Inquiry Lab WHEN is the sum of two integers a negative number? In football, forward progress is represented by a positive integer. Losing yardage is represented by a negative integer. On the first play, a team lost 5 yards. On the second play, the team lost 2 yards. What was the team’s total yardage on the two plays? Hands-­‐On Activity 1 Lets write a numerical expression that describes the above scenario. (MUST READ) The following two properties are important when modeling operations with integers. ü When one positive counter is paired with one negative counter, the result is called a zero pair. The value of a zero pair is 0. ü You can add or remove zero pairs from a mat because adding or removing zero does not change the value of the counters on the mat. Hands-­‐On Activity 2 Use counters and the number line to find -­‐4 + 2 1. How would the models and sum change if the addition expression was 4 + (-­‐2)? Work with a partner. Find each sum. Show your work using counters and a number line. 5 + 6 -­‐3 + (-­‐5) -­‐5 + (-­‐4) 7 + 3 -­‐6 + 5 -­‐2 + 7 8 + (-­‐3) 3 + (-­‐6) 2. Study the exercises in which both addends are negative. What do you notice about the sum? 3. Study the exercise in which one addend is negative and one is positive. What do you notice about the sum? Work with a partner to complete the table. Addition Sign of Sum Justify Expression 5 + (-­‐2) -­‐6 + 2 7 + (-­‐12) -­‐4 + 9 -­‐12 + 20 15 + (-­‐18) 4. Model with Mathematics: Write a rule you can use to find the sum of two negative integers without using counters or a number line. 5. Model with Mathematics: Write a rule you can use to find the sum of a positive integer and a negative integer without using counters or a number line. 6. Write two addition sentences where the sum is zero. Describe the numbers. 7. WHEN is the sum of two integers a negative number?