Module 2 Lesson 3: Understanding Addition of Integers

Problem Set

1.Below is a table showing the change in temperature from morning to afternoon for one week.

a. Use the vertical number line to help you complete the table. As an example, the first row is completed for you.

Change in Temperatures from Morning to Afternoon

Morning Temperature	Change	Afternoon Temperature	Number Sentence
1C	rise of 3C	4C	1 + 3 = 4
2C	rise of 8C	10C	2 + 8 = 10
-2C	fall of 6C	-8C	-2 + (-6) = -8
-4C	rise of 7C	3C	-4 + 7 = 3
6C	fall of 9C	-3C	6 + (-9) = -3
-5C	fall of 5C	-10C	-5 + (-5) = -10
7C	fall of 7C	0C	7 + (-7) = 0

b. Do you agree or disagree with the statement: "A rise of -7C"? Explain.

 I disagree with this statement. We would say that the temperature fell 7C when we are talking about the temperature going down.


For questions 2-3, refer to the Integer Game.

2. Terry selected two cards. The sum of her cards is -10.
a. Can both cards be positive? Explain why or why not.

Both cards cannot be positive. In order for the sum of two cards to be negative, at least one of the cards must be a negative number.
 
b. Can one of the cards be positive and the other be negative? Explain why or why not.

One card can be positive and one card can be negative if the negative number has a larger absolute value. For example, suppose that Terry selected the cards 10 and -20. Her sum would be represented by 10 + (-20). Since we are adding integers with different signs, we subtract 20 - 10 to get 10. Since the absolute value of -20 is larger, then our answer would be -10.
 
c. Can both cards be negative? Explain why or why not.

 Both cards can be negative. For example, suppose that Terry selected the cards -4 and -6. Her sum would be represented by (-4) + (-6).  Since we are adding two negative integers, we have 4 + 6 = 10. Since both -4 and -6 are negative, our answer is -10.


3. When playing the Integer Game, the first two cards you selected were -8 and -10.

a. What is the value of your hand? Write an equation to justify your answer.

 -8 + (-10) = -18

When adding two negative integers, we add the absolute value of the integers and our answer is negative. We add 8 + 10 to get 18 and our answer would be - 18.

b. For part (a), what is the distance of the sum from -8? Does the sum lie to the right or the left of -8 on the number line?

 The distance of the sum from -8 would be 10 since the distance between -8 and -18 is 10. The sum lies to the left of -8 on a number line.

c. If you discarded the -10 and then selected a 10, what would be the value of your hand? Write an equation to justify your answer.

 If we discarded -10 and selected a 10, then our new hand would be -8 + 10 = 2. Since we are adding two integers with different signs, we subtract 10 - 8 to get 2. Since 10 has the bigger absolute value, then our answer is 2.


4. Given the expression 67 + (-35), can you determine, without finding the sum, the distance between 67 and the sum? Is the sum to the right or left of 67 on the number line?

 Since we are adding -35 to 67, then the distance between 67 and the sum is 35. The sum would be to the left of 67 on a number line.


5. Use the information given below to write an equation. Then create an "arrow diagram" of this equation on the number line provided below.

"The p-value is -4, and the sum lies 12 units to the right of the p-value."

-4 + 12 = 8

The p-value is the starting value and sum means that this is an addition problem. Since we are adding two integers with different signs, then we subtract 12 - 4 to get 8. Since 12 has the bigger absolute value, then our answer is 8.