Combining Like Terms

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SWBAT combine like terms.

Big Idea

How can we use order of operations to simplify expressions?

Do Now

10 minutes

At this point, students should be comfortable with algebra vocabulary, translating and evaluating algebraic expressions, and using the distributive property with algebraic expressions.  I will give them 5 minutes to complete the problems below.  As students work, I will circulate, looking for common mistakes.

1)  Write as an algebraic expression:  A number, x, decreased by the sum of 2x and 5

2)  63 x 24

3)  Evaluate 2x3 + 4x2 - 3x - 6 when x = 3

4)  Apply the distributive property to write equivalent expressions.      3(10a + 3b)

5)  Apply the distributive property to write equivalent expressions.      11f + 15f

6) Evaluate   6x + 21 + 3(2x + 7y) x = 3 and y = 4



Developing a Definition for Like Terms

10 minutes

For the first part of this lesson students will work with their groups on developing a distinction between like and unlike terms.  I will post the Combining Like Terms Chart on the board.  I will explain to students that the pairs in the left column are like terms and the pairs in the right column are called unlike terms.  I will pose the following questions to the class:

What similarities do you notice about the pairs in the left column?

What makes the terms in the right column "unlike"?

How can we define like terms?

After 5 minutes of group discussion, I will ask the groups to share out their thoughts.

Many students may notice that the pairs under the category of like terms share the same variable.

To probe further, I will ask:

Does the exponent help determine whether they are like terms?  

What do you notice about the last row?  

What about the order of the variables?  

What operation is xyz and xzy?

Students should notice that the exponents, as well as the variables, must be the same for like terms.  

They should recognize the operation as multiplication and therefore conclude that the order doesn't matter.

By this point, students have developed the definition, which I will formalize and share with the class.

Like Terms - Terms that have the same variables raised to the same exponent, but could have different coefficients.

It is important for students to know that: * We can only add and subtract like terms.


Mini Lesson

10 minutes

For this lesson I will introduce students to the concept of simplifying algebraic expressions.

As a class we will work through some examples and students will develop a set of steps.

Ex. 1 - Simplify 5n - 3n + 4n

Does this expression have like terms?

Students should recognize that since all the variables are n, then they are all like terms.

How can we combine these like terms?  Should I add 3n + 4n first?

Students should realize that the order of operations should be applied when combining like terms.

Ex. 2 - Simplify 12a - a + 8a

What is the coefficient of the second a?

Students should remember from a previous lesson that if there is no visible coefficient, then it is 1.  This will be important when simplifying this expression to 19a.

Ex. 3 - Simplify 13b + 2y + 5b +3y + 8

Does this expression have like terms?

Students should recognize that there are like terms, but different sets of like terms.  Before students move to combining like terms, we will use shapes to identify the like terms. (See Example 3 - Combining Like Terms) This will make it easier for students to simplify multi-variable algebraic expressions.  It is important to mention to students that they should include the operation in the shape so it doesn't get lost.

What do we do with the constant?

We will try another example, so students can have a set of steps to use.

Ex. 4 - Simplify 8a  + 2b + 5a  +31  - 9 + 3a - b

Do we have a set of steps for simplifying expressions that we can apply to this and other examples?

What did we do first?

1. Identify Like Terms

After we identify the like terms, what are we ready to do?

2.  Combine Like Terms

What do we do if there are constants?

3.  Combine Constants





Independent Practice

10 minutes

Students will have about 10 minutes to complete the independent practice.  I will advise them to use the steps that they developed during the lesson to help them combine like terms.

Independent Practice

Simplify the algebraic expressions.

1)5x + 6x

2)10y - 4y

3)4n + 3n + n

4)2a + 6y + 8a - 3y

5)6 + 2x + 12x + 4

6)3x + x3 + 9 + 8x3


Common Mistakes

Problem 3 - Students may forget that the third n has a coefficient of 1.  I will suggest to students that they write the "invisible 1", so they don't forget.

Problem 4 - Students may not subtract 6y minus 3y.  They need to be mindful of the operations and if they are using the shapes strategy, the operation would be within the shape.

Problem 6 - The x3 may confuse students and they may try to combine it with x.  I will refer them to our definition of like terms. 


Lesson Summary

5 minutes

To bring awareness to the common misconceptions that students may make, I will discuss them with students.

What would you advise another student to be careful of when simplifying expressions?

Students may mention:

- the "invisible 1"

- use order of operations

- add the constants

- like terms should have the same variable and the same exponent