Kindergarten

Grade 1

Grade 2

*rote count to 100 and recognize numbers up to 31

*read, write, and compare whole numbers less than 100

*read, write, and compare whole numbers less than 1000

1

1

1

MA 5   1.10

MA 5  1.10

MA 5  1.10

Grade 3

Grade 4

Grade 5

read, write and compare whole numbers up to 10,000

read, write and compare and whole numbers less than 100,000

*read, write and compare whole numbers less than 1,000,000, unit fractions and decimals to hundredths (including location on the number line)

1

1

1

MA 5  1.10

MA 5   1.10

MA 5  1.10

Grade 6

Grade 7

Grade 8

apply and understand whole numbers to millions, fractions and decimals to the thousandths (including location on the number line)

compare and order all positive rational numbers and find their approximate location on a number line

*compare and order  all rational numbers including percents,  and find their approximate location on a number line

1

1

1

MA 5   1.10

MA 5  1.10

MA 5  1.10

K

*recognize ½ of a shape

Grade 1

*recognize ½ and ¼ of a shape

Grade 2

*recognize unit fractions of a shape 

1

1

1

MA 5  1.10

MA 5

MA 5   1.10

Grade 3

*represents halves, thirds and fourths

Grade 4

*use models, benchmarks (0, 1/2 and 1) and equivalent forms to judge the size of fractions

Grade 5

recognize and generate equivalent forms of commonly used fractions and decimals

1

2

2

MA 5  1.10

MA 5   1.10

MA 5  1.10

Grade 6

recognize and generate equivalent forms of fractions, decimals and benchmark percents

Grade 7

recognize and generate equivalent forms of fractions, decimals and percents

Grade 8

use fractions, decimals and percents to solve problems

2

2

2

MA 5  1.10

MA 5  1.10

MA 5  3.3

K

*use concrete objects to compose and decompose values up to 10

Grade 1

*compose or decompose  whole numbers up to 20 using multiple strategies such as known  facts, doubles and close to doubles, tens, and one place value

2

*compose or decompose  numbers by using a variety of strategies, such as using  known facts, tens place value  or landmark numbers to solve problems

2

2

2

MA 1  1.6

MA 1  1.6

MA 1  1.6

Grade 3

recognize equivalent representations for the same number and generate them by decomposing and composing numbers including expanded notation

4

recognize equivalent representations for the same number and generate them by decomposing and composing numbers 

5

*recognize equivalent representations for the same number and generate them by decomposing and composing numbers,

2

2

2

MA 1  1.6

MA 1  1.6

MA 5  1.6

Grade 6

*recognize equivalent representations for the same number and generate them by decomposing and composing numbers

7

*recognize equivalent representations for the same number and generate them by decomposing and composing numbers,

including exponential notation

8

*recognize equivalent representations for the same number and generate them by decomposing and composing numbers, including scientific notation

2

2

2

MA 5  1.6

MA 5  1.6

MA 5  1.6

Kindergarten

Grade 1

Grade 2

*skip count by 2s, 5s and 10s

*skip count by multiples of numbers less than 10

1

1

MA 5  1.6

MA 5  1.6

Grade 3

Grade 4

Grade 5

classify numbers by their characteristics, including odd and even 

classify and describe numbers by their characteristics, including odd, even,  multiples and factors 

*describe numbers according to their characteristics, including whole number common factors and multiples,  prime or composite, and square numbers

1

2

2

MA 5  1.6

MA 5  1.10

MA 5  1.10

Kindergarten

Grade 1

Grade 2

*represent/

model a given situation involving addition and subtraction of whole numbers using pictures, objects, or symbols

*represent/

model a given situation involving two-digit whole number addition or subtraction

2

2

MA 1  1.10

MA 1  1.10

Grade 3

Grade 4

Grade 5

*represent/

model a given situation in-

Volving multi-

plication and related division using various models includ-

ing sets, arrays, areas, repeated addition/sub-traction, sharing and partitioning 

*represent and recognize multiplication and related division using various models, including equal intervals on the number line, equal size groups, distributive property, etc.

represent and recognize division using various models, including quotative and partitive

2

2

2

MA 1  1.0

MA 1  1.10

MA 1  1.10

Grade 3

*describe the effects of adding and subtracting whole numbers as well as the relationship between the two operations

4

describe the effects of multiplying and dividing whole   numbers as well as the relationship between the  two

operations

5

*describe the effects of addition and subtraction on fractions and decimals

2

2

2

MA 1  1.10

MA 1 1.10

MA 1  1.10

6

describe the effects of multiplication and division on fractions and decimals

7

*describe the effects of all operations on rational numbers

including integers

 8

2

2

MA 1  1.10

MA 1  1.10

*apply properties of operations (including order of operations) to positive rational numbers

apply properties of operations (including order of operations) to positive rational numbers   and integers

apply properties of operations to all rational numbers including order of operations and inverse operations

2

2

2

MA 1  1.10

MA 1  1.10

MA 1  1.10

Grade 6

Grade 7

Grade 8

identify square and cubic numbers and  determine whole number roots and cubes

*approximate the value of square roots to the nearest whole number

1

1

M 5  1.6

MA 5  1.6

Kindergarten

Grade 1

Grade 2

*describe or represent  the mental strategy used to compute addition and subtraction problems

*describe or notate the mental strategy used to compute addition or subtraction of whole numbers, including 2-digit numbers

2

2

MA 1 3.2

MA 1  3.2

Grade 3

Grade 4

Grade 5

*represent a mental strategy used to compute a given multiplication problem up to 9 x 9

*represent a mental strategy used to compute a given multiplication problem (up to 2-digit by 2-digit multiple of)

*describe a mental strategy used to compute a given division problem, where the quotient is a multiple of 10 and the divisor is a 1-digit number (e.g., 350 /7)

2

2

2

MA 1  3.2

MA 1  3.2

MA 1  3.2

K

*connect number words (orally) and quantities they represent

Grade 1

*use strategies to develop fluency with basic number relationships of addition and subtraction for sums up to 20

Grade 2

*demonstrate fluency including quick recall with basic number relationships of addition and subtraction for sums up to 20

1

1

1

MA 1  1.10

MA.1  1.6

MA.1  1.6

Grade 3

use strategies to develop fluency with basic number relationships (9 X 9) of multiplication and division

Grade 4

demonstrate  fluency with basic number relationships (12 X 12) of multiplication and related division facts

Grade 5

demonstrate  fluency with efficient procedures for adding and subtracting decimals and fractions (with unlike denominators)

and division of whole numbers

1

1

1

MA.1  1.6

MA.1  1.6

MA 1  1.6

 Grade K

1

*apply and describe the strategy used to solve  addition or subtraction  problems

2

*apply and describe the strategy used to compute

2-digit addition or subtraction  problems with regrouping

2

2

MA 1  3.2

MA 1  3.2

Grade 3

apply and describe the strategy used to compute up to 3-digit addition or subtraction

problems

4

apply and describe the strategy used to compute a given multiplication of 2-digit by 2-digit numbers and related division facts

5

apply and describe the strategy used to compute a  division problem up to a 3- digit by 2-digit and addition and subtraction of fractions and decimals

2

2

2

MA 1  3.2

MA 1  3.2

MA 1  3.2

apply and describe the strategy used to compute a  division problem up to a 3- digit by 2-digit and addition and subtraction of fractions and decimals

multiply and divide positive rational numbers

apply all operations on rational numbers including integers

2

1

2

MA 1  3.2

MA 1  3.1

MA 1  3.1

*recognize or repeat sequences of sounds or shapes

*extend patterns of sound, shape, motion or a simple numeric pattern

*describe and extend simple numeric patterns and change from one representation to another

2

2

2

MA 4  1.6

MA 4 1.6

MA 4 1.6

extend geometric (shapes) and numeric patterns to find the next term

describe geometric and numeric patterns

make and describe generalizations about geometric and numeric patterns

2

2

2

MA 4 1.6

MA 4  1.6

MA 4  1.6

Grade K

*create and continue patterns

1

*describe how simple repeating patterns are generated

2

*describe how simple growing patterns are generated

2

2

2

MA 4 1.6

MA 4 1.6

MA 4 1.6

Grade 3

represent patterns using words, tables or graphs

4

analyze patterns using words, tables and graphs 

5

represent and analyze patterns using words, tables and graphs

2

3

3

MA 4 1.6

MA 4 1.6

MA 4 1.6

Grade 6

represent and describe patterns with tables, graphs, pictures, symbolic rules or words

7

analyze  patterns represented graphically or numerically with words or symbolic rules, including recursive notation

8

generalize patterns represented graphically or numerically with words or symbolic rules, using explicit notation

2

3

2

MA 4 1.6

MA 4 1.6

MA 4 1.6

*compare various forms of representations to identify patterns

compare and contrast various forms of representations of patterns

compare and contrast various forms of representations  of patterns

2

3

3

MA 4 1.6

MA 4 1.6

MA 4 1.6

*identify functions as linear or nonlinear from tables or graphs

identify functions as linear or nonlinear from tables, graphs or equations

identify functions as linear or nonlinear from tables, graphs or equations

1

1

1

MA 4  1.6

MA 4  1.6

MA 4  1.6

Kindergarten

Grade 1

Grade 2

*using addition or subtraction,

represent a mathematical situation as an expression or number sentence

*using addition or subtraction, represent a mathematical situation as an expression or number sentence

2

2

MA 4  1.10

MA 4  1.10

Grade 3

Grade 4

Grade 5

using all operations, represent a mathematical situation as an expression or number sentence

using all operations, represent a mathematical situation as an expression or number sentence

using all operations, represent a mathematical situation as an expression or number sentence using a letter or symbol 

2

2

2

MA 4  1.10

MA 4  1.10

MA 4  1.10

Grade 6

Grade 7

Grade 8

use symbolic algebra to represent unknown quantities in expressions or equations and solve one-step equations

use symbolic algebra to represent unknown quantities in expressions or equations and solve linear equations with one variable

use symbolic algebra to represent  and solve problems that involve linear relationships

2

2

3

MA 4  3.3

MA 4  3.3

MA 4  3.3

 Grade K

1

*apply the commutative and associative properties of addition to whole numbers

2

*solve problems with whole numbers using the commutative and associative properties of addition

2

2

MA 4  1.10

MA 4  3.2

Grade 3

use  the commutative, distributive and associative properties for basic facts of whole numbers

Grade 4

use  the commutative, distributive and associative properties of addition and multiplication for multidigit numbers

Grade 5

*use  the commutative, distributive and associative properties for fractions and decimals

2

2

2

MA 4 3.2

MA 4  3.2

MA 4  3.2

use  the commutative, distributive and associative properties to generate equivalent forms for simple algebraic expressions

use properties to generate equivalent forms for simple algebraic expressions that include positive rationals and integers

use properties to generate equivalent forms for simple algebraic expressions that include all rationals

2

2

2

MA 4  3.2

MA 4  3.2

MA 4  3.2

Kindergarten

Grade 1

Grade 2

*model situations that involve whole numbers, using pictures, objects or symbols

*model situations that involve the addition of whole numbers, using pictures, objects or symbols

*model situations that involve addition and subtraction of whole numbers, using pictures, objects or symbols

2

2

2

MA 1  1.6

MA 1  1..6

MA 1  1.6

Grade 3

Grade 4

Grade 5

*model problem situations, including multiplication with objects or drawings

*model problem situations, using representations such as graphs, tables or number sentences

model problem situations and draw conclusions, using representations such as graphs, tables or number sentence

2

2

3

MA 4  1.6

MA 4  1.6

MA 4  1.6

Grade 6

Grade 7

Grade 8

model and solve problems, using multiple representations such as tables, expressions and   one-step equations

model and solve problems, using multiple representations such as graphs, tables, expressions, and linear equations

model and solve problems, using multiple representations such as graphs, tables, and linear equations

2

2

2

MA 4  3.6

MA 4  1.6,3.6

MA 4  3.6

Kindergarten

Grade 1

Grade 2

*describe qualitative change, such as students growing taller

2

MA 4  1.6

Grade 3

Grade 4

Grade 5

*describe quantitative change, such as students growing two inches in a year

*describe mathematical relationships in terms of constant rates of change

*identify, model and describe situations with constant or varying rates of change

2

2

3

MA 4  1.6

MA 4  1.6

MA 4  1.6

Grade 6

Grade 7

Grade 8

*construct and analyze  representations to compare  situations with constant or varying rates of change

compare situations with constant or varying rates of change

analyze  the nature of changes (including slope and intercepts) in quantities in linear relationships

3

3

3

MA 4  1.6

MA 4  1.6

MA 4  1.6

Kindergarten

Grade 1

Grade 2

*use models to compose and decompose 2-dimensional shapes

2

MA 2  1.6

Grade 3

Grade 4

Grade 5

*predict the results of putting together or taking apart 2- and 3- dimensional shapes

*describe the results of subdividing, combining and transforming shapes

predict and justify the results of subdividing, combining and transforming shapes

3

2

3

MA 2  1.6

MA 2  1.6

MA 2  1.6

Kindergarten

Grade 1

Grade 2

*describe, name and interpret relative positions in space (above, below, front, behind)

*describe, name and interpret relative positions in space (left, right)

*identify locations with simple relationships on a map (coordinate system)

2

2

1

MA 2  1.10

MA 2  1.10

MA 2  3.1

Grade 3

Grade 4

Grade 5

*describe location using common language and geometric vocabulary (forward, back, left, right, north, south, east, west)

*describe movement using common language and geometric vocabulary (forward, back, left, right, north, south, east, west)

*use coordinate systems to specify locations, describe paths and find the distance between points along horizontal and vertical lines

2

2

2

MA 2  1.10

MA 2  3.3

MA 2  1.10

Grade 6

Grade 7

Grade 8

use coordinate systems to construct geometric shapes

use coordinate geometry to construct and identify geometric shapes in the coordinate plane using their properties

use coordinate geometry to analyze properties of right triangles and quadrilaterals (including the use of the Pythagorean Theorem)

2

2

2

MA 2 1.10

MA 2  3.2

MA 2  3.2

Kindergarten

Grade 1

Grade 2

*use manipulatives to recognize from different perspectives and orientations models of slides and turns

*use manipulatives to model flips

*use manipulatives to model slides and turns

2

2

2

MA 2  1.6

MA 2  1.6

MA 2  1.6

Grade 3

Grade 4

Grade 5

determine if two objects are congruent through a slide, flip or turn

predict the results of sliding/ translating, flipping/ reflecting or turning/ rotating around the center point of a polygon

*predict, draw and describe the results of sliding/ translating, flipping/ reflecting and turning/ rotating around a center point of a polygon

2

3

3

MA 2 3.2

MA 2  3.6

MA 2  3.6

Grade 6

Grade 7

Grade 8

*describe the transformation from a given pre-image using the terms reflection/flip, rotation/turn, and translation/

slide

reposition  shapes under formal transformations such as reflection, rotation and translation 

3

2

MA 2  3.3

MA 2  3.3

 Grade 6

Grade 7

describe the relationship between the scale factor and the perimeter of the image using a dilation (contractions- magnifications; stretching/

shrinking)

Grade 8

describe the relationship between the scale factor and the area of the image using a dilation (stretching/

shrinking)

2

MA 2  3.6

 Grade K

1

*recognize shapes that have symmetry

2

*create shapes that have symmetry

1

2

MA 2  1.10

MA 2  1.10

Grade 3

identify lines of symmetry in polygons

Grade 4

create a figure with multiple lines of symmetry and identify the lines of symmetry

Grade 5

identify polygons and designs with rotational symmetry

1

2

1

MA 2  1.10

MA 2  1.10

MA 2  1.6

*create polygons and designs with rotational symmetry

*determine all lines of symmetry of  a polygons

*identify the number of rotational symmetries of regular polygons

2

1

1

MA 2  1.6

MA 2  1.6

MA 2  1.6

Grade 3

Grade 4

Grade 5

*given the picture of a prism, identify the shapes of the faces

given a net of a prism or cylinder, identify the 3-dimensional shape

1

2

MA 2  3.3

MA 2  3.3

Grade 6

Grade 7

Grade 8

*use spatial visualization to identify isometric representations of mat plans

*use spatial visualizations to identify various 2-dimensional views of isometric drawings

create isometric drawings from a given mat plan 

2

2

3

MA 2  3.3

MA 2  3.3

MA 2  3.3

draw or use visual models to represent and solve problems

draw or use visual models to represent and solve problems

draw or use visual models to represent and solve problems

3

3

3

MA 2  3.3

MA 2  3.3

MA 2  3.3

Kindergarten

Grade 1

Grade 2

*compare and order objects according to their size or weight

*select the appropriate tool for the attribute being measured (size, temperature, time, weight)

*select an appropriate unit and tool for the attribute being measured (size, temperature, time, weight) and to the nearest inch, centimeter, degree, hour and pound

2

2

2

MA 2  1.8

MA 2  3.1

MA 2  3.1

Grade 3

Grade 4

Grade 5

*identify, justify and use the appropriate unit of measure (linear, time, weight)

*identify and justify the unit of  linear measure including perimeter and (customary metric)

*identify and justify the unit of measure for area (customary and metric)

3

3

3

MA 2  3.1

MA 2  3.1

MA 2  3.1

Grade 6

Grade 7

Grade 8

identify and justify the unit of measure for area and volume (customary and metric)

*identify and justify the unit of measure for volume (customary and metric)

3

3

MA 2  3.1

MA 2  3.1

 Grade 4

5

identify equivalent linear measures within a system of measurement

6

identify the equivalent weights and equivalent capacities within a system of measurement

1

1

MA 2  1.6

MA 2  1.6

Grade 6 

7

identify the equivalent area and volume measures within a system of measurement (e.g., sq ft. to sq in, m³ to c m³)

 8

1

MA 2  1.6

Grade K

*describe passage of time using terms such as today, yesterday, tomorrow

1

*tell time to the nearest half hour

2

*tell time to the nearest one fourth (quarter)  hour

2

1

1

MA 2  3.1

MA 2  1.10

MA 2  1.10

Grade 3

tell time to the nearest  five minutes

4

tell time to the nearest minute

 5

1

1

MA 2  1.10

MA 2  1.10

Grade 6

*solve problems involving elapsed time (hours and minutes)

7

*solve problems involving addition and subtraction of  time (hours, minutes and seconds)

 8

2

2

MA 5  3.1

MA 5  3.1

Kindergarten

Grade 1

Grade 2

*identify and know the value of a penny, nickel, dime, and quarter

*count money to a dolllar, including half dollars

*make change from a dollar

2

2

2

MA 1 1.10

MA 1 1.10

MA 1 1.10

Grade 3

Grade 4

Grade 5

determine change from $5.00 and add and subtract money values to $5.00

determine change from $10.00 and add and subtract money values to $10.00

2

2

MA 1 1.10

MA 1 1.10

Kindergarten

Grade 1

Grade 2

*measure objects by comparison of lengths (shorter, same, longer)

*use repetition of a single unit to measure something larger than the unit, (e.g. length of book with paper clips)

*use standard units of measure (cm, inch) and the inverse relationships between the size and number of units

1

1

2

MA 2  1.6

MA 2  1.10

MA 2  1.6

Kindergarten

Grade 1

Grade 2

*measure objects by comparison of lengths (shorter, same, longer)

*use repetition of a single unit to measure something larger than the unit, (e.g. length of book with paper clips)

*use standard units of measure (cm, inch) and the inverse relationships between the size and number of units

1

1

2

MA 2  1.6

MA 2  1.10

MA 2  1.6

Grade 3

Grade 4

Grade 5

*use a referent for measures to make comparisons and estimates

*select and use benchmarks to estimate measurements (linear, capacity, weight)