# 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.

### Examples

Given the equation , x can be determined to be because is more than .

### 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.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

• Dividend
• Divisor
• Equation
• Equal Sign
• Number Line

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 5, students multiplied and divided decimals by one tenth and one hundredth, added and subtracted fractions with unlike denominators, and determined if equations were true. In grade 6, students increase their computation with fractions and decimals as well as solve equations with integers. In grade 7, students solve multi-step equations with rational numbers.
• Thinking through the lens of fact families can help students think flexibly about number relationships to determine the unknown value (MTR.5.1).
• This benchmark allows for fractions in equations to include unlike denominators.
• The benchmark expects students to reason and use mental math to build their number sense. Students should not follow a specific set of steps to solve.
• 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 not see the connection to mental mathematics within the benchmark and instead try to apply rules and procedures when finding an unknown quantity.

### Strategies to Support Tiered Instruction

• Instruction includes the use of fact family prompts of whole numbers to help guide students reasoning with positive rational numbers.
• For example, the connection can be made between determining the unknown in the equation 3 ×   = 15 and in the equation $\frac{\text{1}}{\text{3}}$ × = $\frac{\text{1}}{\text{15}}$.
• Teacher provides opportunities for students to identify the relationship between the provided numbers and then co-solve the equation to determine the unknown.

• Given the equation 0.5 = $\frac{\text{c}}{\text{0.15}}$, describe a process or create a visual to explain how you can determine the value of $c$.

• If $\frac{\text{2}}{\text{9}}$ + $g$ = $\frac{\text{8}}{\text{9}}$, what value of g makes the equation true? Support your response with evidence.

• A solar panel can generate $\frac{\text{8}}{\text{25}}$ of a kilowatt of power. The average store needs to generate about 30 kilowatts of power.
• Part A. Write an equation to determine how many solar panels a store needs on its roof.
• Part B. How many solar panels does a store need?

### Instructional Items

Instructional Item 1
• Determine the value of $m$ in the equation 0.15$m$ = 0.60.

Instructional Item 2

• Given the equation $p$ −$\frac{\text{3}}{\text{5}}$ = $\frac{\text{7}}{\text{10}}$, what value of $p$ could be a solution to the equation?

*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.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 benchmark.

## Formative Assessment

Solar Solutions:

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

Type: Formative Assessment

## 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.

Type: Tutorial

## MFAS Formative Assessments

Solar Solutions:

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

## Student Resources

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

## 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.

Type: Tutorial

## Parent Resources

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