Write an integer for each situation. 1. stock market down 56 points 2. a score of 3 3. a bank deposit of $25 Evaluate each expression. 4. 5. 6. What is the value of if k = −6 and m = −2 Course 2, Lesson 3-2

ANSWERS 1. −56 2. 3 3. 25 4. 19 5. 14 6. 4 Course 2, Lesson 3-2

WHAT happens when you add, subtract, multiply, and divide integers? The Number System WHAT happens when you add, subtract, multiply, and divide integers? Course 2, Lesson 3-2

The Number System 7.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. 7.NS.1a Describe situations in which opposite quantities combine to make 0. 7.NS.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.1d Apply properties of operations as strategies to add and subtract rational numbers. Course 2, Lesson 3-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Mathematical Practices The Number System 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics 7 Look for and make use of structure. Course 2, Lesson 3-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

To add integers with the same sign The Number System To add integers with the same sign To add integers with different signs Course 2, Lesson 3-2

opposites 2 and –2 additive inverse The Number System opposites 2 and –2 additive inverse Course 2, Lesson 3-2

Add Integers with the Same Sign The Number System Add Integers with the Same Sign Words To add integers with the same sign, add their absolute values. The sum is: positive if both integers are positive. negative if both integers are negative. Examples 7 + 4 = 11 −7 + (−4) = −11 Course 2, Lesson 3-2

Add Integers with Different Signs The Number System Add Integers with Different Signs Words To add integers with the different signs, subtract their absolute values. The sum is: positive if the positive integer’s absolute value is greater. negative if the negative integer’s absolute value is greater. Examples 9 + (−4) = 5 −9 + 4 = −5 Course 2, Lesson 3-2

How did what you learned today help you answer the The Number System How did what you learned today help you answer the WHAT happens when you add, subtract, multiply, and divide integers? Course 2, Lesson 3-2

How did what you learned today help you answer the The Number System How did what you learned today help you answer the WHAT happens when you add, subtract, multiply, and divide integers? Sample answers: The sum of two positive integers is positive. The sum of two negative integers is negative. To find the sum of two integers with different signs, subtract their absolute values and use the sign of the integer with the greater value. Course 2, Lesson 3-2

The Number System Ratios and Proportional Relationships Find the sum –3 + (– 5) and the sum – 3 + 5. Then write a few sentences comparing and contrasting the expressions. Course 2, Lesson 3-2