eSpark is recommended for grades Kβ5, but provides content outside of this range to allow for classroom differentiation.

6.NS.1

**Dividing Fractions**

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

6.NS.2

**Divide Multi-Digit Numbers**

Fluently divide multi-digit numbers using the standard algorithm.

6.NS.3

**Operations with Decimals**

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

6.NS.4

**Common Multiples & Factors**

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

6.NS.5

**Positive and Negative Numbers**

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

6.NS.6.a

**Opposites of Numbers**

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

6.NS.6.b

**Graphing in the Coordinate Plane**

Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

6.NS.6.c

**Opposites of Numbers**

Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.7.c

**Absolute Value**

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.

6.NS.8

**Graphing in the Coordinate Plane**

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

eSpark is recommended for grades Kβ5, but provides content outside of this range to allow for classroom differentiation.

7.NS.1.a

**Add Rational Numbers**

Describe situations in which opposite quantities combine to make 0.

7.NS.1.b

**Add Rational Numbers**

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

7.NS.1.c

**Subtract Rational Numbers**

Understand subtraction of rational numbers as adding the additive inverse, p β q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

7.NS.1.d

**Subtract Rational Numbers**

Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2.a

**Multiply Rational Numbers**

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

7.NS.2.b

**Division of Rational Numbers**

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

7.NS.2.c

**Division of Rational Numbers**

Apply properties of operations as strategies to multiply and divide rational numbers.

7.NS.2.d

**Convert Numbers to Decimals**

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

7.NS.3

**Four Operations with Numbers**

Solve real-world and mathematical problems involving the four operations with rational numbers.

eSpark is recommended for grades Kβ5, but provides content outside of this range to allow for classroom differentiation.

8.NS.1

**Convert to Rational Numbers**

Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventual

8.NS.2

**Estimate Irrational Numbers**

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., ΟΒ²).

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