# What's Happening! - Unit 1

• ## Quarter 1 2018-2019 - Students in the 7th grade will begin the year with a unit called The Number System.  Below please find an outline of the unit, the mathematics standards that will guide our learning, and corresponding Khan Academy links that students may use for additional exposure to tutorials and practice problems associated with the unit.

The Number System

• Define, move between forms, and utilize rational numbers.

• Add, subtract, multiply and divide rational numbers.  Assess patterns for working with rational numbers.

• Design situations where opposite quantities equal zero. Discover and analyze the concepts of additive inverse.

• Determine the distance between rational numbers on a number line utilizing the idea of absolute values.

• Apply concepts relating the operation of subtraction to being equivalent to adding a negative.

• Fluently move between forms of rational numbers.

• Apply the associative property, commutative property, and distributive property to problem solving.

• 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.

• Solve real-world problems involving rational numbers.

Code Standard 7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. 7.NS.A.1a 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. 7.NS.A.1b 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.A.1c 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. 7.NS.A.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.NS.A.2a 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.A.2b 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.A.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.A.2d 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.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 