Mathematics
Kindergarten
describe and compare
count sequence
measureable attributes
sort and count
cardinality
count
compare
Representing quantity
identify and describe
Whole numbers
instant recognition
Shapes and space
models for join and separate problems
compose and model
compose and decompose
fluency within five
KEY:
Unifying Theme
Organizing Concept
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Mathematics
Preschool
order
Measurement
group by attributes
count
Quantities
Quantifying
represent
match
sort
position
Shape Relationships
KEY:
Unifying Theme
Organizing Concept
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Mathematics
First Grade
count
represent
Whole number relationships
tens and ones
compare
data representation
represent and interpret categorical data
relate to addition and subtraction
iterate equal‐sized units
linear
indirect comparison (transitivity)
Measurement
Composing and decomposing
join
time to half hour
contextualized problems
separate
compare
building shapes from attributes
defining and nondefining
commutative
Addition and subtraction
part‐to‐whole relationships
equal shares of halves and fourths
partition circles and rectangles
properties
Attributes of shapes
compose new shapes
associative
KEY:
relate to counting
Unifying Theme
multiple strategies within 20
fluency within ten
Organizing Concept
Supporting Concept
equation representation
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
equality
Mathematics
Second Grade
represent
partition number
skip count
compare
represent data
visual displays
properties of operations
interpret data
Base‐ten system
place value
strategies to add and subtract
partition into different sized units
estimate and measure length
models
compare unit size and lengths
quantify attributes
represent unknowns
Units of measure
relationship between addition and
subtraction
Unitizing
relate to addition and subtraction
number line
time and money
contextualized problems
attributes of shapes
part/whole relationships
foundation for multiplication
Addition and subtraction
Shape analysis
fluency within 20
partition shapes
foundation for fractions
mental
foundations for multiplication
KEY:
Unifying Theme
Organizing Concept
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
product
contextualized problems
number of items in each equal sized group
commutative
area
perimeter
Multiplication and division
measurement
number of equal sized groups
quotient
Mathematics
Third Grade
relate to multiplication
total in equal sized groups
properties
Arrays
associative
distributive
relationship between area and perimeter
fluency within 100
represent unknown quantities
patterns among four operations
estimation to determine reasonableness
categorize
attributes of figures
express as unit fraction
Shape analysis
Reasoning multiplicatively
partition into equal areas
multiplication
time
liquid volume
place value relationships
addition and subtraction
units of measurement
round
masses
quantify on a number line
partition a quantity into unit fractions
Fractions
KEY:
data representation
visual displays
data interpretation
parts of a whole representations
compare
Unifying Theme
Organizing Concept
equate
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Mathematics
Fourth Grade
explain
generate
explain powers of ten
equivalence
compare
decimal number system
Fractions
compare
round
addition and subtraction
represent equivalence
unit fractions
multiplication
perform algorithms fluently
flexible, accurate, and efficient methods
justify with models
line plots 3.1a
multiplicative comparisons
Multiplication and division
Representing equivalence
data representation
remainder interpretation
contextualized problems
estimation
angles
measurement
choice and opportunity cost
unit conversion
represent unknowns with variable
KEY:
line and angle relationships
points, lines, line segments, rays, and angles
Properties of geometric figures
symmetry
factors and multiples
Unifying Theme
number patterns
Organizing Concept
sequences and tables
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Mathematics
Fifth Grade
area models
multiplication
scale models
identify and generate
fractions as division
Fractions
extend to solve problems
division
quotient interpretation
patterns
explain
equivalent fractions
addition and subtraction
graph
estimation
Partitioning quantities
model
powers of 10
formulas
comparison
decimal number system
compose and decompose
rectangular prisms
Volume
measurement conversion
Place value system
associative property
addition, subtraction, multiplication, division
compute
fluently multiply
multi‐digit whole numbers
compute quotients
write numerical expressions
KEY:
Unifying Theme
Organizing Concept
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
coordinate plane
Mathematics
Sixth Grade
area
measurement of objects
surface area
volume
percents
unit rate
variability
Ratio and rates
comparison of quantity
summary statistics
equivalence
measures of center
one‐variable
dot plots
histograms
part to part to whole
Data analysis
least common multiple
visual displays
Variability
whole numbers
box plots
flexibility, accuracy, & efficiency with
operations
Rational numbers
equivalence
fractions
location in space
write and evaluate expressions
representations of rational numbers
order of operations
absolute value
Expressions and equations
variable
solutions
KEY:
Unifying Theme
independent and dependent variable
symbolic and graphic representations
distributive property
decimals
whole number exponents
equations and inequalities
Organizing Concept
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
greatest common factor
Mathematics
Seventh Grade
representations
unit rates
experimental
Proportional relationships
probability
contextualized problems
theoretical
Samples of populations
percentages
random sampling
statistics
comparative inferences
contextualized problems
properties of operations
Reasoning proportionally
scale drawings
number lines
algorithms with rational numbers
geometric construction
geometric figures and relationships
additive inverses
two‐dimensional cross‐sections
absolute value
Two and three dimensional shapes
Rational number expressions and equations
area and circumference of circle
properties of angles
fraction to decimal form
measurement
equivalent expressions
contextualized area and volume problems
addition, subtraction, factorization and
expansion
connection to context
KEY:
equations and inequalities
Unifying Theme
models of quantitative relationships
Organizing Concept
estimation strategies
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Mathematics
Eighth Grade
solutions
rational numbers
irrational numbers
scientific notation
linear equations
systems
real numbers
Expressions and Equations
quantitative
exponents
bivariate data
categorical
properties
congruence
Modeling linear relationships
transformations
Two and three dimensional shapes
similarity
definitions
Pythagorean Theorem
linear and nonlinear
direct and indirect measurement
representations
volume
model of relationships
Functions
KEY:
slope
linear
Unifying Theme
representations
Organizing Concept
Supporting Concept
Personal Financial Literacy
Standards for Mathematical Practice
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.