- Subject:
- Algebra
- Material Type:
- Lesson Plan
- Level:
- Middle School
- Grade:
- 6
- Provider:
- Pearson
- Tags:

- License:
- Creative Commons Attribution-NonCommercial 4.0
- Language:
- English
- Media Formats:
- Text/HTML

# Mathematical Vocabulary

## Overview

Students play an Expressions Game in which they describe expressions to their partners using the vocabulary of expressions: term, coefficient, exponent, constant, and variable. Their partners try to write the correct expressions based on the descriptions.

# Key Concepts

Mathematical expressions have parts, and these parts have names. These names allow us to communicate with others in a precise way.

- A variable is a symbol (usually a letter) in an expression that can be replaced by a number.
- A term is a number, a variable, or a product of numbers and variables. Terms are separated by the operator symbols + (plus) and – (minus).
- A coefficient is a symbol (usually a number) that multiplies the variable in an algebraic expression.
- An exponent tells how many copies of a number or variable are multiplied together.
- A constant is a number. In an expression, it can be a constant term or a constant coefficient. In the expression 2
*x*+ 3, 2 is a constant coefficient and 3 is a constant term.

# Goals and Learning Objectives

- Identify parts of an expression using appropriate mathematical vocabulary.
- Write expressions that fit specific descriptions (for example, the expression is the sum of two terms each with a different variable).

# Be Precise

# Mathematical Practices in Action

**Mathematical Practice 6: Attend to precision.**

Have students watch the video introducing Mathematical Practice 6: Attend to precision. The video defines *term, coefficient, exponent, constant, *and* variable*.

Ask students to look and listen for how the description of each word became more precise as the students talked about it.

After students watch the video, give partners time to talk about how they could explain those words precisely. Could they have improved the way that Jan and Carlos defined the words?

Tell students that they are going to play the Expressions Game. Write the following expression on a small piece of paper, but do not let students see it:

$3{x}^{2}+2y-3$

Tell students that you have written an expression that includes the following:

- From one to three terms
- One or two variables
- Whole numbers less than 10
- Exponents to the third power or less

Tell students that they may ask questions to get information to help them figure out what the expression is. Sample questions include:

- How many variables are in the expression?
- How many terms are in the expression?
- Are there any exponents in the expression?

SWD: Allow students with language processing and/or attentional variability to preview the video. Cue students to “look out for” particular elements to support students’ understanding of the video’s contents. Provide a list of key ideas for students to review prior to viewing.

ELL: Target and model key language and vocabulary. Specifically, focus on the words *term*, *coefficient*, *exponent*, *constant*, and *variable*. As you’re discussing the key points, write the words on the board or on large sheets of paper and explain/demonstrate what the words mean. Since these are important points that students will be using throughout the module, write them on a large poster board so that students can use it as a reference. Have students record new terms, definitions, and examples into their notebook.

## Opening

# Be Precise

Watch the video of Carlos and Jan talking precisely about the vocabulary of expressions.

Discuss the following questions.

- How did they become more precise in their language as they discussed the math words?
- Can you give a more precise definition for any of the math words Carlos and Jan were discussing?

VIDEO: Mathematical Practice 6

## Hint:

Did you take notes about the words discussed in the video: *term* ,*coefficient* ,*exponent* ,*variable* , and*constant* ?

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will describe expressions to their partners using the vocabulary of expressions: term, coefficient, exponent, constant, and variable. Their partners will try to write the expressions based on the verbal descriptions.

## Opening

Define the parts of algebraic expressions.

# Expressions Game

# Lesson Guide

Have students work in pairs and play the Expressions Game. Review the guidelines for writing expressions.

# Mathematical Practices

**Mathematical Practice 6: Attend to precision.**

Listen for students who ask questions using the appropriate math vocabulary. Students must communicate clearly to determine their partner’s expression.

# Interventions

**Student has difficulty playing the game or writing expressions to match descriptions.**

- Describe the game in your own words to your partner. Explain the guidelines.
- Define
*term*,*coefficient*,*exponent*,*constant*, and*variable*for me. Show me an example of each one. - What operators can separate terms in an expression? How will you know which operator to use?
- Tell me something you understand about this description.
- Tell me what confuses you about this description.

**Student plays the game and writes expressions to match descriptions.**

- Describe how you wrote the expression to match this description.
- Show me a [term, variable, coefficient, exponent, constant] in your expression. Explain what that part of your expression means.
- Explain how you knew what operators to use between the terms in the expression.
- Describe the strategy you used to figure out your partner’s expression during the game. Did you revise your strategy? If so, why?
- What was difficult about this activity? What was easy? Explain why.

# Possible Answers

- Answers will vary. Monitor students as they play the Expressions Game to be sure they are following the guidelines.

## Work Time

# Expressions Game

Play the Expressions Game with a partner. Here are the rules.

- The first partner writes an expression following the guidelines below, but does not let the second partner see the expression. Expressions can have:
- From one to three terms
- One or two variables
- Whole numbers less than 10
- Exponents to the third power or less

- The second partner asks questions to try to figure out what the expression is. Write down the questions that are asked, as you will need them for your presentation.
- After the second partner figures out the expression, switch roles and play the game again using a different expression.

## Hint:

- For the partner writing the expression: Does your expression meet the guidelines? Revise your expression if needed.
- For the partner guessing the expression: Think about the vocabulary words you learned in the video. How can you use these words to ask helpful questions?

# Prepare a Presentation

# Lesson Guide

Pairs should work together on their presentations.

# Preparing for Ways of Thinking

Make note of students who use the terms correctly as they ask and answer questions as well as those who do not, so that you can address misconceptions in Ways of Thinking.

# Challenge Problem

## Answer

- Check that students’ expressions meet the guidelines and use the distributive property.

## Work Time

# Prepare a Presentation

Show one of the expressions you or your partner wrote and document the questions the other partner asked to find the expression. Highlight each mathematical vocabulary word in the questions.

# Challenge Problem

- Play the Expressions Game again, but this time write an expression that meets all of the guidelines and uses the distributive property.

# Make Connections

# Lesson Guide

The goal is for students to be able to identify variables, coefficients, exponents, constants, and terms.

As students make their presentations, consider how you can use the work to focus students on the language of algebra.

- What strategies did you use during the Expressions Game?
- What types of questions did you ask?
- Were [Name]’s questions good? Explain your thinking.
- How were the words
*variable*,*coefficient*,*exponent*,*constant*, and*term*helpful?

Discuss the things that still confuse students. For example, students may be confused about the number of terms in an expression. Discuss examples such as the following:

One term:

3*y*

*xy*

2(*x *+ 3)

**Two terms:**

*x* + 3

2*y* – 5

**Three terms:**

5 + 6 + 9

*x* + *y* + 4

Bring out in the discussion that a variable by itself has a coefficient of 1.

Remind students that they have heard the word *constant* before. When they studied constant rates, two quantities vary, but their ratio remains constant.

## Performance Task

# Ways of Thinking: Make Connections

Takes notes about the expressions that other classmates wrote and the questions that their partners asked.

## Hint:

As your classmates present, ask questions such as:

- How does your expression meet the guidelines outlined in the Expressions Game rules?
- What strategy did you use to figure out your partner’s expression?
- Did you revise your strategy at all? If so, explain why.
- How does your strategy compare with other strategies that students have presented?
- What do you think makes for a “good” question?
- What advice would you give someone playing the Expressions Game for the first time?
- Did knowing the definitions of math words help you ask better questions and figure out your partner’s expression?

# Write Expressions

# Lesson Guide

Ask questions such as the following as students are working:

- How did you get this expression?
- What words helped you write this expression?
- What operation does the word
*factor*imply? - What is the variable in your expression?
- What is the coefficient of the variable?
- What are the terms in your expression?
- What other expression could you write for this description?

SWD: Help students identify key information from the word problems. One way is to have them underline key words and numbers that will help them solve the problem. Allow time for students to master this skill.

# Possible Answers

Answers will vary. Possible answers:

- 2
*x*+ 3*x* - 7(
*t*+ 5) *y*^{2}*w*÷ 6

## Work Time

# Write Expressions

Write an expression that matches each of the following descriptions.

- The expression is the addition of two terms. It has one variable and two different coefficients.
- The expression is the product of two factors. The first factor is a number. The second factor is the sum of a variable and 5.
- The expression has one term. The variable has the exponent 2.
- The expression is the division of a variable by a number.

## Hint:

Review the definitions for *term* ,*variable* ,*coefficient* , and*exponent* to help you understand the descriptions.

# Expressions Definitions

# Mathematics

- Have pairs quietly discuss the definitions, stating an example for each one.
- As student pairs work together, listen for students who may still have difficulty understanding certain definitions. Be sure to clarify any misconceptions during the class discussion.
- Discuss the Summary as a class. Write different expressions on the board and have students name the different parts of each expression.

## Formative Assessment

# Summary of the Math: Expressions Definitions

**Read and Discuss**

- A
*variable*can be a letter or another symbol that stands for an unknown in an equation or expression. - A
*term*is a number, a variable, or a product of numbers and variables. Terms are separated by the operator symbols + (plus) and – (minus). - A
*coefficient*is usually a number multiplying the variable in an algebraic expression. - An
*exponent*tells how many times a number or variable is multiplied by itself. - A
*constant*is a number. In an expression it can be a constant term or a constant coefficient. In the expression 2*x*+ 3, 2 is a constant coefficient and 3 is a constant term.

## Hint:

Can you:

- Explain the parts of an algebraic expression?
- Define and use the words
*variable*,*term*,*coefficient*,*constant*, and*exponent*?

# Reflect On Your Work

# Lesson Guide

Have each student write a brief reflection before the end of class. Review the reflections to find out what students learned about the parts of an expression.

ELL: Present some of the topics in writing to support students. Also, provide sentence frames, as appropriate.

## Work Time

# Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

**Something new I learned today about the parts of an expression is …**