3rd Grade Mathematics Common Core Standards Preparing Students for College and Career Readiness 2013 Steve Kolb, K-12 Instructional Coach Curriculum/Professional Learning Pat Gibson, Teacher Leader Foulks Ranch Elementary Karen Torres, Teacher Leader Prairie Elementary Presented by:

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.

Norms Be 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.

Overview Day 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     910

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 National Governors Association Council of Chief State School Officers

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?

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+ CountriesUnited States 17 A Topical Comparison: Focus Mastery Learning Spirals Focus on learning a few topics in depth Many topics per grade, revisited year after year

A+ CountriesUnited States Mastery Learning Spirals Common Fractions taught in 3 rd – 6 th grades Common Fractions taught in 1 st – forever! 18 A Topical Comparison: Coherence

CCSS Mathematics K – 8 Domain Progressions C 11 Clusters 5 Domains Grade 3 935

Two Types of Standards Content Standards – Vary at each grade level – Bolded, underlined standards specific to California Standards for Mathematical Practice (SMP) – Consistent K-8

Content Standards Structure K - 8 Standards 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. Domain Notation Standard Cluster of Standards Standard (CA Addition) Standard (CA Addition)

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

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

Coherence Domains structured coherently K – 5 and 6 – 8 K 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” 2 nd Grade: 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.

rd Grade4 th Grade 5th Grade 6th Grade How many sixths are there in two-thirds?

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 _____. Tracing Coherence: 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 Practice 1.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 mathematics 5.Use appropriate tools strategically. 6.Attend to precision 7.Look for and make sense of structure 8.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

What is 2.4? Write a few math problems/tasks that result in an answer of 2.4. Is 2.4 the same as 2 remainder 4? Why or why not?

8 Standards of Mathematical Practice—What do they look like? Domain: Numbers and Operations: Fractions Content Standard: Grade 4 NF 6 Use decimal notation for fractions with denominators 10 or 100… Content Standard: Grade 5 NF 3 Interpret 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: Testing is slated to begin in Smarter Balanced Assessment Consortium Testing for grades 3-8, and 11 Includes summative and optional interim assessments

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 ___. 115

Major Shifts Content standards Assessment Standards for Mathematical Practice Instruction

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

Looks Like/Sounds Like Graffiti Wall ShiftLooks LikeSounds 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 … 200

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

Common Core -ification Takes Time ! My experience has taught me … Tips and Traps

As I learn about the shifts in the Mathematics CCSS, what excites me most for my students is ____. Content standards Assessment Standards for Mathematical Practice Instruction

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

Helpful Resources Elk Grove Common Core Blog Hunt Institute video series: Informative Videos about the Common CoreInformative Videos about the Common Core California Dept. of Education Common Core transition plansCommon Core transition plans SMARTER Balance Assessment Consortia, developer of CA's state assessment SMARTER Balance Assessment Consortia Sample tasks on the Smarter Balanced guidelines (MARS tasks)the Smarter Balanced guidelines (MARS tasks) California Math Project CaCCSS-M Resources Home page Illustrative Mathematics provides guidance and tools to support the Standards Illustrative Mathematics 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. EdSource provides California with information on key education challenges Inside Mathematics: classroom examples of Common Core teaching methods Inside Mathematics Silicon Valley Mathematics Initiative, one of California's most innovative assessment projects Silicon Valley Mathematics Initiative Draft of the California Math Framework Sacramento County Office of Education

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