at your grade level from our old standards to CCSS-M?

Focus and Coherence

Bill McCallum, One of three main authors of Mathematics CCSS

Focus• Spending more time on fewer-- essential --

concepts• Negating the issue of “a mile wide and an inch

deep”• Requiring a philosophical shift from content

coverage to content competency

4.NBT.5: Multiply a whole number up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or models.

Area Model Partial Product Distributive Property

Focus

500

1435

5 5

341

340100

1435

200 15

15200500

3401005 )35()405()1005(

500 + 200 + 15

715 715

715

Coherence• A systematic and logical progression

of mathematical elements• A K-12 following of skill and concept

development• A staircase to college and career

readiness, building on the best of previous state standards and evidence from international comparisons and domestic reports and recommendations

CoherenceDomains structured coherently K – 5 and 6 – 8

K - 2 3 - 5 6 - 8•Operations and Algebraic Thinking•Numbers and Operations in Base Ten•Measurement and Data•Geometry•Counting and Cardinality (K)

•Operations and Algebraic Thinking•Numbers and Operations in Base Ten•Measurement and Data•Geometry•Numbers and Operations - Fractions (3 – 5)

•Ratios and Proportional Relationships•The Number System•Expressions and Equations•Functions•Geometry•Statistics and Probability

Coherence: the curriculum has logical progressions from less sophisticated topics into more sophisticated ones. Coherence refers to how the standards are organized across grade levels. “Vertical Alignment”

2nd Grade: 3872

38 72

2

40 70

30 2

34

Subtraction is the “difference” between 2 numbers on the number line

“Benchmark numbers” are essential in developing number sense(develop the conceptual understanding for rounding numbers)

This is called an “open number line” because it is not drawn to scale and all numbers are not identified along the number line.

0 1 2 3

3rd Grade 4th Grade1863

5th Grade 6th Grade

5

23

6

1

3

2

0 1 2 0

6 6 6

5

11

5

6or18

5

2

5

2

5

2

3

1 0 13

2

1234

How many sixths are there in two-thirds?

42

12

5

3

2

11

Tracing Coherence

1. Meet with your 6:00 appointment.

2. Look at the standard overviews for your grade and the grade directly before and after you.

3. Trace the coherence for each domain.

4. Discuss the progression of skills across the three grade levels.

Of all of these changes, the one(s) I find most exciting/positive is/are _____.

The change(s) I am most concerned about is/are _____.

Discussion Points:

My experience has taught me …

Break

The Connection: Content to Mathematical Practice

The core is the Content Standards which we have examined.

The core is wrapped with the Eight Standards for Mathematical Practice.

Standards for Mathematical Practice1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critiques the reasoning

of others.4. Model with mathematics5. Use appropriate tools strategically.6. Attend to precision7. Look for and make sense of structure8. Look for and express regularity in repeated reasoning.

Stay and Stray with the Eight Standards for Mathematical Practice

• Number off 1-8 • Group one will investigate Practice 1, Group 2-

Practice 2…• Each group member should be prepared to explain

the Practice Standard.• Create a poster to represent your Practice

Standard.– Include 3-5 bullet points of detail– Create an illustration and provide an example

8 Standards of Mathematical Practice—What do they look like?

Domain: Numbers and Operations: FractionsContent Standard: Grade 4 NF 6Use decimal notation for fractions with denominators 10 or 100…

Content Standard: Grade 5 NF 3Interpret a fraction as division of the numerator by the denominator…form of fractions, mixed numbers, or decimal fractions…

Standards for Mathematical Practice Debrief

Meet with your 9:00 appointment to discuss the 8 Standards for Mathematical Practice

I saw evidence of SMP ____ in the classroom video when _______.

One thing I might have tried in the lesson was ______ to address SMP _______.

Classroom Implications of the 8 Standards for Mathematical Practice

• Conceptual and procedural approaches to classroom instruction

• Student centered classrooms • Multiple and varied opportunities for students

to grapple with, discuss, explain, verify, collaborate, and think to develop understanding of mathematical concepts.

• Mistakes are valued as learning opportunities.

Classroom Implications of the 8 Standards for Mathematical Practice

My experience has taught me

…

Lunch

Welcome Back! And now for dessert ….

A Move To Authentic Assessments

CCSS Transition Timeline: 2014-15Testing is slated to begin in 2014-15Smarter Balanced Assessment Consortium

Testing for grades 3-8, and 11Includes summative and optional interim

assessmentsPractice tests available online:

www.smarterbalanced.org/practice-test

Sample Assessment Questions from Smarter Balanced

Appointment

Meet with your 12:00 appointment to discuss the Smarter Balanced Assessments.

One Ah-Ha I have regarding the new assessments is _________.

One question I have regarding the new assessment is ______.

One implication for my teaching is ___.

Major Shifts

Content standardsContent

standards

AssessmentAssessment

Standards for Mathematical

Practice

Standards for Mathematical

Practice

InstructionInstruction

SHIFTS in Instruction… Ergo…

The Classroom Connection• Provide multiple representations• Review deliberately• Value and celebrate alternative responses• Focus on number sense and estimation• Encourage a language rich classroom• Embed math in contexts• Use formative assessments• Plan deliberately and with detail• Language rich classrooms

Looks Like/Sounds LikeGraffiti Wall

Shift Looks Like Sounds Like

Multiple Representations

Deliberate Review

Alternative Approaches

Number Sense/Estimation

Math in Contexts

Formative Assessments

Planning

Implications for Instruction

Given that our math instruction will look and sound different, what are implications for our instruction?

My experience has taught me

…

Content Standards + Standards for Mathematical Practice +

Instructional Shifts =Common Core-ification

The Common Core -ification Equation

Common Core -ification Takes Time!

• Time to familiarize yourself with new standards

• Time to plan• Time to implement• Time for increased student interaction• Time for different types of assessment

As I learn about the shifts in the Mathematics CCSS, what excites me most for my students is ____.

Content standardsContent

standards

AssessmentAssessment

Standards for Mathematical

Practice

Standards for Mathematical

Practice

InstructionInstruction

Interactive Activity:Tea Party

As I learn about the shifts in the Mathematics CCSS, what excites me most for my students is ____.

Helpful Resources• http://blogs.egusd.net/ccss/, Elk Grove Common Core Blog• Hunt Institute video series: Informative Videos about the Common Core• California Dept. of Education Common Core transition plans• SMARTER Balance Assessment Consortia, developer of CA's state assessment• Sample tasks on the Smarter Balanced guidelines (MARS tasks)• California Math Project CaCCSS-M Resources Home page• Illustrative Mathematics provides guidance and tools to support the Standards• Projects and programs supporting the Common Core State Standards• EdSource provides California with information on key education challenges

provides links to blogs and information regarding legislation and discussions going on surrounding Common Core.

• Inside Mathematics: classroom examples of Common Core teaching methods• Silicon Valley Mathematics Initiative, one of California's most innovative

assessment projects• http://www.cde.ca.gov/be/cc/cd/draftmathfwchapters.asp, Draft of the

California Math Framework• http://www.scoe.net/castandards/index.html, Sacramento County Office of

Education

Feedback to inform next steps…