1. Combining Like Terms

2. True or False? Explain your answer.
Warm Up
OBJECTIVE: Students will be able to determine if expressions are equivalent by combining like terms.
Language Objective: Students will be able to explain in words how to combine like terms.
True or False? Explain your answer. a. b. c. d.
True
True
False
(5 min) 5 minutes passed
In-Class Notes
Give students about 5 minutes to answer the four questions. Encourage students to explain their answers.
Click the slide to reveal the answers, having a discussion why they are true. (Students will explain their reasoning in different ways, all should be discussed as a group).
Part D: have the discussion that 3x = 3 times x and remind students x could represent any number. Ask students if x was 8, for example, would the statement still be true?
Preparation Notes
The purpose of this slide is to review the understanding that multiplication is repeated addition. A, B, and C lead up to part D. This lesson focuses around the notion of x + x + x = 3x. It is important for students to understand this before moving into the lesson.
Read the slide as it appears. Give students about 5 minutes to answer the questions; they need to explain their answers. Go over each question discussing why the equations are true. Students will have different explanations, all which need to be discussed as a group before moving on. Part D is crucial. Students must be reminded that 3x equals 3 times x. Also, it is important for students to understand that x is a variable and can be replaced with any number. Can suggest if x was a number, would the equation still be true?
True

3. We just combined all the x’s!
Explore- Using Tiles
Think back to the warm up
We just combined all the x’s!
Let each x represent a red tile.
So, how many tiles would we need? x x x
Can we represent 3x another way using tiles?
(5 min) 15 minutes passed
In-Class Notes
Read the slide as it appears.
Once the callout appears, click on the word ‘definition’ for the definition of combined to appear.
You MUST click on ‘click to go back’ to finish this slide.
Read the slide, asking if this is the only way to show 3x. Ask kids for suggestions.
2x + x will appear, but is also room for more discussion to reinforce the commutative property: is x + 2x the same?
Preparation Notes
NOTE: If teachers do not have any sort of manipulatives to demonstrate the explore activity, a worksheet with 8 X-tiles and 8 Y-tiles is provided. Copies would need to be made and cut out. Before reading this slide, hand out enough tiles for the next few slides. 8 X-tiles and 8 Y- tiles.
The goal of this explore is for students to use tiles to show how to combine like terms. Later in the explore, students will be asked to not use their tiles and will be given a set process to copy. Read the slide as it appears. After the 3x appears, students will be prompted that we just combined all the x’s. Once this appears, click at the bottom of the slide, ‘definition’ and the definition of combining will appear. Be sure to click on ‘click to go back’ to continue with this slide. The next question asks students if there is another way to write 3x using their tiles. (This standard focuses around identifying expressions that are equivalent, not necessarily expressions to be simplified in their lowest form.) The answer of 2x + x will appear. Ask students for suggestions before advancing the slide to see if anyone comes up with 2x + x. Suggestion: can also discuss why x + 2x would be the same since in the pervious lessons, commutative properties have been introduced. x x x +
Definition

4. + x x x Using your tiles, what would you get if you combined 2x + 4x?
Explore- Using Tiles
Turn and Talk…
Using your tiles, what would you get
if you combined 2x + 4x?
Now
combine! + x x x
(4 min) 19 minutes passed
In-Class Notes
Read the slide as it appears. Give students a few minutes to use their tiles to answer the problem.
Advance the slide for the x’s to appear. Students will be reminded to combine the x’s.
The next prompt will show all 6 x’s.
Read the questions similar to the last one, “is this the only way to show 6x?”
The next slide will show two different ways.
Preparation Notes
This part of the explore is to give students more practice using their tiles. Give students a few minutes to work on the problem on their own. Advance the slide for the x’s to appear. There is a reminder for students to combine the x’s; advancing the slide will demonstrate this with the answer of 6x to appear. Again, students will be asked if this is the only way to show 6x. The next slide will have two examples.
Is this the only way to show 6x?

5. + + 3x 3x + 5x + 1 x x x x x Is this the only way to show 6x?
Explore- Using Tiles
Turn and Talk…
Is this the only way to show 6x? + x x + 3x 3x + x x
(4 min) 23 minutes passed
In-Class Notes
Ask students for some suggestions.
The first answer to appear is 3x + 3x. The second answer is 5x + x.
When ready to show the tiles, advance the slide. There is not a reminder to combine the x’s, but after the 3x and 3x appear, ask students what to do next. Prompt to understand that we need to combine next.
Show the next example 5x + x. The one will appear in front of the x on this slide. It was not mentioned before, but is crucial to discuss it here. Also, this is a great opportunity to reinforce vocabulary from previous lessons: multiplicative identity.
The next slide is optional. By clicking at the bottom, ‘more practice’ an expression using y variables will be demonstrated. The next slide in this lesson is using both x and y variables, so the extra practice may be helpful for some students.
Preparation Notes
Ask students for some suggestions on a different way other than 2x + 4x to show 6x. The first answer that will appear is 3x + 3x. The second answer is 5x + x. This is a nice connection showing how you can start with the tiles and then end with the expressions.
Once ready to show students the tiles, advance the slide so 3x + 3x appears. Read through the slide reminding students to combine. (There is not a reminder to combine on this slide). As the second example appears, 5x + x, a one will appear in front of the x to show that this is just one x. Earlier in the lesson a single x did appear, but there was not any discussion on why the 1 is there. Now is the time to discuss this understanding and a great opportunity to reinforce the Identity Property of Multiplication. (This concept was in a previous lesson in this unit.)
The next example in the explore is using x and y variables, still using their tiles. If students need practice with the y variable, click at the bottom ‘more practice’ and an example will appear just using the y variable. Otherwise, advance to the next question in the exlpore. 5x + 1 x

6. y x x y y x x What would you get if you combined
Explore- Using Tiles
Turn and Talk…
What would you get if you combined
5x + 3y + 2x + y? Use your tiles. x x y + y y + x + x + + +
(4 min) 27 minutes passed
In-Class Notes
Read the slide as it appears. Give students a few minutes to work with a partner to answer the question.
Have students share their response with an explanation.
Advance the slide to show the visual representation.
Suggestion: may want to have review why y = 1y because of the Identity Property of Multiplication.
Have a discussion why 7x + 4y cannot combine to make 11xy. Point out the fact that the variables are not the same, therefore, cannot combine them.
Preparation Notes
Read the slide as it appears. Similarly to the previous slide, this slide is designed to answer the question using some sort of manipulatives. (The next slide demonstrates the process without using any manipulatives.) Give students a few minutes to work with a partner to come up with an equivalent expression. Ask for volunteers to share their results with an explanation. Advance the slide to show the visual representation. Suggestion: may want to review why y = 1y because of the Identity Property of Multiplication. Have the discussion with students why 7x + 4y cannot combine to make 11xy. Ask for suggestions, but make sure to point out the fact that the variables are not the same, therefore, cannot combine them.

7. Process 5x + 3y 2x + y + 1. Copy the expression
Summary- Process
Process
1. Copy the expression
2. Identify the like terms 5x + 3y 2x + y +
3. Rewrite using the
Commutative Property
4. Combine the variables
that are the same
(5 min) 40 minutes passed
In-Class Notes
Read the slide as it appears, each step at a time.
This is to give students a process to use every time when asked to find a equivalent expression.
Students may copy in their notebooks.
Connect at the end that 5x + 3y + 2x + y = 7x + 4y.
Preparation Notes
This slide ties in the previous slides all in one. The purpose of this slide is to give students a process to follow when combining like terms. Suggestion: have students copy this into their notebooks. Read the steps as they appear explaining that this was done using our tiles, but now try and not use tiles.
This is a great opportunity to emphasize in step three that we did not change the value of the expression since we used the Commutative Property.
This is the same example from the previous slides, so again, just make connection that 5x + 3y + 2x + y = 7x + 4y; we just combined the like terms to form an equivalent expression. There is room for discussion on why students want to combine like terms at this point in the lesson. The understanding that the simplified expression is easier to work with when substituting numbers in and that they are equivalent.

8. With your partner, write an equivalent expression for the following:
Summary- Quick Check
With your partner, write an equivalent expression for the following:
#1. 4a + 6b + 3a + 9b
#2. 15x – 4x + 12
#3. y + y + y
#4. 5y + 7z
7a + 15b
11x + 12 3y
(5 min) 45 minutes passed
In-Class Notes
Have students work on these problems with a partner.
Advancing the slide will show the answers. The visuals in identifying the like terms are different here. This is a great opportunity to discuss that students can provide any type of visual to classify the like terms.
Questions 4 does not have any like terms, therefore we do not underline, circle, or put a box around any term.
Preparation Notes
The purpose of this slide is to see if students grasped the lesson before they start their class work and to connect that combining like terms is the same as finding an equivalent expression. Students are encouraged to work with their partner. Give about 5 minutes on these problems. Through out this lesson, ‘equivalent expression’ was not used. At this point explain that combining the like terms is as if we are finding an equivalent expression. At the bottom, a definition of equivalent expression is provided if needed.
When discussing the answers, different way to identify the like terms will appear. This is a great opportunity to discuss that students can provide any type of visual to classify like terms. The last question does not have any like terms, therefore they cannot be combined and the expression stays the same.
5y + 7z
Click for
definition

9. Write an equivalent expression for the following expressions.
Practice- Partners
Write an equivalent expression for the following expressions. 1. 2. 3.
(10 minutes for the whole Practice) 55 minutes passed
Answer key is provided on the click.
Preparation Notes
This answers on this slide purposely does not provide visuals for the like terms. This a great opportunity for students to verbally explain what they combined and why. Point out the like terms, but again, there are not any visuals showing them.