1. 21st Century Lessons – Teacher Preparation
Please do the following as you prepare to deliver this lesson:
Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets.
Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly.
Feel free to customize this file to match the language and routines in your classroom.
*1st Time Users of 21st Century Lesson:
Click HERE for a detailed description of our project.

2. Lesson Overview (1 of 4) Lesson Objective
Students will be able to determine if expressions are equivalent.
Language Objective: Students will be able to explain in words how to combine like terms
Lesson Description
This lesson is designed around the fact that students have prior knowledge around the properties of math. The Launch of this lesson is based around the notion that students are familiar with the Distributive Property. (The previous lesson in this unit of Expression and Equations focuses on the distributive Property.)
In this lesson, students are shown, through the use of tiles/cards, how expressions that look different really are equivalent. Students are given the opportunity to explore with several expressions and prove why two expressions are equivalent. To end the lesson students are given an exit slip for a quick assessment pertaining to this concept.

3. Lesson Overview (2 of 4) Lesson Vocabulary
Commutative Property: changing the order of numbers does not change the sum or product.
Expression: numbers and symbols grouped together that show the value of something.
Terms: a single number, variable, or numbers and variables multiplied together.
Like Terms: terms that have the same variable of power.
Materials
Tiles or chips (two different colors) or some other form of manipulatives; a template is provided that can be copied and cut. Copies of the class work, homework, and exit slip.
Common Core
State Standard
6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

4. 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
Agenda

5. Agenda: 1) Warm Up True or False?- Individual 5 minutes 2) Launch
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.
1) Warm Up
True or False?- Individual
5 minutes
2) Launch
What is the Area?- Whole Class
5 minutes
3) Explore
Using Tiles- Partners
17 minutes
4) Summary
No Tiles, Vocabulary, Process,
Quick Check- Partners, Whole Class
18 minutes
5) Practice
Partners
15 minutes
6) Assessment
Exit Slip- Individual
5 minutes

6. Launch- What is the Area?
What is the area of the rectangle? x 4 3 x 4 3 x 7 x 4 3 x 4x 3x 7x +
(5 min) 10 minutes passed
In-Class Notes
Give students a few minutes to find the area.
Ask students for answers they may have come up with. You may want to write some of their answers off to the side before showing the answer on the slide. If any suggested answers are incorrect, clarify why and redirect students to the correct responses.
If any students came up with 4x + 3x, ask for students to share their thinking. Advance the slide to show the visual of why the area is 4x + 3x. If they did not obtain this answer, advance the slide to explain and demonstrate why the area is 4x + 3x.
If any students came up with 7x, ask for students to share their thinking. Advance the slide to show the visual of why the area is 7x. If they did not obtain this answer, advance the slide to explain and demonstrate why the area is 7x.
Have a discussion with the students since both answers were derived from the same rectangle, that 4x + 3x must equal 7x. Ask students if they are convinced of this understanding. Advance the slide for 4x + 3x = 7x to appear. Ask students why this must be true? Can you make any connections to why it may be true? Explain to the students that this is what we will be doing today; proving problems like 4x + 3x = 7x.
Preparation Notes
NOTE: The understanding of this launch is obtained from the previous lesson in this unit, the Distributive Property. If students are not familiar with this model, this lesson can be shown without the launch.
The purpose of this slide is to show students that the area of this rectangle can be found in two ways. Some students will come up with 7x and others will come up with 4x + 3x. Ask students to share their responses, but do not advance the slide until all answers have been shared.
The answer 4x + 3x appears first. Go over in detail with students how the area was derived. As you advance the slide, the products of the areas appear to warrant a discussion.
Continue with the second answer 7x. Again, go over in detail with students how the area was derived. As you advance the slide, the 7 appears to warrant a discussion.
The focus of the launch is to connect that those who found the area to be 4x + 3x is the same as those who found the area to be 7x. Take time to discuss that 4x + 3x does equal 7x by explaining the logic that we started with the same rectangle, but different representations of the areas are actually the same. Click to show that 4x + 3x = 7x. Ask students why this might be; can they see any connections between the two expressions? The previous lesson in this unit was showing that two expressions are equal by substituting in a value for the variable. May want to demonstrate using a value for x to prove both expressions are equal. Explain to the students that today’s lesson is showing why two expressions like these are equal without substituting in valuing for x.
Area = 4x + 3x
Area = 7x
Agenda

7. 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
Agenda

8. + 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?
Agenda

9. + + 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
More
Practice
Agenda

10. y y y y x x 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 + 2y? Use your tiles. y + y y + y x x 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.
Agenda

11. Identify variables that are the same
Summary- No Tiles
How can we combine
without using tiles?
Identify variables that are the same 5x
5x + 3y + 2x + y + 3y + 2x y +
Commutative Property
Now Combine! +
(5 min) 32 minutes passed
In-Class Notes
Read the slide as it appears. Ask students if they have any suggestions how we can simplify this without using any tiles.
On the click the x variables will have a box around them and then the y variables will have circle around them. This is explained as identify variables that are the same on this slide.
Advancing the slide will move the x’s and y’s next to each other. Ask students, “why can we do this in math?” to reinforce vocabulary. Commutative Property will appear to remind students.
Ask students what they think we should do next. The next click will prompt students to combine the x’s and y’s.
The remaining of the slide will show the answers on the clicks.
Be sure to wrap up the slide by pointing out that 5x + 3y + 2x + y = 7x + 4y and that 7x and 4y cannot be combined.
Preparation Notes
The purpose of this slide is to show students how to simplify this expression without using tiles. Ask students if they have any suggestions how we can simplify this without using any tiles. Prompt student conversation around the fact that 5x and 2x can be combined since they are both x variables. Similarly with the 3y and y. This is what students gained from using the tiles.
Advance the slide and a box will appear around the x terms and a circle around the y terms. This is stated as “identifying variables that are the same” in the slide. More formal definition using terms and like terms will appear on the next slide.
Advancing the slide again, the terms will move so the x variables and the y variables next to each to other. Commutative Property will appear, again, great way to reinforce vocabulary. On the next click students will be reminded to combine and the answer will appear. Reinforce that 5x + 3y + 2x + y = 7x + 4y and that 7x and 4y cannot be combined.
Agenda

12. Vocabulary Summary- Vocabulary Example
Term: a single number, variable, or number and variables multiplied together.
are terms in this expression.
Like Terms: terms that have the same variable or power.
(3 min) 35 minutes passed
In-Class Notes
This is the vocabulary part of the summary.
Read the first definition out loud to the students. Ask them if they can figure out what the terms are.
Advance the slide for the answers to appear.
Read the definition for like terms. Again, ask students if they figure out the like terms.
Preparation Notes
This part of the summary is for students to learn the vocabulary when combining like terms. The definition of term and like terms are provided here.
Read the slide as it appears. The definition of a term appears first. Read the definition aloud to the students. Ask students what the terms are before advancing the slide. The terms will appear for students to see.
Like terms will appear next. Again, read the definition aloud to the students. Ask students what the like terms are in the expression provided. Advancing the slide will show the answers.
and
and
Agenda

13. 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.
Agenda

14. 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
Agenda

15. I. Model the following expression by drawing squares. Let = x = y a.
Practice- Partners
I. Model the following expression by drawing squares Let = x
= y a. b. +
(10 minutes for the whole Practice) 55 minutes passed
In-Class Notes
Hand out class work assignment.
Have students work with a partner to answer the questions.
Answer key is provided on the click.
Preparation Notes
This class work assignment is designed to give the teacher a quick assessment of what concepts students understood from the lesson. The second question may be a challenge for some students, but is a great way to start conversation with their partner.
The next three slides will provide the answers.
For part b of this question, students may have modeled the expression after using the Commutative Property, which is acceptable, since they are still equivalent. +
Agenda

16. II. Explain why the following statement is true.
Practice- Partners
II. Explain why the following statement is true.
2x and 4y are not like terms, therefore, you cannot combine them.
(10 minutes for the whole Practice) 55 minutes passed
In-Class Notes
Answer key is provided on the click.
Preparation Notes
The answer provided on this slide is a written explanation around like terms. Based on the previous lesson in this unit, students may have substituted values in for x and y to prove that 2x + 4y is not equal to 6xy. By clicking at the bottom, ‘another example’, students can see an example if values were substituted in for x and y.
Another
Explanation
Agenda

17. 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.
Agenda

18. IV. Explain Yvonne’s mistake in the following problem.
Practice- Partners
IV. Explain Yvonne’s mistake in the following problem.
Yvonne just added all the numbers together. She can add numbers that are the like terms, 8x and 6x, but not 2 since it does not have an x.
(10 minutes for the whole Practice) 55 minutes passed
In-Class Notes
Answer key is provided on the click.
Preparation Notes
Ask students for their responses first before showing the answer. Students will have different explanations than what is
provided, but all have the same meaning.
Agenda

19. Assessment- Exit Slip
Jose and Amy were asked to combine 7x + 2y + 6y + 3x. Decide who is correct. Explain.
Jose
7x + 2y + 6y + 3x
Amy
7x + 2y + 6y + 3x
Jose’s work
7x + 3x + 2y + 6y
10x + 8y
18xy
7x + 2y + 6y + 3x = 18xy
Amy’s work
7x + 3x + 2y + 6y
10x + 8y
7x + 2y + 6y + 3x = 10x + 8y
(5 min) 60 minutes passed
In-Class Notes
Hand exit slip to students with 5 minutes left in the class.
Students are encouraged to work on this individually and can be turned in before they leave.
It is suggested to go over the answer. Advancing the slide will show the both student’s work and then that Amy is correct.
Preparation Notes
Give a copy of the exit slip to each student. Have students work on the problem for a few minutes, individually. It is suggested to go over the problem discussing why Jose is incorrect and why Amy is correct. It is crucial to explain again why Jose was incorrect in adding the x and y together.
Agenda