# MAFS.6.EE.2.6Archived Standard

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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Expressions & Equations
Cluster: Level 3: Strategic Thinking & Complex Reasoning
Cluster: Reason about and solve one-variable equations and inequalities. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Numbers in items should not require students to perform operations with negative rational numbers or result in answers with negative rational numbers. Expressions must contain at least one variable.
• Calculator :

No

• Context :

Allowable

Sample Test Items (1)

## 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))
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## 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

## Lesson Plans

Gather Data For Distribution by Programming an App:

This lesson allow students to gather, calculate, and plot data using both computer code and mathematical equations. In this lesson students will create a pedometer app to demonstrate the understanding of algorithms, components (such as buttons, textboxes, sensors, etc.), and If/Then statements. This lesson uses algebraic equations and random data to access the needed components to store data in a spreadsheet.

Type: Lesson Plan

Data Sets Represented in Computers:

This lesson shows how data can be represented by computers, in relation to everyday activities we may not be aware that we use computer. It gives an overview of graphing data by creating a histogram based on population data. Using the data collected, students will get a chance to hand write code to show what structure is needed for computers to collect, analyze and distribute such data. This lesson is lesson 1 of the Data Set and Deviation Statistics Unit and bridges statistical concepts of data collection, graphing and analysis with programming a computer using coding language while reinforcing foundational algebraic skills.

Type: Lesson Plan

Different Bodies of Water:

This is the introductory lesson in a 4-lesson unit of study about different bodies of water, their characteristics, and how to translate natural language into computer language.

Type: Lesson Plan

Waste Not, Want Not:

Students will explore the excretory system through a variety of activities that include an inquiry lab, a reading excerpt, an engineering design challenge, and creating an infomercial. Students will build a simulated kidney and explore what factors improve the filtering ability. Students will analyze the data and formulate findings.

Type: Lesson Plan

Students will use a balance scale graphic organizer to solve for the unknown (variable) in addition and subtraction equations with one variable.

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

How Much was Lunch?:

This lesson explores using substitution to solve one-step equations. Each real world problems involves discussion and students are expected to support their solutions.

Type: Lesson Plan

Bake Sale:

This lesson challenges student to develop and solve equations for mathematical and real world situations. Students will be encouraged to use the work backwards strategy using inverse operations to find a solution.

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 needs 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

## 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

Smiles:

In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems.

Triangular Tables:

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

Firefighter Allocation:

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

## Teaching Idea

True, False, and Open Sentences:

"Students first explore arithmetic sentences to decide whether they are true or false. The lesson then introduces students to sentences that are neither true nor false but are algebraic equations, also called open sentences, such as x + 3 = 7 or 2 x = 12." from Math Solutions.

Type: 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

## MFAS Formative Assessments

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.

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.

## 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

Smiles:

In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems.

Triangular Tables:

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

Firefighter Allocation:

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

## 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

## Parent Resources

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

Smiles:

In this online problem-solving challenge, students apply algebraic reasoning to determine the "costs" of individual types of faces from sums of frowns, smiles, and neutral faces. This page provides three pictorial problems involving solving systems of equations along with tips for thinking through the problem, the solution, and other similar problems.