Transcript CCSS Elementary Math Implementation Day 1-2

Common Core State Standards
Module 2:
Content and Curriculum, K-5
Mathematics
Anthony Quan—Consultant II, STEM
Belinda Lister—Math Consultant
Division of Curriculum and Instructional Services
commoncore.lacoe.edu
AGENDA
• Common Core State Standards Overview
• Mathematical Practices in Action
• Standards Progression: A Closer Look
– K-5 Place Value
– 3-5 Fractions
• Closing
Common Core State Standards
“These standards define what students should
understand and be able to do in their study of
mathematics.”
National Governors Association Center for Best Practices
and Council of Chief State School Officers (2010)
Common Core State Standards for Mathematics
Common Core State Standards
“Any national mathematics curriculum must
emphasize depth over breadth and must focus on the
essential ideas and processes of mathematics.”
National Council of Teachers of Mathematics (2009)
Guiding Principles for Mathematics Curriculum and Assessment
Common Core State Standards
“Mathematics topics may be important for different
reasons, such as their utility in developing other
mathematical ideas, in linking different areas of
mathematics and in preparing students for college, the
workforce, and citizenship.”
National Council of Teachers of Mathematics (2009)
Guiding Principles for Mathematics Curriculum and Assessment
Common Core State Standards
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Focus
Coherence
• Identifies key ideas,
understandings, and skills for
each grade
or course
• Stresses deep learning,
applying concepts and skills
within the same grade or
course
• Articulates a progression of
topics across grades
• Connects ideas with other
ideas, enabling students to
learn with understanding,
develop skill proficiency, and
solve problems
Common Core State Standards
• Standards for Mathematical Practice
Eight standards common to all grade
levels K-12
• Mathematical Content Standards
Standards that vary by grade level
and conceptual category
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Common Core State Standards for
Mathematical Practice
21st Century Skills
• Communication
• Collaboration
• Creativity
• Critical Thinking
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Part 1: Standards for
Mathematical Practice in Action
• Locate the MARS Tasks and Student
Work handout.
• Complete the task on your own.
• Once task is completed, discuss the prompts:
– What mathematical skills and understanding are
needed to successfully complete the task?
– Which Standards for Mathematical Practice did you
use to solve the task?
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Part 2
Mathematical Practices in Action
• Using the MARS Tasks and Student Work handout,
examine the student work provided for the task you
completed.
• Determine which Standards for Mathematical
Practice are represented in the student work.
• Compare your work with the student work.
– How are the practices similar?
– How are the practices different?
Mathematical Habits of Mind
“Mathematical habits of mind allow one to bring
coherence to many different parts of the
curriculum… Building coherence in the
development of mathematical ideas across
grades is key to improving students’
mathematical learning.”
Cuoco, Goldenberg, & Mark (2010)
Organizing a Curriculum around Mathematical Habits of Mind
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Domains and Conceptual Categories
Distribution
Findell & Foughty (2011)
College and Career-Readiness Through the Common Core State Standards for Mathematics
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Example of Domain Flows
Elementary to High School
K-5
6-8
9 - 12
Operations &
Algebraic Thinking
Expressions &
Equations
Algebra
The Number
System
Number &
Quantity
Geometry
Geometry
Statistics &
Probability
Statistics &
Probability
Functions
Functions
Number:
Base Ten
Number:
Fractions
Geometry
Measurement
& Data
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Calahan (2011)
Delving Deeper into the Common Core
Percent of Standards at Each Grade Level
Standards Across the Grades
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Format of the Overview
Domains:
Overarching ideas
that connect
topics across the
grades
Clusters:
Illustrate the
progression of
increasing
complexity from
grade to grade
© Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Format of the Standards
Domain:
Standards:
Define what
students should
know and be able
to do for each
grade level or
course.
Cluster:
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© Copyright 2010. National Governors Association Center for Best Practices
and Council of Chief State School Officers. All rights reserved.
Grade-Level Standards
• Look at the CCSS for Mathematics.
• Read the introduction for your grade level.
• Highlight critical focus areas and mark as follows:
– Expectations similar to CA 1997 Standards
– New expectations
– Questions I have regarding these expectations
• Be ready to discuss.
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Standards Progression
Within and Across Domains
Grades K – 5
Number & Operations:
Base Ten
Grades 6 – 8
Grades 3 – 5
Number & Operations:
Fractions
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The Number System
Operations and Algebraic Thinking
Function
• Grade K: OA.1 Represent addition and subtraction with
objects… expressions, or equations
• Grade 1: OA.1 …Explain ways to get to a next element
in repeating patterns
• Grade 2:OA.1 …Use drawings and equations with a
symbol for the unknown number to represent a problem
• Grade 3:OA.8 …Represent problems using a letter to
represent an unknown quantity…
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Operations and Algebraic Thinking
Functions
• Grade 4:OA.5 Generate a number or shape pattern that
follows a given rule. Identify apparent features of the
pattern that were not explicit in the rule itself
• Grade 5:OA.3 Generate two numerical patterns using
two given rules. Identify apparent relationships between
corresponding terms. Form ordered pairs consisting of
corresponding terms from the two patterns, and graph
the odered pairs on a coordinate plane.
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Connecting to Current Practice
Think/Pair/Share
• How does the progression of standards within the
Operation and Algebraic Thinking domain correspond to
your current practice?
• What are some things you might do now to help
students transition to the CCSS?
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Misconceptions
http://www.youtube.com/watch?v=Bfq5kju627c
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Video Debrief
Misconceptions
Think/Pair/Share
• What are obvious strengths?
• What are misunderstandings regarding the math?
• How might you address these misunderstandings?
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Number and Operations: Fractions Progression (3-5)
Standard 3.NF.2a
“Represent a fraction a/b on a number line diagram
by marking off the lengths 1/b from 0…”
Represent 2/3 on this number line:
0
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Number and Operations: Fractions Progression (3-5)
Standard 4.NF.2
“Compare two fractions… by creating common
denominators or numerators, or by comparing to a
benchmark fraction such as 1/2.”
2 4
?
5 7
0
½
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Number and Operations: Fractions Progression (3-5)
Standard 5.NF.2
“Use benchmark fractions and number sense of fractions to estimate mentally and
assess the reasonableness of answers.”
Determine whether the number sentence is
correct without using common denominators.
Explain how you know.
2 1 3
+ =
5 2 7
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Connecting to Current Practice
Think/Pair/Share
• How does the progression of standards
within the Fraction domain correspond to
your current practice?
• What are some things you might do now to help
students transition to the CCSS?
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KWL
•Reflect on the day and the
things that you have learned.
•Fill in the KWL chart that we did
this morning.
•Were all your “wants”
answered?
•What do you still need to learn?
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Next Steps
• Think about what you learned today.
• Decide on one thing you will do differently to start
transitioning to the CCSS.
• Share your ideas with a partner.
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For Further Investigation
• California’s Common Core State Standards
http://www.cde.ca.gov/ci/cc
• Common Core State Standards Initiative
http://www.corestandards.org
• Tools for the Common Core
(includes the Progressions)
http://www.commoncoretools.wordpress.com
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