1. 3rd Grade Mathematics Common Core Standards
Preparing Students for College and Career Readiness
2013
3rd Grade Mathematics Common Core Standards
Presented by:
Steve Kolb, K-12 Instructional Coach
Curriculum/Professional Learning
Pat Gibson, Teacher Leader
Foulks Ranch Elementary
Karen Torres, Teacher Leader
Prairie 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.
Establish partner A/B for rest of day

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 
910

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
National Governors Association
Council of Chief State School Officers

11. Rationale for the Common Core
Council of Greater City Schools video – click on video camera to play 3 minute video. elaborate on significance of dimmer switch
Dimmer switch

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?
CCSS-M isn’t so much about getting a right answer, it’s about knowing the best way to get to an answer and being able to determine if that answer makes sense.
200 x 300:
Why do you multiply the leading digit and add the zeros?
What are the zeros? (factors of 10 or powers of 10)
This understanding leads us to scientific notation and exponent rules.
1- 3/8
What is one?
What happens when you take away a piece of one?
What tells you how many total pieces there are?
Reference benchmark numbers and decomposition
7 x 9 7/8:
Can be decomposed 2 ways 7(9+7/8) and 7(10 - 1/8)
It’s almost 70. Is it bigger or smaller than 70? How much smaller than 70 is it? 9 10

14. 45 States Have Adopted the CCSS-M
CA Adopts August 2, 2010
CA adopted the revised CCSS on Aug. 2, 2010.
Hold outs-Texas, Alaska, Nebraska, Virginia
Minnesota only adopted ELA, not math

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
Clarify the voluntary aspect to avoid the idea of “federal” standards. (1 min.)
What top performing countries? Singapore, Finland, Japan 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
Clarify the voluntary aspect to avoid the idea of “federal” standards. (1 min.)
What top performing countries? Singapore, Finland 16

17. 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
Why in the CC do we see an adjustment to where the standards are taught? Why do we see fewer standards and more attention to the ones we teach? Let’s take a look at the countries that are leading in math. They have been identified as the A+ countries. The content standards were developed based on a wide variety of research and international comparisons
The six leading (A+) math performance countries were identified by massive testing in 1995 and verified in 1999 (Singapore, Korea, Japan, Hong Kong, Belgium, Czech Republic). These charts compare the math topics in the A+ countries to the math topics covered in the U.S.
So, we are now teaching fewer standards and going deeper with them.
Spirals

18. A Topical Comparison: Coherence
A+ Countries United States
Common Fractions taught in 3rd – 6th grades
Common Fractions taught in 1st – forever!
Mastery Learning
Why in the CC do we see an adjustment to where topics are taught? Why do we see fewer standards and more attention to the ones we teach? Let’s take a look at the countries that are leading in math. They have been identified as the A+ countries. The content standards were developed based on a wide variety of research and international comparisons
The six leading (A+) math performance countries were identified by massive testing in 1995 and verified in 1999 (Singapore, Korea, Japan, Hong Kong, Belgium, Czech Republic). These charts compare the math topics in the A+ countries to the math topics covered in the U.S.
So, we are now teaching fewer standards and going deeper with them.
Spirals

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

20. 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

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.
Notation
Standard
(CA Addition)
Domain
Cluster of Standards
Standard

22. 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.
What are the big differences at your grade level
from our old standards to CCSS-M?

23. Focus and Coherence
click on video camera to play 3 minute video – Focus and Coherence architects of the CCSS video
Bill McCallum, One of three main authors of Mathematics CCSS

24. 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

25. 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
Previously taught the algorithm. Now, we teach several approaches to multiplication with the idea that students will need to choose which approach is most effective for a given problem. It will take much longer to build this understanding and competency with multiplication. 15
200
715
715
500
715
Focus

26. 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
Provide a trace(s) of fluency/math facts and/or, represent and interpret data, multiplication and division, algebraic thinking/expressions and equations. In table groups, discuss what it means for their grade level and mastering the standards that fall into their grade level.

27. 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
Let’s look at how the number line is developed starting in 2nd Grade
This starts building some critical concepts that will continue to be developed across grade levels:
An understanding of benchmark numbers sets the foundation for rounding in later grades.
Adding on is a strategy that can be used in many situations 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.

28. How many sixths are there in two-thirds?
3rd Grade 4th Grade 1 2
5th Grade th Grade
In these examples we see benchmark numbers, developing number sense, number line used as a strategy to develop conceptual understanding
On 5th grade problem: Find 2 and ½ then find three-fifths of that.
On the 6th grade problem ask teachers: What question would you want to ask students, before clicking to show the question. 1 1 2 3
How many sixths are there in two-thirds?

29. 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.
Tie in to video – overview answers “What is my grade level MOSTLY about?” Why is it important that I don’t skip lessons? They won’t be repeated in following years!!

30. Tracing Coherence: 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 …
Female teacher – hide or delete to customize for male presenter
After partners discuss using response frames, allow five minutes for pilot teacher / teacher presenter to share his/her experience/discoveries: the content is different because, I realized the importance of,
Debrief large group

31. Break
10:15 – 10:30

32. 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

33. 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.
Detailed descriptors handout

34. 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

35. 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?

36. 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…
Before watching video have participants do the math: show 3 ways to illustrate 2.4, write 3 math problems that = 2.4 (use at least 2 operations), is 2.4 the same as 2 remainder 4? Explain why or why not. Then, click on video camera to play 10 minute video. Watch 2.4 video

37. 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 _______.

38. 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 engagement with mathematics rather than procedural
Student centered approach rather than teacher center
Conceptual vs. procedural approach to classroom instruction
Student centered classrooms vs. teacher centered

39. Classroom Implications of the 8 Standards for Mathematical Practice
My experience has taught me …
Teacher leaders will share experiences: SMP already built-in, work to embed SMP, focus on a particular SMP
Female teacher – hide or delete to customize for male presenter

40. Lunch
11:45 – 12:45

41. Welcome Back! And now for dessert ….

42. A Move To Authentic Assessments
We’re just so excited!

43. 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
Smarter Balanced testing by grade levels is based on most up to date information.
2nd, 9th, and/or 10th grades could be added to the list.
Paper and pencil option during years of transition

44. Sample Assessment Questions from Smarter Balanced
Click on A+ to go directly to mathematics sample problems
Go through the first problem(swimmers) no matter what grade level you are training-pointing out: claim, item type, standard identification (not doing targets), show rubric
Click on view more sample of mathematics—show overview of all the sample problems
Presenter choice depending on grade level
-go through sample problems in your grade level, pointing out: claim, item type, standard identification (not doing targets)
-not all item types as samples are available in each grade level; you may need to click on another grade level to illustrate the item types and claims 45

45. 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

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

47. SHIFTS in Instruction… Ergo…
Click on video camera to start Steve Leinwand video – begin at 50 seconds
Follow up with slides listing his ERGO statements

48. 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

49. 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
Graffiti wall with groups of about 4-5
Poster with a singular heading and T chart set up
Groups get a different color pen and write on each poster—two minutes
Then walk around room with note taking sheet to see what all groups said for each heading

50. Implications for Instruction
Given that our math instruction will look and sound different, what are implications for our instruction?
My experience has taught me …
Teacher leaders will share experiences: my classroom is different this year, I still need to
Female teacher – hide or delete to customize for male presenter
200

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

52. 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
Give time here for teachers to brainstorm things in their day that may not be necessary any longer and could be cut. Using current schedule, teachers try to block their days so that they have 90 minutes/day allocated to math.

53. Common Core -ification Takes Time!
Tips and Traps
My experience has taught me …
Teacher leaders will share experiences: fewer standards does not mean less time, importance of planning, logistics (manipulatives, workbooks)
Female teacher – hide or delete to customize for male presenter

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
Record on half sheet for tea party activity (next slide)

55. Interactive Activity: Tea Party
As I learn about the shifts in the Mathematics CCSS, what excites me most for my students is ____.
Tea party using reflection half sheets from last slide

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
Pass out resource sheet.
As time permits you may wish to share some of these sites with the group.
The link is a hyperlink.
We want people to sign up so that they will get the updates automatically.
You might want to mention that they will not be getting daily s that will clog their inbox.
Writing exemplars have been added by Smarter Balanced- This is what we are talking about, does not give 4, 3, 2, 1 but tell what it should look like.
Rubrics are there
Prompt writing
4th grade lesson plan sequence- although each person received an , some people still think they are coming…

57. Roll Call!
You must by signed in on the electronic document to receive hours or salary credit

58. Feedback to inform next steps…