Unit 1 builds upon the understanding of rational numbers developed in 6th grade. This unit moves to explore and ultimately formalize rules for operations (addition, subtraction, multiplication, and division) with integers. Using both contextual and numerical problems, students explore what happens when negative numbers and positive numbers are combined. Repeated opportunities over time will allow students to compare the results of adding, subtracting, multiplying, and dividing pairs of numbers, leading to the generalization of rules. Fractional rational numbers and whole numbers should be used in computations and explorations.

__Standards (New standards for 2015/2016 in red)__**MGSE7.NS.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.**MGSE7.NS.1a**- Show that a number and its opposite have a sum of 0 (are additive inverses). Describe situations in which opposite quantities combine to make 0.*For example, your bank account is -$25.00. You deposit $25.00 into your account. The net balance is $0.00.*

**MGSE7.NS.1b**- Understand p + q as the number located a distance from p, in the positive or negative direction depending on whether q is positive or negative. Interpret sums of rational numbers by describing real world contexts.**MGSE7.NS.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 is the absolute value of their difference, and apply this principle in real-world contexts.**MGSE7.NS.1d**- Apply properties of operations as strategies to add and subtract rational numbers.**MGSE7.NS.2**- Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers.**MCC7.NS.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.**MCC7.NS.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.**MCC7.NS.2c**- Apply properties of operations as strategies to multiply and divide rational numbers.**MCC7.NS.3**- Solve real-world and mathematical problems involving the four operations with rational numbers.