# MA.2.AR.2.1

Determine and explain whether equations involving addition and subtraction are true or false.

### Examples

The equation 27+13=26+14 can be determined to be true because 26 is one less than 27 and 14 is one more than 13.

### Clarifications

Clarification 1: Instruction focuses on understanding of the equal sign.

Clarification 2: Problem types are limited to an equation with three or four terms. The sum or difference can be on either side of the equal sign.

Clarification 3: Addition and subtraction are limited to sums up to 100 and related differences.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

## Benchmark Instructional Guide

• Equal sign
• Equation

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is to further develop an understanding of the equal sign by examining equations. In grade 1, students determined and explained whether equations involving addition and subtraction within 20 were true or false.
• Instruction includes the use of manipulatives or drawings to show balanced equations.
• Instruction includes equations where the minuend, subtrahend or addends are on either side of the equal sign.
• Instruction includes equations in different forms such as a + b = c or c = a + b.
• Instruction includes examples of equations that are false.

### Common Misconceptions or Errors

• Students may not understand the equal sign means “the same as” and only relate it to “the answer is.”
• Students may think the equal sign requires them to do something.

### Strategies to Support Tiered Instruction

• Teacher provides opportunities to use a number balance to support understanding of the equal sign.
• For example, students build the expression 5 + 6 on one side of the balance and are asked to build an expression of equal magnitude of the other side. Students may choose to use a 9 and a 2, an 8 and a 3, or a 7 and a 4. Since students cannot use an 11 and must use two separate numbers instead, they are dispelling the misconception that the equal sign means “the answer is.”
• Teacher provides examples of simple equations with no operations to determine if they are true or false using a number balance. Focus should be on the equality of an equation that only contains the equal sign. Students may draw a picture to show the quantities are equal.
• For example, the equation 5 = 5 can be modeled using the number balance below.
• Teacher provides manipulatives to model each side of the equation to determine if an equation is true or false.
• For example, for the equation 8 + 6 = 10 + 5 students would use two-color counters to build each side of the equation and then count to determine if they are equal.
• Teacher provides opportunities to use a balance to explore simple equations that only contain an equal sign.
• For example, students use cubes to represent the equation on the balance using the equations 5 = 5, 8 = 8, and 3 = 3.

Instructional Task 1 (MTR.6.1

Provide students the table below. Ask students to determine and explain how they know that each equation is true or false.

### Instructional Items

Instructional Item 1

Which of the following explains why 15 + 18 = 25 + 8 is a true equation?
• a. The equation 15 + 18 = 25 + 8 is true because 15 is ten less than 25 and 18 is ten more than 8.
• b. The equation 15 + 18 = 25 + 8 is true because both equations are adding 8 ones.
• c. The equation 15 + 18 = 25 + 8 is true because both equations have a number that has a 5 in the ones place.

*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.
5012040: Mathematics - Grade Two (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712030: Access Mathematics Grade 2 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012005: Foundational Skills in Mathematics K-2 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.2.AR.2.AP.1: Determine if addition or subtraction equations with no more than three terms are true or false. Sums may not exceed 20 and their related subtraction facts.

## Related Resources

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

## Lesson Plans

Are Your Numbers Equal to My Numbers?:

This is a lesson that reinforces the meaning of the equal sign while students determine the unknown whole number in an addition equation.

Type: Lesson Plan

Odds and Evens:

This resource helps students identify numbers as odd or even using a variety of methods including creating pairs, skip counting by two’s, using number lines, and arrays. It also leads them to understand that all even numbers can be written as a sum of equal addends and odds can be written as the sum of equal addends plus one.

This resource can be conducted as one lesson or can be spread over multiple mini sessions if needed as noted within this resource as Lesson 1 and Lesson 2.

Type: Lesson Plan

## Perspectives Video: Teaching Idea

Equations on the Math Balance:

Unlock an effective teaching strategy for teaching inequalities and equations with the math balance in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

## 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.