1. Understanding Addition of Integers

2. a. For each example above, what is the distance between 2 and the sum? b. Does the sum lie to the right or left of 2 on a horizontal number line? Vertical number line? c. Given the expression 54 + 81, can you determine, without finding the sum, the distance between 54 and the sum? Why? d. Is the sum to the right or left of 54 on the horizontal number line? On a vertical number line? Given the expression 14 + (−3), can you determine, without finding the sum, the distance between 14 and the sum? Why? f. Is the sum to the right or left of 14 on the number line? On a vertical number line?

5. Using Integer Chips Remember that every positive and negative combine to make zero

6. 3 + 6

7. 7 + -4

8. 5 + -9

9. -2 + -4

10. Did you notice anything about the sign of the sum? Can you create a rule for: – Adding numbers with the same sign – Adding numbers with different signs

11. Same Sign Sum RULE: Add integers with the same sign by adding the absolute values and using the common sign

12. Different Signs Difference RULE: Add integers with opposite signs by subtracting the absolute values and using the sign of the integer with the greater absolute value.

14. Thinking about the problem: Which addend has the greatest absolute value (length of the arrow)? What direction does this arrow point? What is the length of this arrow? What is the final sign? What is the direction of the resulting arrow?

15. Closure What role does the |−16| = 16 play in modeling the expression 2 + (−16)? Why do we keep the sign of the integer with the larger absolute value when adding numbers with different signs?

16. 1) a. Write an equation for the diagram to the right. b. Find the sum. c. What integers do the arrows represent? 2) How do the models for these two addition problems differ on a number line? How are they the same?