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). TI MathForward 1 2010 Texas Instruments Incorporated
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? TI MathForward 2 2010 Texas Instruments Incorporated
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 TI MathForward 3 2010 Texas Instruments Incorporated
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 = x 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 TI MathForward 4 2010 Texas Instruments Incorporated
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 TI MathForward 5 2010 Texas Instruments Incorporated
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. TI MathForward 6 2010 Texas Instruments Incorporated
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. x 2 + 2x 2 g. 2x 2 + x + 4 + x 2 + 3x TI MathForward 7 2010 Texas Instruments Incorporated
7. Teacher may pause the activity to clarify the expression. 8. Students graphs that are correct will match the teacher s graph. TI MathForward 8 2010 Texas Instruments Incorporated
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 = x 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 TI MathForward 9 2010 Texas Instruments Incorporated
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 x 2 + 2x 2 2x 2 + x + 4 + x 2 + 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? TI MathForward 10 2010 Texas Instruments Incorporated
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 TI MathForward 11 2010 Texas Instruments Incorporated
1a 2a 3a 4a 5a 6a 7a 8a 9a 10a 11a 12a TI MathForward 12 2010 Texas Instruments Incorporated
-1a -2a -3a -4a -5a -6a -7a -8a -9a -10a -11a -12a TI MathForward 13 2010 Texas Instruments Incorporated
1b 2b 3b 4b 5b 6b 7b 8b 9b 10b 11b 12b TI MathForward 14 2010 Texas Instruments Incorporated
-1b -2b -3b -4b -5b -6b -7b -8b -9b -10b -11b -12b TI MathForward 15 2010 Texas Instruments Incorporated
1c 2c 3c 4c 5c 6c 7c 8c 9c 10c 11c 12c TI MathForward 16 2010 Texas Instruments Incorporated
-1c -2c -3c -4c -5c -6c -7c -8c -9c -10c -11c -12c TI MathForward 17 2010 Texas Instruments Incorporated
Intentionally left blank to have teachers complete the cards then print for their class TI MathForward 18 2010 Texas Instruments Incorporated
Algebra Tiles for Activity II: White Positive-Shaded Negative TI MathForward 19 2010 Texas Instruments Incorporated