MA.5.AR.2.3

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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
Standard: Demonstrate an understanding of equality, the order of operations and equivalent numerical expressions.
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. 
table
    • 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.

counters, drawings, or base-ten blocks on a t-chart

Instruction includes opportunities for students to organize and structure their algebraic tasks. Teachers should encourage students to label and annotate expressions on both sides of the equation prior to solving. This structured approach enables students to identify occasions where they can apply the properties of operations and the order of operations for problem-solving. Encourage students to contemplate the operations required to solve the expressions on both sides of the equation (MTR.1.1).

 

Instructional Tasks

Instructional Task 1 (MTR.2.1) 

Using the numbers below, create the equation that is true. 

( ___ × ___ ) - ____ = ____ - ____

12, 6.2, 5.2, 0.4, 3.8

Instructional Task 2

Part A. Determine if the following equation is true or false.

(3×4)+2=(24÷2)+(9-7)

Part B. Determine if the models and steps shown correctly represent the expressions on both sides of the equation in Part A.

 

Instructional Task 3

Use each operation symbol (+,-,×,÷) once in the equation below to make it true.

9 ___ (7___4) ___6___2=34

 

 

expression on the left

Instructional Items

Instructional Item 1

Which best explains the equation below?
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. 
Instructional Item 2

Use the operation signs once in the expression below to make the number sentence true.

9 ___ (7___4) ___6___2=34

Instructional Item 3

Place the parentheses in the appropriate place to make the equation true.

352÷12-4×4=176

 

a. The value of x is 2.5 because it makes both expressions equal 13.5.
b. The value of x is 13.5 because it is found when following the order of operations.
c. The value of x is 16 because it is value on the right side of the equal sign.
d. The value of x is 29.5 because 16 + 13.5 is 29.5.

 

 

 

 

*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 - 2024, 2024 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 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 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

With and Without Parentheses:

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

Type: Formative Assessment

Place The Parentheses:

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

Type: Formative Assessment

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.