1. Equivalent Expressions
Objective: To create & identify equivalent expressions by simplifying.

2. Standards: MCC6. EE. 2b, MCC6. EE. 3 and MCC6. EE
Standards: MCC6.EE.2b, MCC6.EE.3 and MCC6.EE.4 (Identify parts of an expression, apply math properties to generate equivalent expressions, and identify when two expressions are equivalent) Essential question: How can I tell when two expressions are equivalent?

3. Equivalent Expressions
In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms.
See if you can create a definition for the word term given the examples on this page. x 3
7x – 3y y +
term
term
term
term
term

4. Let’s look at some vocabulary
A term can be a number, a variable, or the product of numbers and variables. How close was your definition to the actual definition? 3c 35 -2 2c d2 d 2a 5b

5. Let’s look at some vocabulary
An expression is a collection of terms and operations. Terms in an expression are separated by + and –.
35 + 2a
3c + 2
7c - 2c4
2c + 5c
5d2 + 2d2
2(a + 15)

6. Let’s look at some vocabulary
A coefficient is the number multiplying the variable. A variable standing alone, like y, is said to have a coefficient of 1. So y = 1y
12a k 3c 7 x
2c4 5c
15q d2

7. Let’s look at some vocabulary
Like terms are terms with same variable raised to the same power. Constants, like 5, ½, and 3.2, are also like terms.
12 + 3
k + 2k
2c4+ c4
3c+2c
2d2 + d2
15a – 5a

8. You try… Work with a partner to simplify each expression.
In other words, combine like terms!!!

9. Let’s look at some vocabulary
What would be the definition of unlike terms be now that you know what like terms are?
Like Terms
Unlike Terms
3x and 2x
w and 3w
5 and 1.8
5x2 and 2x
6a and 6b
3.2 and n
The exponents
are different.
The variables
are different
Only one term
contains a
variable

10. Kicking things up a notch!
A number and a variable are unlike terms.
7 and x are unlike terms.
Terms that use different variables are unlike terms.
3z, b and 2x are unlike terms.
Terms that use the same variable but different powers are unlike terms.
5x, x2, and 2x3

11. Jack put the fruit shown above in his grocery cart
Jack put the fruit shown above in his grocery cart. The cashier needs all of the same fruit together in piles. Combine the fruit correctly and count the total for each fruit.
3 bananas
2 apples
4 strawberries

12. x 1 2x 3 x2 x2
Combining like terms in algebra is really the same idea, but instead of combining the same fruit, we combine like (same) terms. 3x
2x2 4

13. Identifying Like Terms
Identify like terms in the list. Look for like variables with like powers.
3t w t v w v
Identify like terms in the list.
2x y x z y z

14. When like terms are added or subtracted….
…the coefficient changes
6t – 4t
An expression is simplified when…
There are no ( ) or
other grouping
symbols.
When there are NO
like terms left to be
combined.

15. Let’s Try More Problems Together
45x – 37y + 87
An expression is simplified when…
There are no ( ) or
other grouping
symbols.
When there are NO
like terms left to be
combined.

16. Let’s Try More Problems Together
5y + 3y
An expression is simplified when…
There are no ( ) or
other grouping
symbols.
When there are NO
like terms left to be
combined.

17. Let’s Try More Problems Together
3a2 + 5b + 11b2 – 4b + 2a2 – 6
An expression is simplified when…
There are no ( ) or
other grouping
symbols.
When there are NO
like terms left to be
combined.

18. Let’s Try More Problems Together
Write an expression for the perimeter of the triangle. Then simplify the expression.
An expression is simplified when…
There are no ( ) or
other grouping
symbols.
When there are NO
like terms left to be
combined.
2x + 1
2x + 1 x