Corinne: I m thinking of a number between 220 and 20. What s my number? Benjamin: Is it 25?
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1 Walk the Line Adding Integers, Part I Learning Goals In this lesson, you will: Model the addition of integers on a number line. Develop a rule for adding integers. Corinne: I m thinking of a number between 220 and 20. What s my number? Benjamin: Is it 25? Corinne: Lower. Benjamin: 22? Corinne: That s not lower than 25. Benjamin: Oh, right. How about 211? Corinne: Higher. Benjamin: 28? Corinne: Lower. Benjamin: 29? Corinne: You got it! Try this game with a partner. See who can get the number with the fewest guesses. 4.2 Adding Integers, Part I 205
2 Problem 1 Adding on Number Lines 1. Use the number line and determine the number described by each. Explain your reasoning. a. the number that is 7 more than 29 b. the number that is 2 more than 26 c. the number that is 10 more than 28 d. the number that is 10 less than 6 e. the number that is 5 less than 24 f. the number that is 2 less than Chapter 4 Addition and Subtraction with Rational Numbers
3 A number line can be used to model integer addition. When adding a positive integer, move to the right on a number line. When adding a negative integer, move to the left on a number line. Example 1: The number line shows how to determine Step 1 5 Step 2 8 Example 2: The number line shows how to determine 5 1 (28). 8 5 Step 1 Step 2 2. Compare the first steps in each example. a. What distance is shown by the first term in each example? b. Describe the graphical representation of the first term. Where does it start and in which direction does it move? Why? c. What is the absolute value of the first term in each example? Remember that the absolute value of a number is its distance from Adding Integers, Part I 207
4 3. Compare the second steps in each example. a. What distance is shown by the second term in each example? b. Why did the graphical representation for the second terms both start at the endpoints of the first terms but then continue in opposite directions? Explain your reasoning. c. What are the absolute values of the second terms? 4. Use the number line to determine each sum. Show your work. a b. 3 1 (27) Chapter 4 Addition and Subtraction with Rational Numbers
5 c (27) 5 d Notice that the first term in each expression in parts (a) through (d) was either 3 or (23). a. What do you notice about the distances shown by these terms on the number lines? b. What is the absolute value of each term? 6. Notice that the second term in each expression was either 7 or (27). a. What do you notice about the distances shown by these terms on the number lines? b. What is the absolute value of each term? 4.2 Adding Integers, Part I 209
6 7. Use the number line to determine each sum. Show your work. a b. 9 1 (25) 5 c (25) 5 d Chapter 4 Addition and Subtraction with Rational Numbers
7 8. Notice that the first term in each expression in parts (a) through (d) was either 9 or (29). a. What do you notice about the distances shown by these terms on the number lines? b. What is the absolute value of each term? 9. Notice that the second term in each expression was either 5 or (25). a. What do you notice about the distances shown by these terms on the number lines? b. What is the absolute value of each term? How is knowing the absolute value of each term important? 4.2 Adding Integers, Part I 211
8 10. Use the number line to determine each sum. Show your work. a b. 8 1 (22) 5 c (22) 5 d Use the number line to determine each sum. Show your work. a Chapter 4 Addition and Subtraction with Rational Numbers
9 b. 4 1 (211) 5 c (211) 5 d In Questions 4 through 11, what patterns do you notice when: a. you are adding two positive numbers? b. you are adding two negative numbers? c. you are adding a negative and a positive number? Can you see how knowing the absolute value is important when adding and subtracting signed numbers? 4.2 Adding Integers, Part I 213
10 13. Complete each number line model and number sentence. a b c d Be prepared to share your solutions and methods. 214 Chapter 4 Addition and Subtraction with Rational Numbers
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