MS After School Intervention
Unit: Simplifying Expressions
Theme: Entertainment
Day 4 Lesson
Objective
Students will simplify algebraic expressions represented as physical models by
combining like terms.
Common Core Standards:
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 expression y  y  y and 3y are equivalent because they name the same
number regardless of which number y stands for.
7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand
linear expressions with rational coefficients.
7.EE.2 Understand that rewriting an expression in different forms in a problem context
can shed light on the problem of how the quantities in it are related. For example, a +
0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
Materials
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Overhead projector or document camera
Tape
White boards (or page protectors with white paper)
Envelopes or folders
QuietShape algebra tiles
Markers
Erasers
Six pieces of paper for seek and solve activity
“Algebra Tiles Mix Up” resource sheets (cut prior to lesson and place in
envelopes, one set per pair)
“Design It” resource sheets (one per student)
Entertainment Warm Up (10 minutes)
Arrange students into groups of three or four and present the class with the following
scenario:
“You and a group of friends are going to a baseball game. Each ticket costs $10.00.
While at the game, your friend Shannon buys a bag of peanuts for $3.50 and a large soda
for $6.00 for everyone to share. Then, your friend, Ricardo purchases two bags of cotton
candy for $3.75 a piece. Finally, since you are all very thirsty after devouring all of the
cotton candy, you buy the group two large lemonades for $4.25 each. Write an
expression to model the total cost of your trip to the baseball game.”
Answer: (Answers may vary depending on format written by students. 10x  25.50 or
10x  3.5  6  7.5  8.5 )
Ask groups to develop an expression to model the situation and then have them answer
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the following questions:
1. How did you develop your expression?
2. What does your variable represent?
3. What would be the total cost of the game if you and 7 of your friends attended?
Explain how you got your answer.
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Answers:
1. Explanations may vary.
2. Number of people attending the game in your group.
3. 10(8)  25.50  $105.50
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Discussion Topics: If students did not combine the costs of all of the food and drink
items, ask them, “How can we make our expression simpler?” or “How can we combine
some of these terms?” Remind them that today’s lesson will focus on making
expressions “simpler” or in other words, combining like terms.
Algebra Tiles Exploration (10 minutes)
Explain to students that today they will be learning how to simplify expressions, like
some of them already did in their groups for the baseball problem. Explain that they will
be using Algebra Tiles to help simplify these expressions.
Teacher Option: Create large Algebra Tiles using colored paper to match the student set
of Algebra Tiles.
If using the large Algebra Tiles, place an example of each type on the board. Explain to
students that the green rectangular rods represent x and the red rectangular rods
respresent x . Then, explain that the yellow squares represent positive one and the red
squares represent negative one. If students have used the red/yellow counters for
operations with integers, remind them that the squares are the same thing. Ask students
 x and the negative x . The students should be
what will happen when you have a positive
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able to recognize this is a zero pair. (Note: Refrain from using the x 2 tiles, until students
fully understand simplifying.)
problem, (Use an
Display on the board the following
expression so that all students will
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be able to participate.):
15 students: 3x  5  2x  3  2
20 students: 5x  5  3x  3  4
25 students: 6x  7  4x  5  3
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Have students volunteer to come up and model the expression in the order in which it is
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written on the board. Ask students, “How can I represent “positive three x?” Then, have
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three students come up to hold a green rectangular rod. Then, repeat for each term.
Introduce the vocabulary words: coefficient, term, and constant as the expression is
being represented.
Explain to students that when they “simplify” an expression, they will be combining all
of the “like terms.” Ask them to explain what they think a “like term” is. Then, have the
students simplify the expression by grouping themselves with other like terms. Once
they are standing with the like terms, have the students cancel out any “zero pairs” they
see by having those students sit down. (The only students remaining should represent the
answer of the simplified expression.) Together, translate the student expression into an
algebraic expression on the front board. Point out to students how much easier the
expression is to use when put into simplest form. Students try to simplify with the
variable first and the constant last.
Review with students the steps for simplifying an expression.
1. Show the problem using Algebra Tiles.
2. Group the like terms.
3. Simplify to find the final answer.
Answers:
15 Students: x  6
20 Students: 2x  4
25 Students: 10x  9
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Player/Coach
Activity (20 minutes)
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Pair students with a partner and assign one student to be the coach and one student to be
the player. Put up the following expressions on the board:
1.
2.
3.
4.
5.
x  3x 1 2x 10
5  5x  2x  3  7
4  3x  2  4 x  2  x
7x 1 3x  5  8
6  5  2x  3  4 x
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Each pair will need one whiteboard, marker, and eraser. The player will begin by
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“showing” the problem using the Algebra Tiles. Then, he or she will “group” the like
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terms, and finally, “simplify” to get the final answer. Once they translate their Algebra
Tile answer into their whiteboard, the coach will check his/her work. Then, the partners
will continue to take turns being the coach and the player.
After the given time, allow review the answers with students and clear up any
misconceptions. (ex. Remind students that “x” represents “1x” and “-x” represents “1x.”)
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Answers:
1. 4 x 11
2. 3x  9
3. 8x or 8x  0
4. 4 x  4
5. 2x  2
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“Algebra Tile Mix Up” Activity (20 minutes)
Pair students up with a different partner. Give each pair a color copy of the “Algebra Tile
Mix Up” cards cut up in an envelope. Together the students will simplify the algebraic
expressions given on the cards using algebra tiles and then match it with the correct card
that represents the answer in Algebra Tiles.
Answer: The original “Algebra Tile Mix Up” document displays the answer across from
the expression.
Simplifying Expressions Seek and Solve (15 minutes)
To make the Simplifying Expressions Seek and Solve write each of the problems on a
piece of paper folded in half. Then, on the inside of each problem, write the correct
answer, so students can check their work. Tape each problem around the room.
Seek and Solve Problems:
1. 20 13x  5  2x
2. 5  7x  2x  3
3. 2x  3 15x 16
4. 5x 1x  4  4 x  4
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5. 8x  25  6x 19
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6. 18  20  6x 13x
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Answers:
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1. 11x  25
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2. 5x  2
3. 13x 19
4. 0
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5. 2x  6
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6. 7x  38
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Then, arrange students into groups of three or four. Before allowing them to move
around the room to complete the Seek and Solve, present students with the following
expression:
21x 15  4 x  7
Then, ask students, “What would be the problem when simplifying the expression?”
(Possible Answer: We do not have enough Algebra Tiles.) Ask students to work with
their groups to simplify this expression in their own way. Give students three-five
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minutes to simplify the expression.
Then, as a class, discuss different strategies for
combining like terms without using Algebra Tiles.
Answer: 17x  8
In their groups, have the students move around the room to solve and check their answers
for the six problems.
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“Design-It!” Exit Ticket (10 minutes)
Have students complete the “Design It” exit ticket individually. Remind them to use the
correct vocabulary in their explanation.
Answer: 8t  9 (Written explanations will vary.)
Closure (5 minutes)
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Place the following vocabulary words under the document camera:
 coefficient
 term
 like terms
 constant
Have students summarize how to simplify an expression with and without Algebra Tiles
using each vocabulary word at least once.
Algebra Tile Mix Up
2x  3  4 x  7  x
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x  2  3x  7x  4
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x  6  2x  2  x  5
3  2x  4  x
1 x  5x  2x
9  x  2x  3  4 x
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6x  6  2x 10
2  x  2x  x  2
Name: _____________________
Date: _______________
Design It!
George and his friends have formed a dodge ball team and
they want to design t-shirts for their uniform. The Terrific
T-shirt Shop charges $8 per shirt plus a one-time charge
for each design. The team decides on a design that costs
$5.00 and a second design that costs $4.00. Write an
expression in simplest form to represent the total cost of the
t-shirts.
Your Team
Name Here!
http://www.clker.com/clipart-15794
 Using what you know about writing algebraic expressions, explain why
you answer is correct.
 If they order 20 t-shirts, what will be the total cost including the design?
Explain how you got your answer.