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Unit 1-Operations with Rational Numbers

Unit 1:

Unit 1: This unit builds upon the student's understanding of rational numbers that was developed in 6th grade. In Grade 7, learning now moves to explore and ultimately formalizing rules for operations (addition, subtraction, multiplication, and division) with integers. Using both contextual and numerical problems, students should 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 the rules. Fractional rational numbers and whole numbers should be used in computations and explorations. Students will be able to give contextual examples of integer operations, write and solve equations for real-world problems and explain how the properties of operations apply. Real-world situations could include profit/loss, money, weight, sea level, debit/credit, football yardage, etc.

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**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 balance 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 number line 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 and of fractions to multiply and divide rational numbers.

**MGSE7.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.

**MGSE7.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.

**MGSE7.NS.2c** Apply properties of operations as strategies to multiply and divide rational numbers.

**MGSE7.NS.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.

**MGSE7.NS.3** Solve real‐world and mathematical problems involving the four operations with rational numbers.

Video on Negative Numbers called Integers

Adding and Subtracting Integers

Multiplying and Dividing Integers

GAMES: Reviewing Integers

PRACTICE: Adding and Subtracting Integers

Multiplying and Dividing Integers

Integers - An integer is a whole number that can be positive, negative, or zero.

Example of integers are: -5, 1, 5, 8, 97, and 3,043.

Examples of numbers that are not integers are: -1.43, 1 3/4, and 3.14.