Equivalent Expressions

Identifying Equivalent Expressions

6.EE.A.4

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Lesson Goals:

- Identify two equivalent expressions in different forms. - Recognize like terms in at least three examples. - Come up with one real world example using equivalent expressions. - Build on our understanding of simplifying expressions and factoring. - Discuss and explain our thinking to peers or to the group.

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Norms:

Be respectful of peers and their responses. Ask questions! Collaborate with your group. There is never one set way to understand something. Be honest during group check-in times.

Review

I can use prior knowledge to make conclusions about new material.

Now, identify the like terms in the following expression (underline, circle, etc.) and simplify the expression. 6x - 2 - x + 8

6 + 7x - 13 In this scenario, the only terms with the same base are 6 and -13. So, we combine the two to simplify our problem. Simplified: 7x - 7

Examples:

Recognize and combine Like Terms

Math Grade 6

What do we already know about like-terms?

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01

Simplify the following expression with your teammates, make sure to break up terms into seperate forms of multiplication (i.e. 4x3 + 2x1). 2 (5x + 7)

4 (3x +1) Here, we will distribute the 4 to both 3x and the 1. This is an example of the Foil Method. (4)(3x) + (4)(1) Simplified: 12x + 4

Examples:

Foil Method and Factoring

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Math Grade 6

02

3(7x - 1) 7x + 2 4x - 3 + 2x If we look at these exressions, we can identify that the only expression in mx + b form is 7x + 2. This means we can leave the expression as is. The next step, is to look for like terms, since there are no like terms in 3(7x - 1), we can move to 4x - 3 + 2x. This expression does have like terms, and can be simplified to 6x - 3. With the last expression we can distribute the 3, creating a simplified expression of 6x - 3. Meaning, 3(7x - 1) and 4x - 3 + 2x are equivalent because both simplify to 6x - 3.

Examples:

Ask yourself, "Is this expression already in mx + b form?" If the answer is no, look for opportunities to combine like terms. If there are no like terms, look to simplify the expression through multiplication (FOIL).

Step-by-Step:

Making Connections

Math Grade 6

What are the steps we can take to identify equivalent expressions?

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Equivalent Expressions Example

Math Grade 6

Try it on your own!

Real-Life Examples

How can we use equivalent exressions in daily life?

Real Life Example

Math Grade 6

At the begining of the week, Jake has "x" amount of basball cards in his collection. Every Friday, he buys 2 cards from the comic book store after school. Write an expression that is equivalent to the amount of baseball cards Jake has after 3 weeks.

Questions?

Brandon Block, Sarah Sneed

01

Like-Terms

Math Grade 6

Like terms are parts of an equation that share a common variable or no variable at all. These terms can be positive, or negative, and can be combined through addition and subtraction. Example: 6x and -10x.

03

Equivalent Expressions

Math Grade 6

We can use our knowledge of like terms and simplifying. First, we look for any like terms in the expression. If there aren't any like terms, look for expressions that can be simplified through multiplication or foil. If the expression is already in mx + b, then leave it as it is. Once all expressions are simplified, compare.

02

Simplifying

Math Grade 6

Through order of operations like PEMDAS and the Foil Method, we can create expressions that are much easier to understand. One of the easiest ways to identify whether or not an expression is simplified is to ask yourself: Is this in mx + b form?