| 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 problem-solving 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 base-ten 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 one-digit whole numbers by multiples of 10 in the range 10-90. |
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 whole-number degrees using a protractor. |
MD |
|
| Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. |
G |
|
| Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines. |
G |
|
| Identify line-symmetric 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 multi-digit 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 real-world 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 real-world 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 real-world 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 three-dimensional 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 real-world and mathematical problems involving volume of cylinders, cones, and spheres. |
MP |
MD |
|
| Basic Statistics |
Investigate patterns of association in bivariate data. |
MD |
MP |
|
