Transcript Comparing The Standards Across Grade Levels PK – High School

Comparing The Standards
Across Grade Levels
K – High School
High School Number and Quantity
Numbers and Number Systems

It’s about extending the students
conception of number.
Number for K - 5
Counting and
Cardinality
 Numbers and
Operations in Base
Ten
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K
1
2
3
4
5
6
7
8
Geometry
Measurement and Data
Statistics and Probability
Number and Operations in Base Ten
The Number System
Operations and Algebraic Thinking
Expressions and Equations
Counting
and
Cardinality
Number
and
Operations--Fractions
Ratios and
Proportional
Relationships
Functions
Kindergarten
Counting and Cardinality
Kindergarten
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K.CC
Know number names and
the count sequence.
Count to tell the number of
objects.
Compare numbers.
Number and Operations in
Base Ten
Kindergarten
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K.NBT
Work with numbers 11--19 to
gain foundations for place
value.
First Grade
Numbers and Operations in Base Ten
 Extend
1.NBT
the counting sequence.
 Understand place value.
 Use place value understanding and properties
of operations to add and subtract.
Second Grade
Numbers and Operations in Base Ten
 Understand
2.NBT
place value.
 Use place value understanding and properties
of operations to add and subtract.
Third Grade
Numbers and Operations in
Base Ten
3.NBT
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Use place value
understanding and
properties of
operations to perform
multi-digit arithmetic.
Number and Operations--Fractions
3.NF

Develop understanding
of fractions as
numbers.
Fourth Grade
Numbers and Operations in
Base Ten
4.NBT
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Generalize place value
understanding for multidigit whole numbers.
Use place value
understanding and
properties of operations to
perform multi-digit
arithmetic.
Number and Operations--Fractions
4.NF
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Extend understanding of
fraction equivalence and
ordering.
Build fractions from unit
fractions by applying and
extending previous
understandings of
operations on whole
numbers.
Understand decimal
notation for fractions, and
compare decimal fractions.
Fifth Grade
Numbers and Operations in
Base Ten
5.NBT
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Understand the place value
system.
Perform operations with
multi-digit whole numbers
and with decimals to
hundredths.
Number and Operations--Fractions
5.NF
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Use equivalent fractions as
a strategy to add and
subtract fractions.
Apply and extend previous
understandings of
multiplication and division
to multiply and divide
fractions.
Number for 6 - 8

The Number System
K
1
2
3
4
5
6
7
8
Geometry
Measurement and Data
Statistics and Probability
Number and Operations in Base Ten
The Number System
Operations and Algebraic Thinking
Expressions and Equations
Counting
and
Cardinality
Number
and
Operations--Fractions
Ratios and
Proportional
Relationships
Functions
Sixth Grade
The Number System
 Apply
6.NS
and extend previous understandings of
multiplication and division to divide fractions
by fractions.
 Compute fluently with multi-digit numbers
and find common factors and multiples.
 Apply and extend previous understandings of
numbers to the system of rational numbers.
Seventh Grade
The Number System
 Apply
7.NS
and extend previous understandings of
operations with fractions to add, subtract,
multiply, and divide rational numbers.
Eighth Grade
The Number System
 Know
8.NS
that there are numbers that are not
rational, and approximate them by rational
numbers.
High School
The Real Number System
 Extend
N-RN
the properties of exponents to rational
exponents.
 Use properties of rational and irrational
numbers.
High School
Complex Numbers
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N-CN
Perform arithmetic
operations with complex
numbers.
Represent complex
numbers and their
operations on the complex
plane.
Use complex numbers in
polynomial identities and
equations.
Vector and Matrix Quantities N-VM
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Represent and model with
vector quantities.
Perform operations on
vectors.
Perform operations on
matrices and use matrices in
applications.
What did I learn about “Number”?
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At first, “number” means “counting number”: 1, 2, 3, …
Soon after that, 0 is used to represent “none” and the
whole numbers are formed by the counting numbers
together with zero.
The next extension is fractions. At first, fractions are
barely numbers and tied strongly to pictorial
representations.
The concept of fractions as numbers is used to connect
them to their decimal representations, with the base-ten
system used to represent the whole numbers.
During middle school, fractions are augmented
by negative fractions to form the rational
numbers.
 In Grade 8, students extend this system by,
augmenting the rational numbers with the
irrational numbers to form the real numbers.
 Finally, in high school, students are exposed to
another extension of number, when the real
numbers are augmented by the imaginary
numbers to form the complex numbers.
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The End for “Number”
Quantity
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When applying mathematics to real world
problems, the answers are usually not
numbers but quantities: numbers with
units, which involves measurement.
Quantity for PK - 5
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Measurement and
Data
Kindergarten
Measurement and Data
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Describe and compare measurable
attributes.
K.MD
First Grade
Measurement and Data
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1.MD
Measure lengths indirectly and by iterating
length units.
Second Grade
Measurement and Data
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2.MD
Measure and estimate lengths in standard
units.
Third Grade
Measurement and Data
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3.MD
Solve problems involving measurement
and estimation of intervals of time, liquid
volumes, and masses of objects.
Fourth Grade
Measurement and Data
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4.MD
Solve problems involving measurement
and conversion of measurements from a
larger unit to a smaller unit.
Fifth Grade
Measurement and Data
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5.MD
Convert like measurement units within a
given measurement system.
Quantity for 6 - 8
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Geometry
K
1
2
3
4
5
6
7
8
Geometry
Measurement and Data
Statistics and Probability
Number and Operations in Base Ten
The Number System
Operations and Algebraic Thinking
Expressions and Equations
Counting
and
Cardinality
Number
and
Operations--Fractions
Ratios and
Proportional
Relationships
Functions
Sixth Grade
Geometry
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6.G
Solve real-world and mathematical
problems involving area, surface area, and
volume.
Seventh Grade
Geometry
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7.G
Solve real-life and mathematical problems
involving angle measure, area, surface
area, and volume.
Eighth Grade
Geometry
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8.G
Solve real-world and mathematical
problems involving volume of cylinders,
cones, and spheres.
High School
Quantities
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N-Q
Reason quantitatively and use units to solve problems.
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Use units as a way to understand problems and to
guide the solution of multi-step problems; choose and
interpret units consistently in formulas; choose and
interpret the scale and the origin in graphs and data
displays.
Define appropriate quantities for the purpose of
descriptive modeling.
Choose a level of accuracy appropriate to limitations
on measurement when reporting quantities.
What did I learn about “Quantity”?
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Quantity is about the real world problems.
The answers are usually not numbers but quantities:
numbers with units, which involves measurement.
In their work in measurement up through Grade 8,
students primarily measure commonly used attributes
such as length, area, and volume.
In high school, students encounter a wider variety of
units in modeling, e.g. acceleration, currency conversions,
social science rates such as per-capita income, and rates
in everyday life such as points scored per game or batting
averages.
The End