### 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.**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**6

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

- MA.6.NSO.1.2
- MA.6.NSO.1.3
- MA.6.NSO.2.1
- MA.6.NSO.2.2
- MA.6.NSO.2.3
- MA.6.AR.2.2
- MA.6.AR.2.3
- MA.6.AR.3.5
- MA.6.GR.2.2
- MA.6.GR.2.3

### Terms from the K-12 Glossary

- Associative Property
- Absolute Value
- Coefficient
- Commutative Property of Addition
- 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?

### Instructional Tasks

*Instructional Task 1 (MTR.7.1) *

*s*− 9.50

*d*, 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.

*Instructional Task 2 (MTR.2.1) *

*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*

*Instructional Item 2 *

*w*and 4.”

*Instructional Item 3 *

*y*.”

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

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

## Problem-Solving Tasks

## Tutorials

## MFAS Formative Assessments

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

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

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

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

## Original Student Tutorials Science - Grades K-8

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

## Original Student Tutorials Mathematics - Grades 6-8

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

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.

**Algebraic Expressions Part 1: Addition and Subtraction**- Part 3 (Coming Soon)

## Computer Science Original Student Tutorials

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.

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.

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

## Original Student Tutorials

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.

**Algebraic Expressions Part 1: Addition and Subtraction**- Part 3 (Coming Soon)

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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

Type: Original Student Tutorial

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.

**MacCoder’s Farm Part 1: Declare Variables****MacCoder's Farm Part 2: Condition Statements****MacCoder's Farm Part 4: Repeat Loops**

Type: Original Student Tutorial

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 1: Declare Variables****MacCoder’s Farm Part 3: If Statements****MacCoder's Farm Part 4: Repeat Loops**

Type: Original Student Tutorial

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

## Problem-Solving Tasks

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Type: Problem-Solving Task

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the two variables.

Type: Problem-Solving Task

In this task students are asked to write an equation to solve a real-world problem.

Type: Problem-Solving Task

## Tutorials

Learn how to write basic algebraic expressions.

Type: Tutorial

Learn how to write simple algebraic expressions.

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

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

Type: Tutorial

## Parent Resources

## Problem-Solving Tasks

Students are asked to use a diagram or table to write an algebraic expression and use the expression to solve problems.

Type: Problem-Solving Task

This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the two variables.

Type: Problem-Solving Task

In this task students are asked to write an equation to solve a real-world problem.

Type: Problem-Solving Task