### 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.

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

**Grade:**4

**Strand:**Algebraic Reasoning

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

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- 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.

### Instructional Tasks

*Instructional Task 1*

### Instructional Items

*Instructional Item 1 *

**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 Plan

## Original Student Tutorial

## Teaching Idea

## MFAS Formative Assessments

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

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.

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

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

## Original Student Tutorials Mathematics - Grades K-5

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

## Original Student Tutorial

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