Standard 2 : Develop an understanding for solving equations and inequalities. Write and solve one-step equations in one variable.



This document was generated on CPALMS - www.cpalms.org


General Information

Number: MA.6.AR.2
Title: Develop an understanding for solving equations and inequalities. Write and solve one-step equations in one variable.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 6
Strand: Algebraic Reasoning

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.6.AR.2.1: Given an equation or inequality and a specified set of integer values, determine which values make the equation or inequality true or false.
Clarifications:
Clarification 1: Problems include the variable in multiple terms or on either side of the equal sign or inequality symbol.
MA.6.AR.2.2: Write and solve one-step equations in one variable within a mathematical or real-world context using addition and subtraction, where all terms and solutions are integers.
Clarifications:
Clarification 1: Instruction includes using manipulatives, drawings, number lines and inverse operations.

Clarification 2: Instruction includes equations in the forms x+p=q and p+x=q, where x,p and q are any integer.

Clarification 3: Problems include equations where the variable may be on either side of the equal sign.

MA.6.AR.2.3: Write and solve one-step equations in one variable within a mathematical or real-world context using multiplication and division, where all terms and solutions are integers.
Clarifications:
Clarification 1: Instruction includes using manipulatives, drawings, number lines and inverse operations.

Clarification 2: Instruction includes equations in the forms x/p = q, where p ≠ 0, and px = q.

Clarification 3: Problems include equations where the variable may be on either side of the equal sign.

MA.6.AR.2.4: Determine the unknown decimal or fraction in an equation involving any of the four operations, relating three numbers, with the unknown in any position.
Clarifications:
Clarification 1: Instruction focuses on using algebraic reasoning, drawings, and mental math to determine unknowns.

Clarification 2: Problems include the unknown and different operations on either side of the equal sign. All terms and solutions are limited to positive rational numbers.



Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MA.6.AR.2.AP.1: Choose which values, from a set of five or fewer integers, make an equation or inequality true.
MA.6.AR.2.AP.2: Solve real-world, one-step linear equations using addition and subtraction involving integers.
MA.6.AR.2.AP.3: Solve real-world, one-step linear equations using multiplication and division involving integers.
MA.6.AR.2.AP.4: Solve a one-step equation using fractions with like denominators or decimals with place value ranging from the thousand to the thousandths.


Related Resources

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

Original Student Tutorials

Name Description
Dr. E. Quation Part 2: One Step Multiplication & Division Equations:

Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials.  You'll also learn how to check your answers to make sure your answer is the solution to the equation. 

Click here to open Part 1

Dr. E. Quation Part 1: One Step Addition & Subtraction Equations:

Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial.

Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations

Balancing the Machine:

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

Formative Assessments

Name Description
Finding Solutions of Inequalities:

Students are given three inequalities and asked to determine if any numbers from a given set are solutions.

Equally Driven:

Students are asked to solve a real-world problem by writing and solving an equation.

Center Section:

Students are asked to solve a real-world problem by writing and solving an equation.

Solar Solutions:

Students are asked to solve a real-world problem by writing and solving an equation.

University Parking:

Students are asked to solve a real-world problem by writing and solving an equation.

Solutions of Inequalities:

Students are asked to explain what it means for a number to be a solution of an inequality.

Solutions of Equations:

Students are asked to explain what it means for a number to be a solution of an equation.

Finding Solutions of Equations:

Students are given three equations and asked to determine if any numbers from a given set are solutions.

Lesson Plans

Name Description
How Will the Ninja Capture the Valuable Princess?:

This lesson allows students to solve two-step equations involving a mythological story line in which the princess (variable) is protected by a bodyguard (number added or subtracted in an equation) and by a protector (number multiplied or divided by the variable). The three characters live in a castle, surrounded by the moat (equal sign) and an innocent bystander that lives outside the castle (number on the opposite side of the variable). However, Ninjas are infiltrating the castle to steal the “valuable” princess. Using this story line, students must then decide who the Ninja must eliminate first to get to the princess. This lesson can also be used to solve equations with like terms on the same side and equations with the same variable on each side.

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.

Solving Addition and Subtraction Equations with Beans:

Students will use dried white and black beans to solve one-step addition and subtraction equations to realize the Addition Property of Equality and Subtraction Property of Equality through the use of inverse operations (zero pairs).

Capture the Boat - Sink the Teacher's Fleet!:

In this lesson, students learn about the four quadrants of a coordinate plane and how to plot points in those quadrants. Students also learn how to use linear equations to predict future input and output pairs. Students work together to try to sink the teacher's fleet in a Battleship-type game while the teacher tries to sink theirs first.

Perspectives Video: Expert

Name Description
Improving Hurricane Scales:

Meteorologist, Michael Kozar, discusses the limitations to existing hurricane scales and how he is helping to develop an improved scale.

Download the CPALMS Perspectives video student note taking guide.

Perspectives Video: Teaching Idea

Name Description
Adding Integers:

Unlock an effective teaching strategy for using patterns to help students make generalizations when adding integers in this Teacher Perspectives video for educators.

Problem-Solving Tasks

Name Description
Busy Day:

Students are asked to write and solve an equation in one variable to answer a real world question.

Firefighter Allocation:

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

Morning Walk:

Students are asked to write an equation with one variable in order to find the distance walked.

Tutorials

Name Description
How to Solve Equations of the Form ax = b:

Here's an introduction to basic algebraic equations of the form ax = b in this tutorial.

How to Solve One-Step Multiplication and Division Equations with Fractions and Decimals:

In this tutorial, we will solve equations in one step by multiplying or dividing a number on both sides.

How to Test Solutions to Inequalities:

Learn how to test if a certain value of a variable makes an inequality true in this tutorial.

How to Test Solutions to Equations Using Substitution:

Learn how to test if a certain value of a variable makes an equation true in this tutorial.

How to Represent a Relationship with a Simple Equation:

This video demonstrates how to write and solve a one-step addition equation.

Solving One-Step Equations Using Division:

To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation. 

Why to Divide on Both Sides of an Equation:

This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.



Student Resources

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

Original Student Tutorials

Title Description
Dr. E. Quation Part 2: One Step Multiplication & Division Equations:

Learn how to solve 1-step multiplication and division equations with Dr. E. Quation in Part 2 of this series of interactive tutorials.  You'll also learn how to check your answers to make sure your answer is the solution to the equation. 

Click here to open Part 1

Dr. E. Quation Part 1: One Step Addition & Subtraction Equations:

Learn how to solve and check one-step addition and subtraction equations with Dr. E. Quation as you complete this interactive tutorial.

Click here to open Dr. E. Quation Part 2: One-Step Multiplication and Division Equations

Balancing the Machine:

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

Problem-Solving Tasks

Title Description
Busy Day:

Students are asked to write and solve an equation in one variable to answer a real world question.

Firefighter Allocation:

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

Morning Walk:

Students are asked to write an equation with one variable in order to find the distance walked.

Tutorials

Title Description
How to Solve Equations of the Form ax = b:

Here's an introduction to basic algebraic equations of the form ax = b in this tutorial.

How to Solve One-Step Multiplication and Division Equations with Fractions and Decimals:

In this tutorial, we will solve equations in one step by multiplying or dividing a number on both sides.

How to Test Solutions to Inequalities:

Learn how to test if a certain value of a variable makes an inequality true in this tutorial.

How to Test Solutions to Equations Using Substitution:

Learn how to test if a certain value of a variable makes an equation true in this tutorial.

How to Represent a Relationship with a Simple Equation:

This video demonstrates how to write and solve a one-step addition equation.

Solving One-Step Equations Using Division:

To find the value of a variable, you have to get it on one side of the equation alone. To do that, you'll need to do something to BOTH sides of the equation. 

Why to Divide on Both Sides of an Equation:

This video provides a conceptual explanation of why one needs to divide both sides of an equation to solve for a variable.



Parent Resources

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

Problem-Solving Tasks

Title Description
Busy Day:

Students are asked to write and solve an equation in one variable to answer a real world question.

Firefighter Allocation:

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

Morning Walk:

Students are asked to write an equation with one variable in order to find the distance walked.