Grades 
Clusters 
Description 
Domain 
Kindergarten 
Counting 
Count to 100 by ones and by tens. 
NBT 
NS 
MP 
Count forward beginning from a given number (instead of having to begin at 1). 
NBT 
NS 
Write numbers from 0 to 20. 
NBT 
NS 
Represent a number of objects with a given numeral (0 represents no objects). 
MP 

Count to tell the number of objects. 
MP 

Nature of Mathematics 
Represent and describe numbers 2 to 10, in two parts. 
MP 

Understanding Addition & Subtraction using objects. 
MP 

Working with higher numbers (e.g., 18 = 10 + 8). 
MP 

Shape and Space 
Describing length & weight. 
MP 

Describe Shapes (Squares, Circles, Triangles, Rectangles, Hexagons, Cubes, Cones, Cylinders, and Spheres). 
G 


Grade 1 
Easy Calculation 
Count forward between any two given numbers. 
NBT 
NS 
MP 
Count backward from 20 to 0. 
NBT 
NS 
Count 5s forward from 0 to 100. 
NBT 
NS 
Mathematics Foundation 
Demonstrate and explain the effect of adding zero to, or subtracting zero from, any number. 
MP 

Describe and use mental mathematics strategies (Addition & Subtraction). 
MP 

Describe equalities, using the equal symbol. 
MP 

Describe equality as a balance and inequality as an imbalance. 
MP 

Patterns and Relations 
Sort objects, using one attribute, and explain the sorting rule. 
G 

Sort 3D objects and 2D shapes, using its attributes, and explain the sorting rule. 
G 

Compare 2D shapes to parts of 3D objects in the environment. 
G 

Grade 2 
General Arithmetic 
Addition and Subtraction of any two digit numbers. 
MP 
NS 
MP 
Multiplication tables from 1 to 10. 
MP 
NS 
Demonstrate a number is even or odd (up to 100). 
MP 
NS 
Measurement 
Relate the number of days to a week and the number of months to a year in a problemsolving context. 
MD 

Describe length and mass and explain its unit and calculation. 
MD 

Compare and order objects by length, height, distance around and mass, using nonstandard units, and make statements of comparison. 
MD 

Constructing Shapes 
Demonstrate that changing the orientation of an object does not alter the measurements of its attributes. 
G 


Describe, compare and construct 2D shapes, including: triangles, squares, rectangles, circles. 
G 


Describe, compare and construct 3D objects, including: cubes, spheres, cones, cylinders, pyramids. 
G 


Grade 3 
Algebraic Thinking 
Fluently add and subtract within 1000. 
OA 
NS 
MP 
Understanding of the meanings of multiplication and division. 
OA 
NS 
MP 
Read and write decimals to thousandths using baseten numerals, number names, and expanded form, (eg., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000)). 
OA 
NS 

Operations 
Multiply onedigit whole numbers by multiples of 10 in the range 1090. 
NF 
NS 
MP 
Understanding of fractions on a number line diagram by defining the interval from 0 to 10. 
NF 


Compare two fractions with the same numerator or the same denominator by reasoning about their size. 
NF 


Representing numbers equal to, less than, and greater than one. 
NF 
EE 

Basic Geometry 
Measuring area for 2D shapes including: triangles, squares, rectangles, circles. 
G 
MD 

Calculating area of triangles, squares, rectangles, circles. 
G 


Partition of shapes into parts with equal areas. 
G 

MP 
Grade 4 
Multiplication & Comparision 
Describing multiplication equation as a comparison (eg., 35=5*7). 
EE 

Gain familiarity with factors and multiples. 
EE 

Understanding of place value to 1,000,000 
NS 
MP 
Understanding of fraction equivalence and operations with fractions (eg., 15/9 = 5/3). 
NF 

Conversion 
Measurement and conversion of measurements including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. 
MD 

Angle Determination 
Measure angles in wholenumber degrees using a protractor. 
MD 

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. 
G 

Classify twodimensional figures based on the presence or absence of parallel or perpendicular lines. 
G 

Identify linesymmetric figures and draw lines of symmetry. 
G 

Grade 5 
Interesting Calculations 
Add and subtract fractions with unlike denominators 
NS 

MP 
Understandings of multiplication to multiply a fraction or whole number by a fraction. 
NS 

Finalize fluency with multidigit addition, subtraction, multiplication, and division (with fractions also). 
EE 
NS 
Basic Expressions 
Using parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 
EE 
F 
Volume Estimation 
Understanding concepts of volume measurement. 
MD 

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 
MD 

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 
MP 

Knowing Coordinate Plane 
Graph points on the coordinate plane to solve realworld and mathematical problems. 
MP 

Grade 6 
Ratio & Expressions 
Understanding the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 
RP 

MP 
Write, read, and evaluate expressions in which letters stand for numbers (eg., y + y + y = 3y) 
EE 

Solve realworld and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 
EE 
F 
Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem 
EE 
NF 
3D Calculations 
Find the volume of a right rectangular prism with fractional edge lengths 
MD 

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 
MD 

Knowing Statistics 
Recognizing a statistical question. (eg., How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question) 
MP 

Measuring of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation) 
MD 

Grade 7 
Ratio in Real World 
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. 
RP 


Understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. 
RP 


Advanced Arithmetic 
Explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. 
F 


Convert a rational number to a decimal using long division 
NF 


Introduction of π 
Solving problems involving the area and circumference of a circle and surface area of threedimensional objects. 
MP 


Basic Probability & Sampling 
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. 
MP 


Comparing two data distributions and address questions about differences between populations. 
MD 


Develop a probability model and use it to find probabilities of events. 
MD 


Grade 8 
Roots and Cubes 
Using square root and cube root symbols and evaluate square roots of small perfect squares and cube roots of small perfect cubes. 
F 


Introducing Linear Equations 
Analyzing linear equations and solve a variety of problems 
EE 


Solve pairs of simultaneous linear equations. 
EE 


Functions 
Define, evaluate, and compare functions. 
F 
RP 

Use functions to model relationships between quantities. 
F 


Introducing Pythagorean Theorem 
Understand and apply the Pythagorean Theorem. 
MP 


Solve realworld and mathematical problems involving volume of cylinders, cones, and spheres. 
MP 
MD 

Basic Statistics 
Investigate patterns of association in bivariate data. 
MD 
MP 
