# MA.4.AR.2.1

Determine and explain whether an equation involving any of the four operations with whole numbers is true or false.

### Examples

The equation 32÷8=32-8-8-8-8 can be determined to be false because the expression on the left side of the equal sign is not equivalent to the expression on the right side of the equal sign.

### Clarifications

Clarification 1: Multiplication is limited to whole number factors within 12 and related division facts.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

• Equation
• Expression

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is to determine if students can connect their understanding of using the four operations fluently (MTR.3.1) to the concept of the meaning of the equal sign. This concept builds on the understanding of determining if addition and subtraction equations (MA.2.AR.2.2) and multiplication and division equations (MA.3.AR.2.2) are true and false.
• Students will determine if the expression on the left of the equal sign is equivalent to the expression to the right of the equal sign. If these expressions are equivalent, then the equation will be deemed true.
• Students may use comparative relational thinking or estimation, instead of solving, to determine if the equation is true or false.

### Common Misconceptions or Errors

• Many students have difficulty understanding that the equal sign is a relational symbol. They believe that the equal sign makes the expression on the right side of the equation equal to the expression on the left side so that all equations would be true. Instead an equation with an equal sign can be true or false, depending on whether the expressions on each side of the equal sign are equal to each other or not.

### Strategies to Support Tiered Instruction

• Instruction includes opportunities to explore the meaning of the equal sign. The teacher provides clarification that the equal sign means “the same as” rather than “the answer is,” providing multiple examples for students to evaluate equations as true or false using the four operations with the answers on both the left and right side of the equation. The teacher begins by using single numbers on either side of the equal sign to build understanding and uses the same equations written in different ways to reinforce the concept.
• For example, the teacher shows the following equations. Students are asked if they are true or false statements and to explain why. This is repeated with additional true and false equations using the four operations.

• Teacher provides opportunities to explore the meaning of the equal sign using visual representations (e.g., counters, drawings, base-ten blocks) on a t-chart to represent the equations. The teacher provides clarification that the equal sign means “the same as” rather than “the answer is,” and provides multiple examples for students to evaluate equations as true or false using the four operations with the answers on both the left and right side of the equation. The teacher begins by using single numbers on either side of the equal sign to build understanding, using the same equations written in different ways to reinforce the concept.
• For example, the teacher shows the following equations. Students use counters, drawings, or base-ten blocks on a t-chart to represent the equation. The teacher asks students if they are true or false statements and to explain why. This is repeated with additional true and false equations using the four operations.

Using the numbers below, create an equation that is true.
__ × __ = __ × __
3, 5, 6, 10

### Instructional Items

Instructional Item 1

Determine whether the equation below is true or false.
86 + 58 = 144 ÷ 12

*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.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.4.AR.2.AP.1: Determine whether an equation (with no more than three terms) involving any of the four operations with whole numbers is true or false. Sums may not exceed 100 and their related subtraction facts. Multiplication may not exceed two-digit by one-digit and division must be related to one-digit by one-digit multiplication facts.

## Related Resources

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

## Formative Assessments

True and False Multiplication Equations:

Students are asked to determine if each of two equations is true without performing any operations.

Type: Formative Assessment

True and False Division Equations:

Students are asked to determine if each of two equations is true by comparing mathematical expressions and without actually carrying out the indicated calculations.

Type: Formative Assessment

Determining If an Equation Is True:

Students are asked to determine if each of two equations involving subtraction is true by comparing mathematical expressions and without actually carrying out the calculations.

Type: Formative Assessment

Are the Equations True?:

Students are asked to determine if each of two equations is true without performing any operations.

Type: Formative Assessment

## Lesson Plans

Is the Equation True and Finding the Missing Number:

Students will determine if an equation is true or false based on using comparative relational thinking and knowledge of operations. The students will also determine the unknown number in some equations involving addition.

Type: Lesson Plan

Is my equation TRUE or FALSE?:

In this lesson, students will determine if equations are true or false and justify their reasoning. The lesson focuses on the meaning operations and properties.

Type: Lesson Plan

## Original Student Tutorial

Think Different: Relationships in Math:

Learn how to think differently to see if an equation is true or false, without even having to do the given math problem in this interactive tutorial on addition and subtraction relationships.

Type: Original Student Tutorial

## 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

## MFAS Formative Assessments

Are the Equations True?:

Students are asked to determine if each of two equations is true without performing any operations.

Determining If an Equation Is True:

Students are asked to determine if each of two equations involving subtraction is true by comparing mathematical expressions and without actually carrying out the calculations.

True and False Division Equations:

Students are asked to determine if each of two equations is true by comparing mathematical expressions and without actually carrying out the indicated calculations.

True and False Multiplication Equations:

Students are asked to determine if each of two equations is true without performing any operations.

## Original Student Tutorials Mathematics - Grades K-5

Think Different: Relationships in Math:

Learn how to think differently to see if an equation is true or false, without even having to do the given math problem in this interactive tutorial on addition and subtraction relationships.

## Student Resources

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

## Original Student Tutorial

Think Different: Relationships in Math:

Learn how to think differently to see if an equation is true or false, without even having to do the given math problem in this interactive tutorial on addition and subtraction relationships.

Type: Original Student Tutorial

## Parent Resources

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