# MA.6.AR.1.1

Given a mathematical or real-world context, translate written descriptions into algebraic expressions and translate algebraic expressions into written descriptions.

### Examples

The algebraic expression 7.2x-20 can be used to describe the daily profit of a company who makes \$7.20 per product sold with daily expenses of \$20.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Associative Property
• Absolute Value
• Coefficient
• Commutative Property of Multiplication
• Expression

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

Students are focusing on appropriate mathematical language when writing or reading expressions. In earlier grade levels, students have had experience with unknown whole numbers within equations. Grade 6 extends this knowledge by focusing on using verbal and written descriptions using constants, variables and operating with algebraic expressions. In grade 7, students use this knowledge when solving equations involving mathematical and real-world contexts.
• Within this benchmark, instruction includes connections to the properties of operations, including the associative property, commutative property and distributive property. Students need to understand subtraction and division do not comply with the commutative property, whereas addition and multiplication do. Students should have multiple experiences writing expressions (MTR.2.1, MTR.5.1).
• Instruction focuses on different ways to represent operations when translating written descriptions into algebraic expressions. For translating multiplication descriptions, students should understand that multiplication can be represented by putting a coefficient in front of a variable.
• For instance, if students were translating “six times a number $n$,” they can write the algebraic expression as 6$n$.
• For translating division descriptions, students should understand that division can be represented by using a fraction bar or fractions as coefficients in front of the variables (MTR.2.1).
• For example, if students were translating “a third of a number $n$,” they can write the algebraic expression as $\frac{\text{1}}{\text{3}}$$n$ or $\frac{\text{n}}{\text{3}}$.
• Students are expected to identify the parts of an algebraic expression, including variables, coefficients and constants, and the names of operations (sum, difference, product and quotient).
• Variables are not limited to $x$; instruction includes using a variety of lowercase letters for their variables; however, $o$, $i$, and $l$ should be avoided as they too closely resemble zero and one.

### Common Misconceptions or Errors

• Students may incorrectly assume that there is not a coefficient in front of a variable if there is not a number explicitly written to indicate a coefficient (MTR.2.1).
• $x$ is the same as 1$x$
• Students may incorrectly think that terms that are being combined using addition and subtraction have to be written in a specific order and not realize that the term being subtracted can come first in the form of a negative number (MTR.2.1).
• $x$ −3 is the same as −3 + 2$x$
• Students may incorrectly oversimplify a problem by circling the numbers, underlining the question, boxing in key words, and try to eliminate information that is important to the context. This process can cause students to not be able to comprehend the context or the situation (MTR.2.1, MTR.4.1, MTR.5.1, MTR.7.1).
• Teachers and students should engage in questions such as:
• What do you know from the problem?
• What is the problem asking you to find?
• Are you putting groups together? Taking groups apart? Or both?
• Are the groups you are working with the same sizes or different sizes?
• Can you create a visual model to help you understand or see patterns in your problem?

### Strategies to Support Tiered Instruction

• Instruction includes the use of pictorial representations, tape diagrams, or algebra tiles to represent the written situation before writing an expression.
• Instruction includes identifying unknowns, constants, negative values, and mathematical operations in a written description or algebraic expression.
• Instruction includes co-creating a graphic organizer that includes words used in written descriptions for each of the operations. The graphic organizer should continue to grow as new contexts are encountered.
• Teacher provides opportunities for students to comprehend the context or situation by engaging in questions such as:
• What do you know from the problem?
• What is the problem asking you to find?
• Are you putting groups together? Taking groups apart? Or both?
• Are the groups you are working with the same sizes or different sizes?
• Can you create a visual model to help you understand or see patterns in your problem?

The amount of money Jazmine has left after going to the mall could be described by the algebraic expression 75 − 12.75s − 9.50d, where s is the number of shirts purchased and d is the number of dresses purchased.
• Part A. Describe what each of the terms represent within the context.
• Part B. What are possible numbers of shirts and dresses Jazmine purchased.

Some of the students at Kahlo Middle School like to ride their bikes to and from school. They always ride unless it rains. Let d represent the distance, in miles, from a student’s home to the school. Write two different expressions that represent how far a student travels by bike in a four-week period if there is one rainy day each week.

### Instructional Items

Instructional Item 1

Rewrite the algebraic expression as a written description: 10− $\frac{\text{6}}{\text{x}}$.

Instructional Item 2

Write an expression to represent the phrase “9 plus the quotient of w and 4.”

Instructional Item 3

Write an expression to represent the phrase “7 fewer than the product of 3 and y.”

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.AR.1.AP.1: Write or select an algebraic expression that represents a real-world situation.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Writing Real-World Expressions:

Students are asked to use variables to write expressions that represent quantities described in context.

Type: Formative Assessment

Gavin’s Pocket:

Students are asked to interpret the significance of a variable and its possible values when given a variable expression in a real-world context.

Type: Formative Assessment

Inventing X:

Students are asked to write and explain a real-world situation to accompany an algebraic expression.

Type: Formative Assessment

Parts of Expressions:

Students are asked to identify key parts of algebraic expressions.

Type: Formative Assessment

Cube House:

Students are asked to write a numerical expression using exponents.

Type: Formative Assessment

Writing Expressions:

Students are asked to write expressions that record operations with numbers and variables.

Type: Formative Assessment

## Lesson Plans

Dissecting an Expression:

This lesson will focus on how to write, translate, and interpret an algebraic expression. Students will be able to identify the parts of an algebraic expression and the meaning of those parts.

Type: Lesson Plan

Going The Distance:

This lesson provides a hands-on activity where students can apply solving one-step multiplication and division equations to a real-world problem. The lesson focuses on the relationship between distance, rate, and time. The students will also represent data on graphs and draw conclusions and make interpretations based on the graphs.

Type: Lesson Plan

Decoding Word Phrases-Translating verbal phrases to variable expressions:

This lesson is designed to help students decode word phrases and then translate them from word form into numerical form. It provides a resource, in the form of a foldable, that can be kept all year and used anytime the students need to decode word phrases.

Type: Lesson Plan

Analyzing Polyhedra:

Students will construct several simple polyhedra, then count the number of faces, edges, and vertices. These data should suggest Euler's formula.

Type: Lesson Plan

Gummy vs. Gum (Number Pattern):

In this lesson from the Beacon Learning Center, students use gummy bears and sticks of gum to discover a number pattern and write an representation that describes it.

This lesson can be adapted for several grade levels and instead of writing an equation, students can write a "rule" or expression based on the pattern or relationship between number of pieces of gum and gummy bears.  Consider scaffolding this activity to meet your grade-level needs.

Type: Lesson Plan

## Original Student Tutorials

Algebraic Expressions Part 2: Multiplication and Division:

Help Oscar translate written real-world descriptions of multiplication and division into algebraic expressions in this interactive tutorial.

This is part 2 of 3. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Algebraic Expressions Part 1: Addition and Subtraction:

Follow Oscar as he writes algebraic expressions of addition and subtraction about his new puppy Scooter in this interactive tutorial.

Type: Original Student Tutorial

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: Original Student Tutorial

MacCoder’s Farm Part 3: If Statements:

Explore computer coding on the farm by using relational operators and IF statements to evaluate expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

MacCoder’s Farm Part 2: Condition Statements:

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

MacCoder’s Farm Part 1: Declare Variables:

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiast

Using Algebra to Program Robots and Microcontrollers:

There are 10 ways to use algebra to program a binary-counting circuit: fun and more fun.

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

Programming Mathematics: Algebra, and Variables to control Open-source Hardware:

If you are having trouble understanding variables, this video might help you see the light.

Type: Perspectives Video: Teaching Idea

## Tutorials

How to Write Basic Expressions with Variables:

Learn how to write basic algebraic expressions.

Type: Tutorial

How to Write Expressions with Variables:

Learn how to write simple algebraic expressions.

Type: Tutorial

How to Write Basic Algebraic Expressions from Word Problems:

Learn how to write basic expressions with variables to portray situations described in word problems.

Type: Tutorial

What is a Variable?:

The focus here is understanding that a variable is just a symbol that can represent different values in an expression.

Type: Tutorial

Why aren't we using the multiplication sign?:

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.

Type: Tutorial

## MFAS Formative Assessments

Cube House:

Students are asked to write a numerical expression using exponents.

Gavin’s Pocket:

Students are asked to interpret the significance of a variable and its possible values when given a variable expression in a real-world context.

Inventing X:

Students are asked to write and explain a real-world situation to accompany an algebraic expression.

Parts of Expressions:

Students are asked to identify key parts of algebraic expressions.

Writing Expressions:

Students are asked to write expressions that record operations with numbers and variables.

Writing Real-World Expressions:

Students are asked to use variables to write expressions that represent quantities described in context.

## Original Student Tutorials Science - Grades K-8

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

## Original Student Tutorials Mathematics - Grades 6-8

Algebraic Expressions Part 1: Addition and Subtraction:

Follow Oscar as he writes algebraic expressions of addition and subtraction about his new puppy Scooter in this interactive tutorial.

Algebraic Expressions Part 2: Multiplication and Division:

Help Oscar translate written real-world descriptions of multiplication and division into algebraic expressions in this interactive tutorial.

This is part 2 of 3. Click below to open the other tutorials in this series.

## Computer Science Original Student Tutorials

MacCoder’s Farm Part 1: Declare Variables:

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

MacCoder’s Farm Part 2: Condition Statements:

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

Click below to check out the other tutorials in the series.

MacCoder’s Farm Part 3: If Statements:

Explore computer coding on the farm by using relational operators and IF statements to evaluate expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Algebraic Expressions Part 2: Multiplication and Division:

Help Oscar translate written real-world descriptions of multiplication and division into algebraic expressions in this interactive tutorial.

This is part 2 of 3. Click below to open the other tutorials in this series.

Type: Original Student Tutorial

Algebraic Expressions Part 1: Addition and Subtraction:

Follow Oscar as he writes algebraic expressions of addition and subtraction about his new puppy Scooter in this interactive tutorial.

Type: Original Student Tutorial

Balancing the Machine:

Use models to solve balance problems on a space station in this interactive, math and science tutorial.

Type: Original Student Tutorial

MacCoder’s Farm Part 3: If Statements:

Explore computer coding on the farm by using relational operators and IF statements to evaluate expressions. In this interactive tutorial, you'll also solve problems involving inequalities.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

MacCoder’s Farm Part 2: Condition Statements:

Explore computer coding on the farm by using condition and IF statements in this interactive tutorial. You'll also get a chance to apply the order of operations as you using coding to solve problems.

Click below to check out the other tutorials in the series.

Type: Original Student Tutorial

MacCoder’s Farm Part 1: Declare Variables:

Explore computer coding on the farm by declaring and initializing variables in this interactive tutorial. You'll also get a chance to practice your long division skills.

Type: Original Student Tutorial

## Tutorials

How to Write Basic Expressions with Variables:

Learn how to write basic algebraic expressions.

Type: Tutorial

How to Write Expressions with Variables:

Learn how to write simple algebraic expressions.

Type: Tutorial

How to Write Basic Algebraic Expressions from Word Problems:

Learn how to write basic expressions with variables to portray situations described in word problems.

Type: Tutorial

What is a Variable?:

The focus here is understanding that a variable is just a symbol that can represent different values in an expression.

Type: Tutorial

Why aren't we using the multiplication sign?:

Great question. In algebra, we do indeed avoid using the multiplication sign. We'll explain it for you here.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.