Transcript Slide 1

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
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



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Please make appointments for
12:00, 3:00, 6:00 and 9:00
9
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?
3
1 
8
200  300 
2 10 10  3 10 10 
6 10 
4
7
79 
8
97  38 
97 + 3 + 35
9
7

7 9   
8

or
1

710   
8

10
45 States Have Adopted the CCSS-M
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 Topical Comparison: Coherence
A+ Countries
Common Fractions taught in 3rd – 6th grades
Mastery
Learning
United States
Common Fractions taught in 1st – forever!
Spirals
17
A Topical Comparison: Focus
A+ Countries
Focus on learning a few topics in depth
Mastery
Learning
United States
Many topics per grade, revisited year after year
Spirals
18
CCSS Mathematics K – 8
Domain 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 - 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
Cluster of
Standards
Notation
Standard
(CA Addition)
Standard
Grade
5
CCSS Mathematics K – 8
Domain Progressions
C
5
Domains
11
Clusters
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
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.
4.NBT.5:
5  143
Area Model
100 40  3
5 500 200 15
715
Partial Product
14 3
 5
15
200
500
715
Focus
Distributive Property
5 143 
 5  100 40  3
 (5 100)  (5  40)  (5  3)
500
+ 200 + 15
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
Domains structured coherently K – 5 and 6 – 8
K-2
3-5
•Operations and
Algebraic Thinking
•Numbers and
Operations in Base
Ten
•Measurement and
Data
•Geometry
•Operations and
Algebraic Thinking
•Numbers and
Operations in Base
Ten
•Measurement and
Data
•Geometry
•Counting and
Cardinality (K)
•Numbers and
Operations Fractions (3 – 5)
6-8
•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”
72  38  34
2nd Grade:
Subtraction is the “difference” between 2 numbers on the number line
2
38
40
 30
2
70
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.
3  6  18
3rd Grade
18
0
3
1
2 
5
2
5th Grade
5

6
6
6
4th Grade 3  2 
2
5

2
5

2
5
0
1
6th Grade
2 1
 
3 6
4 3 2
0
0
1
1
1
2
2
2
6
1
or 1
5
5
1
3
3
How many
sixths are there
in two-thirds?
4
1
2
3
1
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.
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 …
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 2Practice 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: 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: 2014-15
 Testing is slated to begin in 2014-15
 Smarter Balanced Assessment Consortium
 Testing for grades 3-8, and 11
 Includes summative and optional interim
assessments
 Practice 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
standards
Standards for
Mathematical
Practice
Instruction
Assessment
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 Like
Graffiti Wall
Shift
Multiple Representations
Deliberate Review
Alternative Approaches
Number Sense/Estimation
Math in Contexts
Formative Assessments
Planning
Looks Like
Sounds Like
Implications for Instruction
Given that our math instruction will look and
sound different, what are implications for our
instruction?
My experience
has taught me …
The Common Core -ification
Equation
Content Standards +
Standards for Mathematical Practice +
Instructional Shifts =
Common Core-ification
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
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•
•
•
•
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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…