3rd grade mathematics common core standards preparing students for college and career readiness 2013...
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3rd Grade MathematicsCommon Core Standards
Preparing Students for College and Career Readiness
2013
Steve Kolb, K-12 Instructional CoachCurriculum/Professional Learning
Pat Gibson, Teacher LeaderFoulks Ranch Elementary
Karen Torres, Teacher LeaderPrairie 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.
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
Engagement Strategy: Appointment Clock
9
Please make appointments for 12:00, 3:00, 6:00 and 9:00
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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. 5National Governors AssociationCouncil 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?
8
797
300200 8
31
3897
1010310102
4106
8
797
8
1107or
9 1097 + 3 + 35
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
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A Topical Comparison: Focus
Mastery Learning
Spirals
Focus on learning a few topics in depth Many topics per grade, revisited year after year
A+ Countries United States
Mastery Learning
Spirals
Common Fractions taught in 3rd – 6th grades Common Fractions taught in 1st – forever!
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A Topical Comparison: Coherence
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 - 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.
Domain
Notation
Standard
Cluster of Standards
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
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
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 _____.
Tracing Coherence: Discussion Points
My experience has taught me …
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.
Co
nte
nt
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
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: 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.
CCSS Transition Timeline: 2014-15
Testing is slated to begin in 2014-15
Smarter Balanced Assessment ConsortiumTesting for grades 3-8, and 11Includes summative and optional interim
assessments
Sample Assessment Questions from Smarter Balanced
http://www.smarterbalanced.org/practice-test/
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 ___.
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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 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 …
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
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• 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