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The Language and Structure
of the Common Core State
Standards for Mathematics
or,
Geology of the CCSS
Or,
Stones of the Standards
“The Standards”
0 Not what we teach
0 Not the curriculum
0 We teach mathematics
0 The standards are the goals
0 http://bit.ly/noprez
0 Tweet about it using hashtag #ccssm
The Common Core State
Standards for
Mathematics
The Common Core State Standards in Mathematics
K
1
2
3
4
5
Measurement and Data
6
7
Statistics and
Probability
Ratios and
Proportional
Relationships
CC
8
9
10
11
Statistics and Probability
F
Functions
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
Conceptual Categories
These categories reach back to the beginning of the
students’ academic careers …
The Common Core State Standards in Mathematics
K
1
2
3
4
5
Measurement and Data
6
7
Statistics and
Probability
Ratios and
Proportional
Relationships
CC
8
9
10
11
Statistics and Probability
F
Functions
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
Measurement and Data
5
6
7
8
Statistics and
Probability
Ratios and
Proportional
Relationships
Counting and Cardinality (K)
F
Know Number
number
names
and the count sequence
and
Operations
CC
Count to tellFractions
the number of objects
Compare numbers
The Number
System
Number and Operations in Base Ten
9
10
11
Statistics and Probability
Functions
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
6
7
Number and Operations in Base Ten (K – 5)
Place value understanding
Statistics and
Measurement
and
Data
Develop base-ten algorithms using place Probability
value and
properties of operations
Computation competencies (fluency, estimation)
Ratios and
Proportional
Relationships
CC
8
9
10
11
Statistics and Probability
F
Functions
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
6
7
8
9
10
11
12
Operations and Algebraic Thinking (K-5)
Statistics and
Statistics and Probability
Concrete
uses and
meanings
Measurement
and
Data of the basic operations (word problems)
Probability
Mathematical meaning and formal properties
of the basic operations
Prepare for later work with expressions and equations in middle school
Ratios and
Functions
Proportional
F
Relationships
CC
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
6
7
8
9
10
11
12
Number and Operations Fractions (3 – 5)
Statistics and
Enlarge
conceptand
of number
fractionsand Probability
Measurement
Data beyond whole numbers, to includeStatistics
Use understanding of the four operationsProbability
to extend arithmetic to fractions
Solve word problems related to the equation ax = b (a and b fractions)
Ratios and
Functions
Proportional
F
Relationships
CC
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
6
7
8
The Number System (6 – 8)
Statistics and
Build
concepts of
positive
Measurement
and
Data and negative numbers
Probability
Work with the rational numbers as a system
governed
by properties of operations
Begin work with irrational numbers Ratios and
Proportional
F
9
10
11
Statistics and Probability
Functions
Relationships
CC
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
6
7
8
9
10
11
12
Expressions and Equations (6 – 8)
Treat expressions as objects to reason about (not as instructions to
Statistics and
Statistics and Probability
compute an answer)
Measurement
and Data
Probability
Transform expressions using properties
of operations
Solve linear equations
Ratios and to solve word problems
Use variables and equations as techniques
Functions
Proportional
F
Relationships
CC
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
6
7
8
Algebra (9 - 12)
Statistics and
Seeing Structure
in Expressions
Measurement
and Data
Probability
Arithmetic with Polynomials & Rational
Expressions
Creating Equations
Ratios and
Reasoning with Equations and Inequalities
Proportional
F
9
10
11
Statistics and Probability
Functions
Relationships
CC
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
Number and Quantity (9 – 12)
The Real Number System
Measurement
Quantities and Data
The Complex Number System
Vector and Matrix Quantities
CC
6
7
8
Statistics and
Probability
Ratios and
Proportional
Relationships
9
10
11
Statistics and Probability
F
Functions
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
Measurement and Data
5
6
7
8
Statistics and
Probability
9
10
11
Statistics and Probability
Geometry (K – 8)
Ratios and
Ascend through progressively higher
levels of Flogical
Functions
Proportional
Relationships
reasoning about shapes
Number and Operations
Reason spatially
with shapes, leading to logical reasoning
CC
Fractions
about transformations
Number and Quantity
The
Number
Connect geometry to number, operations, and
System
measurement
via
notion
of
partitioning
Number and Operations in Base Ten
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
Measurement and Data
5
6
7
8
Statistics and
Probability
Geometry (9 – 12)
Ratios and
Congruence
Proportional
F
Similarity, Right Triangles, andRelationships
Trigonometry
Number and Operations
Circles
CC
Fractions
Expressing Geometric Properties with Equations
The Number
Geometric Measurement and Dimension
System
Modeling
with
Geometry
Number and Operations in Base Ten
9
10
11
Statistics and Probability
Functions
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
Measurement and Data
6
7
Statistics and
Probability
Ratios and
Proportional
Relationships
CC
8
9
10
11
12
Statistics and Probability
F
Functions
Number and Operations
Fractions
Number and Quantity
The Number
System
Number andRatios
Operations
in Base Ten Relationships (6 – 8)
and Proportional
Algebra
Extend work on multiplication and division; consolidate
multiplicative reasoning
Expressions and
Operations Lay
andgroundwork
Algebraic Thinking
for linear functions in Grade 8 by studying
Equations
quantities that vary together
Solve a wide variety of problems with ratios, rates, percents Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
Measurement and Data
6
7
Statistics and
Probability
Ratios and
Proportional
Relationships
CC
8
9
10
11
Statistics and Probability
F
Functions
Number and Operations
Fractions
The Number
System
12
Number and Quantity
Number and Operations in Base Ten
Functions (8)
Algebra
Extend and formalize understanding of quantitative relationships from
Grades 3-7
Lay groundwork for more extensive work
with functions
in High School
Expressions
and
Operations and Algebraic Thinking
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
Measurement and Data
6
7
Statistics and
Probability
Ratios and
Proportional
Relationships
CC
8
9
10
11
12
Statistics and Probability
F
Functions
Number and Operations
Fractions
Number and Quantity
The Number
System
Number and Operations in Base TenFunctions (9 – 12)
Interpreting Functions
Algebra
Building Functions
Expressions and
Operations and Algebraic Thinking Linear Quadratic and Exponential Models
Equations
Trigonometric
Functions
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
Measurement and Data
5
6
7
Statistics and
Probability
8
9
10
11
12
Statistics and Probability
Ratios and
Functions
Measurement and Data (K – 5)
Proportional
F
Relationships
Emphasize the common nature of all measurement
as iterating
Number and Operations
CC by a unit
Fractions
Build understanding of linear spacing of numbers and support Number and Quantity
The Number
learning of the number line
System
Develop
geometric
measures
Number and Operations in Base Ten
Work with data to prepare for Statistics and Probability in middle
Algebra
school
Expressions and
Operations and Algebraic Thinking
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
Measurement and Data
5
6
7
8
Statistics and
Probability
Ratios and
Proportional
Relationships
9
10
11
Statistics and Probability
F
Functions
Number
Operations (6 – 8)
Statistics
and and
Probability
CC
Fractions
Introduce concepts
of central tendency, variability, and distribution
Number and Quantity
Connect randomness with statistical
The inference
Number
Lay foundations for High School Statistics
Systemand Probability
Number and Operations in Base Ten
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
Measurement and Data
5
6
7
8
Statistics and
Probability
Ratios and
Proportional
12)Relationships
9
10
11
Statistics and Probability
F
StatisticsNumber
and Probability
(9 and Operations
Interpreting Categorical
CC
Fractions and Quantitative Data
Making Inferences and Justifying Conclusions
TheofNumber
Conditional Probability and the Rules
Probability
System
Using
Probability
to Make
Number and
Operations
in Base
Ten Decisions
Functions
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
Modeling (9 – 12)
Measurement and Data
6
7
Statistics and
Probability
Ratios and
Proportional
Relationships
CC
8
9
10
11
12
Statistics and Probability
F
Functions
Number and Operations
Fractions
The Number
Modeling is best interpreted not as a collection of isolated
System
topics
but
rather
in
relation
to
other
standards.
Making
Number and Operations in Base Ten
mathematical models is a Standard for Mathematical
Practice, and specific modeling standards appear throughout
Expressions and
the
high school
standards
Operations
and
Algebraicindicated
Thinkingby a star symbol (★).
Equations
Number and Quantity
Algebra
Geometry
Geometry
Modeling
The Common Core State Standards in Mathematics
K
1
2
3
4
5
Measurement and Data
6
7
Statistics and
Probability
Ratios and
Proportional
Relationships
CC
8
9
10
11
Statistics and Probability
F
Functions
Number and Operations
Fractions
Number and Operations in Base Ten
The Number
System
Number and Quantity
Algebra
Operations and Algebraic Thinking
12
Expressions and
Equations
Geometry
Geometry
Modeling
The Common Core
State Standards
in Mathematics
• Turn/flip to page 5
• No copy?
– http://bit.ly/noccss
– Required image is on next slide so don’t panic!
Vocabulary (pg. 5)
F.BF-1a
0 What does this notation mean?
0 Where is it? (Hint: It’s in the standards somewhere!)
0 What does it mean?
0 And, when you get there... hey, what's up with the
star?
4.MD-3
0 What does this notation mean?
0 Where is it?
0 What does it mean?
Will this be on the test?
0 Yes but you’ll have plenty of practice