# MA.1.AR.2.2

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

### Examples

Given the following equations, 8=8, 9-1=7, 5+2=2+5 and 1=9-8, 9-1=7 can be determined to be false.

### Clarifications

Clarification 1: Instruction focuses on understanding of the equal sign.
Clarification 2: Problem types are limited to an equation with no more than four terms. The sum or difference can be on either side of the equal sign.
Clarification 3: Addition and subtraction are limited to sums within 20 and related subtraction facts.
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
• Expression

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

The purpose of this benchmark is for students to understand that the equal sign means “the same as.” In Kindergarten, students used objects or drawings to explain why addition or subtraction equations are true or false.
• Instruction should include a variety of problem types where the sum or difference can be on either side of the equal sign. adding 2 and 4.
• Instruction may include the use of a balance with cubes to help students understand that the equal sign means the same as (MTR.2.1, MTR.6.1).
• For example, 8 = 3 + 5 is true because 8 is the result of adding 5 and 3.
• For example, 8 = 2 + 4 is false because 8 is more than 6, which is the result of adding 2 and 4.
• For example, 8 = 3 + 7 is false because 8 is less than 10, which is the result of adding 3 and 7.

### Common Misconceptions or Errors

• Students may not understand that the equal sign means “the same as,” since they may think the equal sign signals that the answer comes at the end. In these cases it can be beneficial to use a scale where students can complete problems to discover if in fact they are equal.

### Strategies to Support Tiered Instruction

• Teacher provides number cards to build balanced equations.
• For example, using two sets of number cards 0 – 9, students build equations with two single digit addends on both sides.
4+3=6+1
• Alternatively, the teacher provides two of the missing addends and allows students to make the equation true using their number cards.
4 + ___ = 6 + ___

• Instruction 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.”

Instructional Task 1 (MTR.3.1

Lee had 14 building blocks. He then shared 6 of his blocks with his friend Remi. Create a true statement to show how many building blocks Lee has left.

Instructional Task 2 (MTR.4.1

The answer to a problem is 15. Halsey says a true statement is 15 = 20 − 5. Henry says a true statement is 11 + 4 = 15. Who is correct? How do you know?

### Instructional Items

Instructional Item 1

Tiffany says that 9 = 8 + 1 is a true statement. Paulie says it is a false statement. Who do you agree with Tiffany or Paulie? Why?

Instructional Item 2

What does the equal sign in 11 = 10 + 1 mean?

Instructional Item 3

Which of the following statements are true?
a. 17 = 18 − 1
b. 16 = 16 + 1
c. 14 − 6 = 8
d. 12 = 12
e. 2 + 8 = 11

Instructional Item 4

Create a true statement where 19 is the sum.

Instructional Item 5

Create a true statement where 17 is the difference.

*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.
5012030: Mathematics - Grade One (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712020: Access Mathematics Grade 1 (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.1.AR.2.AP.2: Determine if addition or subtraction equations (with no more than three terms) are true or false. Sums may not exceed 10 and their related subtraction facts.

## Related Resources

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

## Formative Assessments

Is the Equation True or False?:

Students are given sets of equations and asked to circle the equations that are true.

Type: Formative Assessment

More True and False Equations:

Students are given a set of equations and asked to circle the equations that are true.

Type: Formative Assessment

Does It Work For Subtraction?:

Students discuss if the Commutative Property holds for subtraction.

Type: Formative Assessment

True or Not True:

Students examine four equations and state if they are true or not true. Students must also justify their reasoning.

Type: Formative Assessment

Equality:

Students are asked to justify why two equations are true using two different strategies.

Type: Formative Assessment

Equal or Not Equal:

The student determines if a given equation is true or false.

Type: Formative Assessment

## Lesson Plans

Make Mine Equal:

Students will explore the meaning of the equal sign by creating and completing equations that have two addends on each side of the equation. Note that this lesson focuses on addition equations, though it can easily be adapted to include subtraction equations.

Type: Lesson Plan

Students will explore the meaning of the equal sign by representing an equation with manipulatives on a scale. The students will be asked to decide if an addition or subtraction equation is true or false by proving it with and without a scale. Students will determine the missing number in addition or subtraction equations.

Type: Lesson Plan

Understanding the Equal Sign:

This lesson helps students to understand the meaning of the equal sign and to realize that one side of an equation must equal (balance) the other side of the equation.

Type: Lesson Plan

True or False?:

In this lesson, students will explore true and false addition and subtraction equations through a variety of hands-on learning activities. Detailed center ideas are also covered in this lesson.

Type: Lesson Plan

## Original Student Tutorial

Teams with the Same Amount:

Learn how to tell whether an equation is true or false based on what you know about the equal sign as you complete this interactive tutorial.

Type: Original Student Tutorial

## 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

Equality Number Sentences:

The purpose of this instructional task is for students to help students understand the meaning of the equal sign and to use it appropriately. The idea is that students should be comparing the number of circles in each of the rectangles and to write an equation that reflects the fact there are an equal number in each of the boxes (when this is the case).

Kiri's Mathematics Match Game:

In all versions, students must engage basic addition and subtraction facts. In the memory version, after a student has turned over one card, in order to know whether there is a match using cards they've seen, they need to to solve equations of the form ?+b=c, b+?=c, ?-b=c, and b-?=c.

Valid Equalities?:

The purpose of this task is to help broaden and deepen students' understanding of the equals sign and equality. This task helps students attend to precision by helping them explicitly attend to the meaning of mathematical notation and carefully analyze whether it is being used correctly.

Using lengths to represent equality:

The act of trying to find equal lengths with the rods helps students develop a physical understanding for the meaning of equality. Students are more likely to generate and understand complex equalities than they would be able to do only abstractly.

## Tutorial

Understanding the Meaning of the Equal Sign:

In this tutorial, you will learn more about what the equals sign means and how to balance equations.

Type: Tutorial

## MFAS Formative Assessments

Does It Work For Subtraction?:

Students discuss if the Commutative Property holds for subtraction.

Equal or Not Equal:

The student determines if a given equation is true or false.

Equality:

Students are asked to justify why two equations are true using two different strategies.

Is the Equation True or False?:

Students are given sets of equations and asked to circle the equations that are true.

More True and False Equations:

Students are given a set of equations and asked to circle the equations that are true.

True or Not True:

Students examine four equations and state if they are true or not true. Students must also justify their reasoning.

## Original Student Tutorials Mathematics - Grades K-5

Teams with the Same Amount:

Learn how to tell whether an equation is true or false based on what you know about the equal sign as you complete this interactive tutorial.

## Student Resources

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

## Original Student Tutorial

Teams with the Same Amount:

Learn how to tell whether an equation is true or false based on what you know about the equal sign as you complete this interactive tutorial.

Type: Original Student Tutorial

Equality Number Sentences:

The purpose of this instructional task is for students to help students understand the meaning of the equal sign and to use it appropriately. The idea is that students should be comparing the number of circles in each of the rectangles and to write an equation that reflects the fact there are an equal number in each of the boxes (when this is the case).

Valid Equalities?:

The purpose of this task is to help broaden and deepen students' understanding of the equals sign and equality. This task helps students attend to precision by helping them explicitly attend to the meaning of mathematical notation and carefully analyze whether it is being used correctly.

## Tutorial

Understanding the Meaning of the Equal Sign:

In this tutorial, you will learn more about what the equals sign means and how to balance equations.

Type: Tutorial

## Parent Resources

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

Equality Number Sentences:

The purpose of this instructional task is for students to help students understand the meaning of the equal sign and to use it appropriately. The idea is that students should be comparing the number of circles in each of the rectangles and to write an equation that reflects the fact there are an equal number in each of the boxes (when this is the case).

Kiri's Mathematics Match Game:

In all versions, students must engage basic addition and subtraction facts. In the memory version, after a student has turned over one card, in order to know whether there is a match using cards they've seen, they need to to solve equations of the form ?+b=c, b+?=c, ?-b=c, and b-?=c.