# Common Core: The Number System

##### 8.NS.A2

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., π2). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to … Read More “8.NS.A2”

October 1, 2018
##### 8.NS.A1

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 eventually into a rational number.

October 1, 2018
##### 7.NS.A3

Solve real-world and mathematical problems involving the four operations with rational numbers.1

October 1, 2018
##### 7.NS.A2d

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.

October 1, 2018
##### 7.NS.A2c

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

October 1, 2018
##### 7.NS.A2b

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.

October 1, 2018
##### 7.NS.A2a

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.

October 1, 2018
##### 7.NS.A2

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

October 1, 2018
##### 7.NS.A1d

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

October 1, 2018
##### 7.NS.A1c

Understand subtraction of rational numbers as adding the additive inverse, p – 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.

October 1, 2018
##### 7.NS.A1b

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.

October 1, 2018
##### 7.NS.A1a

Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

October 1, 2018