1. Unit 1 Day 2: Combining Like Terms Using Integers
Essential Questions: What is the coefficient of a variable? What are the rules for adding and subtracting integers?

2. Vocabulary
Variable: a letter used to represent a value that can change. The value “varies”, or changes.
Integer: a positive or negative whole number or zero.
Coefficient: the number in front of a variable.
Term: a variable and a coefficient put together.
Power: exponent of a variable.
Like Terms: terms that have the same variable and power.

3. Place the following in groups of like terms:
2x2, -3x, y, x2, -7y, 5y, -5x2, 10x, -2x
2x2
-3x y x2
10x
-7y
-5x2
-2x 5y
Variable?
Power? x x y 2 1 1

4. Example 1: Adding Integers
When adding integers, remember that same sign means you add. Different sign means you subtract, and your answer is the sign of the bigger number.
5 + -3
-5 + 3
(-5) + (-3)
(5) + (-3)
(-5) + (3)
Same Signs
Different Signs
Different Signs
(-5) + (-3) = -8
(5) + (-3) = 2
(-5) + (3) = -2

5. Example 2: Subtracting Integers
Remember that all subtracting means is the opposite of the next term.
-5 - 3
5 - 3
-5 - (-3)
(-5) + (-3)
(5) + (-3)
(-5) + (3)
Same Signs
Different Signs
Different Signs
(-5) + (-3) = -8
(5) + (-3) = 2
(-5) + (3) = -2

6. Example 3: Combining Like Terms
When we combine like terms, we just add or subtract the numbers in front of the variable. We can only do this if they have the exact same variable and power.
2x2 x2
-5x2
-3x
10x
-2x y
-7y 5y
(2) + (1) + (-5)
(-3) + (10) + (-2)
(1) + (-7) + (5)
(3) + (-5)
(7) + (-2)
(-6) + (5)
-2x2 5x
-1y or -y

7. You can also see these operations using positive and negative symbols
You can also see these operations using positive and negative symbols. Lets say that a is a negative value and a is a positive value.
= -8
5 + -3
= 2
-5 + 3
= -2

8. You can also see these operations using positive and negative symbols
You can also see these operations using positive and negative symbols. Lets say that a is a negative value and a is a positive value.
-5 - 3
(-5) + (-3)
= -8
5 - 3
(5) + (-3)
= 2
-5 - (-3)
(-5) + (3)
= -2

9. Example 4:
Each side of a triangle is multiplied by a common variable. Find the perimeter of the triangle.
3x ft
2x ft
36x in
In order to add these all together, they all need to have the same units.
12 in
1 ft
36x in 1 =
36x 12
= 3x ft

10. Example 5:
Each side of a triangle is multiplied by a common variable. Find the perimeter of the triangle.
3x ft
2x ft
3x ft
3x + 2x + 3x
(3) + (2) + (3) = 8
Perimeter = 8x ft

11. Example 6:
This graph shows the change in average sea level over a 5 year period.
a. What is the change from 2010 to 2011?
(100) - (-25)
(100) + (25)
125 feet
b. What is the change from 2010 to 2012?
(-75) + (25)
(-75) - (-25)
-50 feet

12. Summary
Essential Questions: What is the coefficient of a variable? What are the rules for adding and subtracting integers?
Use 1 minute to write 2 sentences answering the essential questions.