Common Core State Standards for
Mathematics: Coherence
Grade 2
Essential Questions
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How and why were the Common Core State
Standards developed and by whom?
What are the 3 shifts in math instruction in the CCSS?
Why the need for Coherence?
How is Coherence reflected in the classroom?
What are the next steps in implementing Coherence?
Overview of the
Common Core State Standards
Rationale for CCSS
• Declining US competitiveness with other developed
countries
• NAEP performance that is largely flat over the past 40
years in 8th grade
• Slight improvement on NAEP performance at the 4th
grade level
• Slight decline on NAEP performance at the high school
level
• High rates of college remediation
Background of CCSS
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Initiated by the National Governor’s Association
(NGA) and Council of Chief State School Officers
(CCSSO) with the following design principles:
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Result in College and Career Readiness
Based on solid research and practice evidence
Fewer, higher (greater DOK), and clearer
standards
College Math Professors Feel HS
Students Today are Not Prepared
for College Math
What The Disconnect
Means for Students
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Nationwide, many students in two-year and four-year
colleges need remediation in math.
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Remedial classes lower the odds of finishing the
degree or program.
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Need to set the agenda in high school math to prepare
more students for postsecondary education and
training.
The Common Core State Standards
Require Three Instructional Shifts in Mathematics
• Focus: Focus strongly where the standards focus.
• Coherence: Think across grades and link to major
topics.
• Rigor: In major topics, pursue conceptual
understanding, procedural skill and fluency, and
application.
Shift 2: Coherence
The Standards are designed around coherent
progressions from grade to grade. Principals
and teachers carefully connect the learning
across grades so that students can build new
understanding onto foundations built in previous
years. Teachers can begin to count on deep
conceptual understanding of core content and
build on it. Each standard is not a new event,
but an extension of previous learning.
William McCallum on Coherence
Coherence: Think Across
Grades
CCSS Place Value Progression
K
K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some
further ones.
1.NBT.2 Understand that the two digits of a two-digit number represent amounts of
tens and ones.
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1.NBT.4 Add within 100 – Understand that in adding two-digit numbers, one adds
tens and tens, ones and ones, and sometimes it is necessary to compose a ten.
1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less.
2.NBT.1 Understand that the three digits of a three-digit number represent amounts
of hundreds, tens, and ones.
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2. NBT.3 Read and write numbers to 1000 using base-ten numerals, number
names, and expanded form.
2.NBT.6 Add up to four two-digit numbers using strategies based on place value.
2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract
10 or 100 from a given number 100-900.
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Coherence: Link to Major Topics Within Grades
Example: Number and Operations in Base Ten 2.NBT
Use place value understanding and properties of operations to add
and subtract.
Example: Measurement 2.MD
Work with time and money.
Solve word problems involving dollar bills, quarters, dimes, nickels, and
pennies, using $ and ¢ symbols appropriately. Example: If you have 2
dimes and 3 pennies, how many cents do you have?
Coherence Card
Activity
Your goal as a team is to correctly place the
cards within each grade in an accurate
progression. The only parameters are that no
two of the same color cards will appear in the
same grade, and that there will not necessarily
be on card in each grade for each progression.
NOTE: It may be helpful to first identify the
theme for each set of cards, so that you
collectively understand each strand that you are
Engaging with the Shift: Investigate Coherence
in the Standards with Respect to Multiplication.
In the space below, copy all of the standards
related to multiplication and note how coherence
is evident in these standards. Note also
standards that are outside of the Operations and
Algebraic Thinking domain but are related to, or
in support of, multiplication.
Examples of Opportunities for Connections
among Standards, Clusters or Domains
Extending students’ understanding of the base-ten system is
essential for future work with numbers. It is critical that
students at this grade are able to compose and decompose
numbers in order to add and subtract fluently.
Directions: Solve the following problem.
Think about how the problem connects
to the standard and how it looks different
than what we currently do in the
classroom.
Louis wants to give $15 to help kids who need
school supplies. He also wants to buy a pair of
shoes for $39. If Louis gets $1 every day for
his allowance, how many days will it take him
to save enough money for both? Explain how
you know.
Examples of Major Within-Grade
Dependencies
Students must begin work with place value and properties of
operations to add and subtract (2.NBT) at or near the very
start of the year to allow time for understanding and fluency
to develop. Note that work with time and money (2.MD)
should be integrated throughout the year.
Directions: Solve the following problem.
Think about how the problem connects
to the standard and how it looks different
than what we currently do in the
classroom.
Jamir has collected some pennies in a jar. Recently, he added coins other
than pennies to his jar. Jamir reached his hand into the jar and pulled out
this combination:
a.Jamir wants to count the total value of these coins. What coin do you
suggest he start with? Why would Jamir want to start counting with this
coin?
b.What is the total value of these coins? Write a number sentence that
represents the total value of the coins.
c.Jamir reached into the jar again and was surprised to pull out a different
combination of coins with the same total value as before. Draw a
collection of coins that Jamir could have pulled from the jar. Write a
number sentence that represents the total value of the coins.
Processing the shift
Math Shift
Coherence:
Think across
grades, and
link to major
topics within
grades.
What is this Opportunities Challenges
shift?
Why this
shift?