73 – 84 - Combine Like Terms
Lesson
Focus
Materials
Grouping
Prerequisite
Knowledge
and Skills
Overview of
the lesson
Time
Number, operation, and quantitative reasoning: The student will
develop an initial conceptual understanding of uses of variables. The
student will apply basic properties of arithmetic in simplifying algebraic
expressions.
TI-73 Explorer™ or TI-84 Plus graphing calculator
TI-Navigator™
Student Activity sheets
Copy sets of Game Cards for Activity I
Copy of Algebra Tiles for each student.
Activity Center Expressions (Activity II, Part II a-g)
Pairs and group investigation
Students should have an understanding of basic operations with integers
along with some knowledge of variables and algebraic expressions.
Students may have limited experience in modeling algebraic expressions.
Key vocabulary words: terms (of an expression), like terms.
In Activity 1, students will play a card game similar to Rummy to
understand like terms. They will explore algebraic expressions. In
Activity 2, students will work with algebra tiles to combine like terms
and extend their learning by applying it to a graphical representation in
Activity Center.
Suggested for Activity 1:
Activity 2:
Activity I:
1. Open Navigator and Start Class.
2. Have students log in to NavNet.
3. Combining Like Terms Card Game is played with two or three people (called players). The
game cards are made up of sets of like terms: -a, a, 2a, 3a, through 12a. Another set has been
made for b terms and c terms. Included is a blank page to make additional cards if needed
with more variables, multiple variables, or exponents.
Rules of the Game
a. Each player is dealt 7 cards.
b. The remaining cards are placed face down (The draw pile)
c. The top card is flipped over to another pile (The discard pile)
d. Each player draws a card from the draw pile and looks for a 3 or 4 card set of like
terms, and places those cards face up on the table in front of them if they have any
cards of like terms. For example: 6a, 2a, a…
e. A player discards one card at the end of their turn; whether they have a play or just
draw. Each player will have7 cards in their possession at all times (includes the cards
on the table and those in their hand).
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f. The next player may choose to draw a card from the draw pile or use the top card of
the discard pile for their turn.
g. Play continues until someone discards their last card and has no cards left in their
hand. This player receives a 3 point bonus.
h. The player who is out of cards in their hand first, adds up the coefficients of their
expressions on the table. All other players subtract the coefficients of the cards in
their hand from the coefficients of the cards on the table.
i. The winner is the player with the highest value of their coefficients.
Alternate way to determine winner:
Teacher can decide to assign a value to the variables a, b, and c. Each player then
determines the value of their expressions. The player with the highest value is
declared the winner.
4. Pass out Activity I worksheet and have students complete.
5. Quick Poll their responses.
4p + p
x + 7x
r+r
k + 12k +23
6d + d + 15
14bx + 31bx + 9bx
10k – 3k + 5h
13 + 4b + 6b – 5
9n + 13 – 8n – 6
6. Discuss the following questions with the students.
a) What is a term?
b) What is the same in an expression containing like terms?
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c) What can be different in an expression containing like terms?
d) What does it mean to combine like terms?
e) Numbers without a variable could only be combined with…
f) When I had a hand of 3 or 4 cards from the game, combining them meant that I had to…
7. Wrap Up questions: use TI-Navigator Quick Poll for these sample questions.
Quick Poll (open response)
Which of the following terms are considered like terms? Simplify each expression.
1)
2x, 2, 4x
2)
4, 6, 8y
3)
9b, 3a, 5c
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Activity 2:
PART I
Using Algebra tiles and the key to create an expression for each example. Then, combine the like
tiles to explore the meaning of like terms.
Key
=1
Like terms have the
same variable
expression but do not
need to have the same
coefficient.
=x
To simplify an expression with variables and constants, students should group similar tiles together.
Then simplify.
Example 1) x + x + 1+ 1
Answer: 2x + 2
Example 2) x +
2 +
3x
+ 1
Answer: 4x + 3
What if we have to subtract? Shaded tiles can represent terms being subtracted.
Example 3)
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3x
-2
-x
4
+ 4
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Group similar tiles together.
Take away any zero pairs of tiles that are the same size but different colors then simplify.
Answer: 2x + 2
PART II:
In this activity students will explore that combining like terms will produce an equivalent linear
representation of the expression.
1. Open TI-Navigator and begin class.
2. Open Activity Center and make these settings
Tech Tip
Clear activity data before configuring the next activity. This will ensure no extra data or
information.
a. Contribute:
Equations
b. Configure:
# of equations per student = 1
c. Check the following:
Let students view graphs of equation
Let student resubmit equation
d. Students start with:
Empty equations
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Press OK
Window Settings:
X min -15 X max 15
Y min -15 Y max 15
X Scale 1
Y Scale 1
3. Instruct the students to select Activity Center from TI-Navigator Home Screen.
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4. On the computer, click on the Graph-Equation tab and enter the first equation.
5. Highlight the equation and go to View and select Mask Teacher Input to hide the equation.
Press Start Activity to begin.
6.
Students then can enter in their expression at Y1
The following are saved Activity Center settings.
Expressions to try:
a. 2x + 7 + 5x
b. x + 4 + 3x
c. 4x + 5 - 3x
d. 2x + 3 + 4x + 5 + x
e. x + 4 – x
Try these for an extension:
f. x2 + 2x2
g. 2x2 + x + 4 + x2 + 3x
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7.
Teacher may pause the activity to clarify the expression.
8.
Students’ graphs that are correct will match the teacher’s graph.
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Name ______________________________Class __________________Student Activity Sheet
Activity 2: (page 1 of 2)
PART I
Using Algebra tiles and the key, create an expression for each example. Combine the like tiles to
explore the meaning of like terms.
Key
=1
Like terms have the
same variable. They
do not need to have
the same coefficient.
=x
To simplify an expression with coefficients, variables and constants students should group similar
tiles together. Then simplify. Draw the before simplified and after simplified tiles.
Example 1)
x + x + 1+ 1
Example 2)
x +
2 +
3x
+ 1
What if we have to subtract? Shaded tiles can represent terms being subtracted.
Example 3)
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3x
-2
-x
9
+ 4
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PART II-(page 2 of 2)
Expressions to try:
First, simplify the following expressions. Select Activity Center from the TI-Navigator home
screen. The teacher will send you a Y1 prompt to enter in your simplified expression.
2x + 7 + 5x
x + 4 + 3x
4x + 5 - 3x
2x + 3 + 4x + 5 + x
x+4–x
x2 + 2x2
2x2 + x + 4 + x2 + 3x
1. What did you observe when you entered your simplified expression and pressed enter?
2. What would you see if you entered your expression incorrectly?
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Name ______________________________Class __________________Student Activity Sheet
Activity I Practice worksheet Combine Like Terms
4p + p
x + 7x
r+r
k + 12k +23
6d + d + 15
14bx + 31bx + 9bx
10k – 3k + 5h
13 + 4b + 6b – 5
9n + 13 – 8n – 6
Complete the following statements
1. What is a term?
2. What is the same in like terms?
3. What can be different in like terms?
4. What does it mean to combine like terms?
5. Numbers without a variable could only be combined with…
6. When I had a group of 3 or 4 cards, combining them meant that I had to…
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Intentionally left blank to have teachers complete the cards then print for their class
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Algebra Tiles for Activity II: White Positive-Shaded Negative
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