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

### Examples

The equation 2.5+(6×2)=16-1.5 can be determined to be true because the expression on both sides of the equal sign are equivalent to 14.5.### Clarifications

*Clarification 1:*Problem types include equations that include parenthesis but not nested parentheses.

*Clarification 2:* Instruction focuses on the connection between properties of equality and order of operations.

General Information

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

**Grade:**5

**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

- Equal Sign
- 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 reliably or fluently (MTR.3.1) to the concept of the meaning of the equal sign. Students have evaluated whether equations are true or false since grade 2. In grade 5, additional expectations include non-whole numbers and parentheses. In grade 6, students extend this work to involve negative numbers and inequalities (MA.6.AR.2.1).- Students will use their understanding of order of operations (MA.5.AR.2.2) to simplify expressions on each side of an equation (MTR.5.1).
- Students will determine if the expression on the left of equal sign is equivalent to the expression to the right of the equal sign. If these expressions are equivalent, then the equation is true.
- Students may use comparative relational thinking, instead of solving, in order to determine if the equation is true or false (MTR.2.1, MTR.3.1, MTR.5.1).

### Common Misconceptions or Errors

- Some students may not understand that the equal sign is a relational symbol showing expressions on both sides that are the same. While justifying whether equations are true or false, students should explain what makes the equation true.

### Strategies to Support Tiered Instruction

- Instruction includes opportunities to explore the meaning of the equal sign. The teacher provides explicit clarification that the equal sign means “the same as” rather than “the answer is” along with 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. Instruction 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, asking students if they are true or false statements. Students explain why each equation is true or false. This is repeated with additional true and false equations using the four operations.

- For example, the teacher shows the following equations having 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 what makes equations true. This is repeated with additional true and false equations using the four operations.

### Instructional Tasks

*Instructional Task 1* (MTR.2.1)

( ___ × ___ ) − ____ = ____ − ____

12, 6.2, 5 1, 4, 3.5

### Instructional Items

*Instructional Item 1*

13.8 − 6 + 3 = 4 × 1.2

- a. This equation is true because both sides of the equation are equal to 4.8.
- b. This equation is true because both sides of the equation are equal to 10.8.
- c. This equation is false because both sides of the equation are equal to 4.8.
- d. This equation is false because both sides of the equation are unequal.

**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.

5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))

7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

5012065: Grade 4 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.5.AR.2.AP.3: Determine whether an equation (with no more than four terms and up to one set of parentheses) involving any of the four operations with whole numbers is true or false. Limit addition and subtraction to within 100 and limit multiplication and division to the products of two single-digit whole numbers and their related division facts.

## Related Resources

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

## Formative Assessments

## MFAS Formative Assessments

Place The Parentheses:

Students are given an equation and asked to place parentheses within the equation to make the equation true.

With and Without Parentheses:

Students consider two different yet similar equations and determine if they are true.

## Student Resources

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

## Parent Resources

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