## Join the Club: Identifying and Combining Like Terms

- Lesson

In this lesson, students learn the definition of like terms and gain practice in identifying key features to sort and combine them. Most middle school students are adept at recognizing the nuances of dress and manner that identify groups and cliques among their peers. This lesson applies the observation and sorting skills that students already possess to the important task of identifying and combining like terms. Students will play the game Ker-Splash and derive rules for working with like terms.

This lesson is broken up into three games. Students will begin the lesson by playing several rounds of the game Ker-Splash, which relies on strategic sorting and combining of like coins to win. The second game involves students recording a set of like terms from Ker-Splash to aid in discussing strategies for winning the game. Students will then finally play two card games to apply skills in recognizing and combining like terms to a more abstract task.

To prepare for this lesson, print, cut, and shuffle one set of the term cards for each student. They will be used when students play the card games at the end of the lesson.

Students will play the math strategy game Ker-Splash to begin the lesson.

Introduce students to the Calculation Nation^{®}
site, have them log in as guests, and provide a brief demo on how to play the
game.

Afterwards, direct the students to play several games of Ker-Splash. Tell students to pay close attention to the rules that lead to successfully combining coins. (Note that students’ first game may take 10-15 minutes, as they are getting used to the rules.) Introduce relevant vocabulary to students on the Vocabulary Overhead. Have students use the Ker-Splash Record Sheet to sort and record the coins earned from five rounds of one game. They should also answer the questions 2 and 3.

Have students discuss activity sheet questions 2 and 3 with a partner or in small groups. Bring the groups together to discuss attributes of the game coins and summarize the rules for combining coin values. Emphasis should be placed on how they were able to identify coins that were like terms. Students should note that the only successful combinations resulted from correctly adding like terms.

Discuss with students the standard form for combining like terms in expressions and equations. The terms should be arranged alphabetically in descending order. The constant should be the last term written.

Some misconceptions that could be addressed in the discussion are:

- Not recognizing that a single letter variable has a coefficient of 1 ( r = 1r).
- Adding the coefficients of unlike terms.
- Failing to identify all like terms in a sum.
- Making sign errors (failing to recognize that –n = + - n).

To play the “sorting terms” card game, pair students and distribute a set of term cards to each student. Using their own set, students should stack and place cards face down on the desk. Each student, in turn, should draw the top card from the stack, placing it face up on the table. Students should compare pairs and distribute cards as follows:

- If unlike terms, return to the bottom of the stack.
- If like terms that are equal, each player takes one card.
- If like terms of different values, the pair goes to the player with the higher value card. Continue until all like terms have been matched, or remaining cards have no partner. The player with the most cards wins.

To play the “combining terms” card game, pair students and have them use the same sets of cards. Have students deal a “face down” 3 X 4 array of cards, with each student contributing 6 cards. The first student turns up two cards and decides if they are like terms. If the pair represents like terms, the student must correctly add the terms to keep the pair. If the cards are not like terms or if the addition is incorrect, they are returned, face down, to the array. The opponent may challenge an incorrect sum by stating the correct sum and claiming the pair. Play continues until all cards have been played to the array and no like terms pairs remain. A student wins by having the most pairs of cards.

- Computers with internet access
- Join the Club Vocabulary Overhead
- Join the Club Ker-Splash Record Sheet
- Term Cards Activity Sheet, one per student, duplicated on card stock.

**Assessment Options**

- Listen for correct student responses during the on line game portion of the lesson and during the class discussion.
- Review Activity Sheet for properly sorted terms.
- Have students display pairs of like term cards used in the card game. Evaluate for correct sums and/ or identify common errors.

**Extensions**

- Investigate common misconceptions about combining like terms using the lesson, “my favorite no,” by Joanne Jacobs
- Explore models for assessing personality traits. These models ask questions based on activity and interest preferences, and then compare an individual’s response to the larger population.

**Questions for Students:**

1. What traits do you focus on in sorting your friends/peers into groups? How can you apply this skill to sorting and combining like terms?

[Answers may vary. Sample answers include: clothing choices indicate values, gender, and interest in certain sports. Terms also have attributes that allow them to be identified and sorted.]

2. What are important attributes used in identifying a coin?

[Terms are sorted based on the presence or absence of a letter, then according to the kind of letter. These traits are highlighted in Ker-Splash with color.]

3. What strategies did you use to maximize the coefficients for X, Y and number coins in Ker-Splash? How did you use the + and – coins?

[Choose a path that collects the largest number of positive terms, considering the cost of opening doors and the spaces available in the holding bin. Apply coins to increase the value of your X or Y coins.]

**Teacher Reflection: **

- How many trials were needed for students to grasp the rules and strategies of the game?
- What behaviors were observed when students realized that in order to successfully combine coins, the coins needed common characteristics (i.e. x & x, y & y, or constant & constant)?
- Were students able to attend to the significant features of terms in order to combine them?
- Did students need to continue to refer the metaphor of characteristics of their own peer groups?
- Was Ker-Splash challenging to students of varying skill levels? Was it frustrating to any groups of students?

### Other Related Resources

- Calculation Nation

Ker-Splash

### Learning Objectives

Students will:

- Define vocabulary: term, like term, variable, constant, and coefficient.
- Identify and applying key features of like terms in rules for combining.
- Calculate the sum of like terms.
- Develop effective and efficient rules for combining like terms, so that they may successfully solve equations with multiple like terms and/or distributive property.
- Transfer skills of sorting and combining coins in the game to more abstract task of sorting cards in preparation for quantitative work.

### NCTM Standards and Expectations

- Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

- Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.

### Common Core State Standards – Mathematics

Grade 6, Expression/Equation

- CCSS.Math.Content.6.EE.A.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Grade 6, Expression/Equation

- CCSS.Math.Content.6.EE.A.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.

Grade 6, Expression/Equation

- CCSS.Math.Content.6.EE.B.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Grade 7, Expression/Equation

- CCSS.Math.Content.7.EE.A.1

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

### Common Core State Standards – Practice

- CCSS.Math.Practice.MP1

Make sense of problems and persevere in solving them.

- CCSS.Math.Practice.MP2

Reason abstractly and quantitatively.