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

- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Text/HTML

# Expressions in Words & Symbols

## Overview

Students do a card sort in which they match expressions in words with their equivalent algebraic expressions.

# Key Concepts

- A mathematical expression that uses letters to represent numbers is an algebraic expression.
- A letter used in place of a number in an expression is called a variable.
- An algebraic expression combines both numbers and letters using the arithmetic operations of addition (+), subtraction (–), multiplication (·), and division (÷) to express a quantity.
- Words can be used to describe algebraic expressions.
- There are conventions for writing algebraic expressions:
- The product of a number and a variable lists the number first with no multiplication sign. For example, the product of 5 and
*n*is written as 5*n*, not*n*5. - The product of a number and a factor in parentheses lists the number first with no multiplication sign. For example, write 5(
*x*+ 3), not (*x*+ 3)5. - For the product of 1 and a variable, either write the multiplication sign or do not write the "1." For example, the product of 1 and
*z*is written either 1 ⋅*z*or*z*, not 1*z*.

- The product of a number and a variable lists the number first with no multiplication sign. For example, the product of 5 and

# Goals and Learning Objectives

- Translate between expressions in words and expressions in symbols.

# Describe the Expression

# Lesson Guide

Give students a chance to share ideas.

Then point out that the algebraic expression *x* − 3 means “subtract 3 from any number.” The language here is tricky. Note that English Language Learners (ELLs) may need help understanding why this expression is not

3 − *x*.

ELL: Check in to ensure that students understand the meaning of domain specific vocabulary terms such as *algebraic expression*, *equation*, *variable*, and *product*.

Have students add these new vocabulary terms, definitions, and examples to their notebook.

## Opening

# Describe the Expression

- Which of these expressions shows “subtract 3 from
*x*”?

*x *− 3 or 3 – *x*

# Math Mission

# Lesson Guide

Discuss the Math Mission. Students will complete a card sort in which they match an expression in words with its equivalent algebraic expression.

## Opening

Use words to describe algebraic expressions.

# Match Algebraic and Written Expressions

# Lesson Guide

Have the students do the card sort. Have partners explain how they sorted the cards to each other.

SWD: Use card sorting activities to encourage students to experiment—they can move the cards around if they change their minds. This type of activity encourages discussion because students have to explain to each other why they think certain cards match.

ELL: When listening to student responses, let students know in advance that they will be presenting their work on a specific problem during Ways of Thinking. This will give them ample time to prepare a thoughtful presentation.

Make note of cards that students pair incorrectly as well as cards that they pair correctly in order to address misconceptions during Ways of Thinking.

# Mathematical Practices

**Mathematical Practice 1: Make sense of problems and persevere in solving them.**

In this card sort, students must make sense of verbal descriptions and algebraic expressions. Some descriptions may be tricky for students. For example, the descriptions “Divide 2 by any number” and “Divide any number by 2" may be confusing. Watch for students who understand the difference between the two.

**Mathematical Practice 3: Construct viable arguments and critique the reasoning of others.**

Listen as partners explain their card sorts to each other. Are students able to justify their matches and communicate their reasoning clearly and completely?

# Interventions

**Student has an incorrect solution.**

- Have you checked your work?
- Does your answer for [card name] make sense? What if you replaced the variable and “any number” with "2"? Do the cards still match?
- Describe what this card [point to expression card] means.
- When reading a description involving subtraction, how do you know which number goes first in the expression?
- What operation does the fraction bar represent?

**Student has a solution.**

- How did you approach looking for matches?
- Did you change your mind about any matches? Which ones? How did you identify your error? What did you learn?
- What makes matching the cards easy? What makes matching the cards difficult?

SWD: If students with disabilities need help interpreting algebraic expressions as words:

- When you are subtracting from a number, you are taking an amount away from that number; so, does this number go before or after the minus sign? Example: “Subtract 1 from 4” is the same as 4 − 1.
- Division can be represented by using a ÷ sign or a fraction bar. Example: “Divide 4 by 2"

is the same as 4 ÷ 2 and $\frac{4}{2}$.

# Answers

## Work Time

# Match Algebraic and Written Expressions

Match each algebraic expression card with a written description card.

INTERACTIVE: Matching Algebraic and Written Expressions

## Hint:

Replace the words “any number” in the descriptions with the letters in the algebraic expressions.

# Prepare a Presentation

# Lesson Guide

Students may work on their presentations individually or with a partner.

# Prepare for Ways of Thinking

Look for students who have different methods for deciding which verbal expressions and which algebraic expressions match up. Use these in the Ways of Thinking discussion in the next step.

# Challenge Problem

## Answer

- Answers will vary. Possible answer: Subtract 10 from any number and then multiply by 2; 2(
*n*− 10).

## Work Time

# Prepare a Presentation

Prepare a presentation about the strategy you used to match cards.

# Challenge Problem

- Make up a verbal description of a multi-step calculation that has the words “any number” in it, and then write the algebraic expression for the calculation.

# Make Connections

# Lesson Guide

Facilitate the discussion to help students understand each other’s methods for deciding which verbal and which algebraic expressions go together.

ELL: In asking prompting questions, be sure to use adequate pace with ELLs, and be sure that they understand the meaning of the questions.

This lesson may be particularly challenging for ELLs and students who are unfamiliar with standard algebraic conventions. You may want to pair ELLs with students whose primary language is English. You may also want to pair students who are unfamiliar with standard algebraic conventions with students who are familiar with those conventions.

# Mathematics

Watch for the following common errors that students might make:

[common error] Some students may think that the letters and numbers in an algebraic expression should appear in the same order as they appear in the verbal description. Thus, these students may think that “Subtract 3 from *p*” is written as “3 − *p*.”

[common error] Other students may misinterpret an algebraic expression such as 5*x* as meaning a two-digit number with 5 in the ten’s place and an *x* in the one’s place.

As you choose which students will present their work, consider how you can use the work to focus students on the language and the conventions of algebra.

- Describe what strategy you used to match the cards.
- What do you think of [Name]’s strategy?
- Did anyone use a different strategy? Explain what you did.
- How do you know that [Subtract 3 from any number] can be written as [
*p*− 3] and not [3 −*p*]? - What does a letter mean in an expression?
- What does a number in front of a letter mean?
- What does a number in front of parentheses mean?
- Describe the description and algebraic expression you wrote for the challenge problem. Why do they match?

## Performance Task

# Ways of Thinking: Make Connections

Takes notes about the strategies your classmates used to match algebraic expressions with written expressions.

## Hint:

As your classmates present, ask questions such as:

- What strategy did you use to complete the card sort?
- Which cards were easiest to match? Which cards were most difficult to match?
- In the challenge problem, was it difficult for you to write the description first, and then write the algebraic expression? Do you think it would have been easier to write the algebraic expression first?

# Algebraic Expressions and Variables

# Mathematics

- Have pairs discuss the information about algebraic expressions.
- As student pairs work together, listen for students who may confuse an algebraic expression with a numerical expression or an expression with an equation. Make a note to clarify any misunderstandings in the class discussion.
- After a few minutes, discuss the Summary as a class. Review the following conventions:
- The product of a number and a variable lists the number first with no multiplication sign. For example, the product of 5 and
*n*is written as 5*n*, not*n*5. - The product of a number and a factor in parentheses lists the number first with no multiplication sign. For example, write 5(
*x*+ 3), not (*x*+ 3)5. - For the product of 1 and a variable, either write the multiplication sign or do not write the "1." For example, the product of 1 and
*z*is written either 1 ·*z*or*z*, not 1*z*.

- The product of a number and a variable lists the number first with no multiplication sign. For example, the product of 5 and

## Formative Assessment

# Algebraic Expressions and Variables

**Read and Discuss**

- In algebraic expressions, letters stand for numbers. You can use any letter to represent an unknown value. A letter used in place of a number in an expression is called a
*variable*. - Words can be used to describe algebraic expressions.
- An algebraic expression combines both numbers and letters using the arithmetic operations of addition (+), subtraction (–), multiplication (⋅), and division (÷) to express a quantity.

## Hint:

Can you:

- Describe how letters are used in algebraic expressions?
- Describe what elements might be included in an algebraic expression?

# 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 expressions.

ELL: Make sure that ELLs have access to a dictionary and that they have time to discuss their reflection with a partner before writing so that they can organize their thoughts. Allow ELLs who share the same primary language to discuss in that language if they wish.

## 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 expressions is …**