Add and Subtract Integers Learning Objective We will

Add and Subtract Integers Learning Objective: We will add and subtract positive and negative integers. Math NS 1. 3

What do we already know? • Positive integers are on the right side of zero. 4 • Negative integers are on the left side of zero. -4 • This means that they are opposites. Negative Positive -3 + 3 = 0

You know how to plot an expression on the number line and find the sum. 5 + -2 = 3 Step 1: Plot the first integer on the number line. Step 2: Plot the second integer on the number line beginning where the last number left off. -2 5

You know how to plot an expression on the number line and find the difference. 5 + -2= 3 Step 1: Plot the first integer on the number line. Step 2: Plot the second integer on the number line beginning where the last number left off. -2 5

You know how to plot an expression on the number line and find each sum. Step 1: Plot the first integer on the number line. Step 2: Plot the second integer on the number line beginning where the last number left off. -3 + -1 = - 4 -1 -3

You already learned that subtracting a negative integer gives the same solution as adding its opposite.

Vocabulary • Define integers: a positive or negative number. • Define a positive integer: whole numbers to the left of zero. • Define a negative integer: whole numbers to the right of zero. negative positive

Vocabulary Define absolute value: the distance from zero. Plot each of the integers below on a number line and then tell the absolute value of each. -1 (1) 2 (2) -5 (5) -1 -5 2

You already learned that subtracting a negative integer gives the same solution as adding its opposite. To help predict whether the sum of two integers will be positive or negative, you can use these rules.

1 st Variation Is the sum of 2 and 7 positive or negative? Rule: The sum of two positive integers is positive. Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. 2+7= 9 2 Solution: The sum of 2 and 7 is positive. 7

2 nd Variation Is the sum of -2 and -7 positive or negative? Rule: the sum of two negative integers is negative. Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. -2 + -7= -9 -7 -2 Solution: The sum of -2 and -7 is negative.

3 rd Variation Is the sum of -2 and 7 positive or negative? Rule: the sum of a positive integer and a negative integer will have the same sign as the integer with the greater absolute value. -2 + 7= 5 7 -2 Solution: The sum of -2 and 7 is positive. Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off.

Why is this important? If the temperature was 10ｰF at lunch time and dropped to -5ｰF in the evening. What is the difference between these temperatures? 10 - -5= 15 degrees Mauricio were at the corner store. Mauricio forgot his money and needs $10 to pay for his treats. If Omar let Mauricio borrow $10, Mauricio now has $10. - $10 + $10 = 0

Guided Practice - I Do It Rule: The sum of two positive integers is positive. 1 + 4= 5 Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. 1 4 Solution: The sum of 1 and 4 is positive.

Guided Practice - We Do It Rule: The sum of two positive integers is positive. 5 + 3= 8 Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. 5 Solution: The sum of 5 and 3 is positive. 3

Guided Practice - You Do It Rule: The sum of two positive integers is positive. 7 + 3= 10 Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. 7 Solution: The sum of 7 and 3 is positive. 3

Guided Practice - I Do It Rule: the sum of two negative integers is negative. -2 + -3= -5 Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. -3 -2 Solution: The sum of -2 and -3 is negative.

Guided Practice - We Do It Rule: the sum of two negative integers is negative. -1 + -4= -5 Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. -4 -1 Solution: The sum of -1 and -4 is negative.

Guided Practice - You Do It Rule: the sum of two negative integers is negative. Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. -4 + -6= -10 -6 -4 Solution: The sum of -6 and- 4 is negative.

Guided Practice - I Do It Rule: the sum of a positive integer and a negative integer will have the same sign as the integer with the greater absolute value. 4 - -2= 4 + 2= 6 Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. 4 Solution: The difference of 4 and -2 is positive. 2

Guided Practice - We Do It Rule: the sum of a positive integer and a negative integer will have the same sign as the integer with the greater absolute value. Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. 4 Solution: The difference of 4 and -6 is positive. 4 - -6= 4 + 6= 10 6

Guided Practice - You Do It Rule: the sum of a positive integer and a negative integer will have the same sign as the integer with the greater absolute value. Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off. 3 - -7= 3 + 7 = 10 3 Solution: The difference of 3 and -7 is positive. 7

Closure • What is a whole number to the right of zero? • It is a positive integer. • What is a whole number to the left of zero? • It is a negative integer • What is the distance from zero? • It is the absolute value. Negative Positive

Closure Decide if the sum or difference is positive or negative. Explain how you decided. Solve the expression. -10 + -6 = 8 - -6= Share with your partner one thing that you learned today.

Step 1: Change the expression to an addition by using the absolute value. Step 2: Plot the first integer on the number line. Step 3: Plot the second integer on the number line beginning where the last number left off.