Combine Like Terms

73 – 84 - Combine Like Terms

Lesson Focus / 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.
Materials / 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)
Grouping / Pairs and group investigation
Prerequisite Knowledge and Skills / 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.
Overview of the lesson / 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.
Time / 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).

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.

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?

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.

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
/ Like terms have the same variable expression but do not need to have the same coefficient.

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) 3x - 2 - x + 4

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

Contribute: Equations

Configure: # of equations per student = 1
Check the following: Let students view graphs of equation

Let student resubmit equation

Students start with: Empty equations

Press OK

Window Settings:

X min -15 X max 15 X Scale 1

Y min -15 Y max 15 Y Scale 1

3. Instruct the students to select Activity Center from TI-Navigator Home Screen.

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

7. Teacher may pause the activity to clarify the expression.

8. Students’ graphs that are correct will match the teacher’s graph.

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
/ Like terms have the same variable. They do not need to have the same coefficient.

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) 3x - 2 - x + 4

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?
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…

1a / 2a / 3a
4a / 5a / 6a
7a / 8a / 9a
10a / 11a / 12a
-1a / -2a / -3a
-4a / -5a / -6a
-7a / -8a / -9a
-10a / -11a / -12a
1b / 2b / 3b
4b / 5b / 6b
7b / 8b / 9b
10b / 11b / 12b
-1b / -2b / -3b
-4b / -5b / -6b
-7b / -8b / -9b
-10b / -11b / -12b
1c / 2c / 3c
4c / 5c / 6c
7c / 8c / 9c
10c / 11c / 12c
-1c / -2c / -3c
-4c / -5c / -6c
-7c / -8c / -9c
-10c / -11c / -12c

Intentionally left blank to have teachers complete the cards then print for their class

Algebra Tiles for Activity II: White Positive-Shaded Negative