1. 5th Grade Mathematics Common Core Standards
Preparing Students for College and Career Readiness
2013
5th Grade Mathematics Common Core Standards
Katy Thomas, K-12 Instructional Coach
Curriculum/Professional Learning
Kim Bemis, Teacher Leader
Joseph Sims Elementary
Terri Mills, Teacher Leader
David Reese Elementary

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

3. 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.

4. 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.

5. Overview
Day 1: Teachers will gain an understanding of the relationships between CCSS math rationale, content standards, and Standards for Mathematical Practice.

6. 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.

7. Today’s Outcomes Build an understanding of:
Background and rationale of the CCSS
Content standards
Standards for Mathematical Practice
Smarter Balanced assessments
Instructional shifts

8. Do You Have Additional Questions?

9. Engagement Strategy: Appointment Clock
Please make appointments for
12:00, 3:00, 6:00 and 9:00 

10. 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

11. Rationale for the Common Core

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

13. Try to do these problems mentally
Try to do these problems mentally. What mathematics do students need to know to understand what they are doing? 9 10

14. 45 States Have Adopted the CCSS-M
CA Adopts August 2, 2010

15. 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 15

16. 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 16

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

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

19. CCSS Mathematics K – 8
Domain Progressions

20. 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

21. 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
Cluster of Standards
Standard
(CA Addition)
Standard

22. CCSS Mathematics K – 8 Domain Progressions
Grade 5 C
5 Domains
11 Clusters

23. Examining Content Standards
You will need your Grade Level Content Standards.
With your partner, examine the domains
emphasized at your grade level.
Determine which clusters are
included in each domain at your grade level.
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?

24. Focus and Coherence
Bill McCallum, One of three main authors of Mathematics CCSS

25. 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

26. 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
500
200 15 15
200
715
715
500
715
Focus

27. 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

28. Coherence
Domains 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)
Numbers and Operations - Fractions (3 – 5)
Ratios and Proportional Relationships
The Number System
Expressions and Equations
Functions
Statistics and Probability

29. 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: 34
Subtraction is the “difference” between 2 numbers on the number line 38 72
“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.

30. How many sixths are there in two-thirds?
3rd Grade 4th Grade 1 2
5th Grade th Grade 1 1 2 3
How many sixths are there in two-thirds?

31. Tracing Coherence Meet with your 6:00 appointment.
Look at the standard overviews for your grade and the grade directly before and after you.
Trace the coherence for each domain.
Discuss the progression of skills across the three grade levels.

32. My experience has taught me …
Discussion Points:
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 _____.
My experience has taught me …

33. Break

34. 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.
Practice

35. Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critiques the reasoning of others.
Model with mathematics
Use appropriate tools strategically.
Attend to precision
Look for and make sense of structure
Look for and express regularity in repeated reasoning.

36. 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

37. 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…

38. 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 _______.

39. 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.
Conceptual vs. procedural approach to classroom instruction
Student centered classrooms vs. teacher centered

40. Classroom Implications of the 8 Standards for Mathematical Practice
My experience has taught me …

41. Lunch

42. Welcome Back! And now for dessert ….

43. A Move To Authentic Assessments

44. CCSS Transition Timeline: 2014-15
Testing is slated to begin in
Smarter Balanced Assessment Consortium
Testing for grades 3-8, and 11
Includes summative and optional interim assessments
Practice tests available online:

45. Sample Assessment Questions from Smarter Balanced45

46. 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 ___.

47. Standards for Mathematical Practice
Major Shifts
Standards for Mathematical Practice
Content standards
Instruction
Assessment

48. SHIFTS in Instruction… Ergo…

49. 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

50. Looks Like/Sounds Like Graffiti Wall
Shift
Looks Like
Sounds Like
Multiple Representations
Deliberate Review
Alternative Approaches
Number Sense/Estimation
Math in Contexts
Formative Assessments
Planning

51. Implications for Instruction
Given that our math instruction will look and sound different, what are implications for our instruction?
My experience has taught me …

52. The Common Core -ification Equation
Content Standards + Standards for Mathematical Practice + Instructional Shifts = Common Core-ification

53. 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

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

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

56. Helpful Resources
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
Draft of the California Math Framework
Sacramento County Office of Education

57. Feedback to inform next steps…