Standard #: MA.1.AR.2.2


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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.)
Grade: 1
Strand: Algebraic Reasoning
Standard: Develop an understanding of the relationship between addition and subtraction.
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 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.
straight balance with cubes
    • For example, 8 = 2 + 4 is false because 8 is more than 6, which is the result of adding 2 and 4. 
left balance with cubes
    • For example, 8 = 3 + 7 is false because 8 is less than 10, which is the result of adding 3 and 7.
right balance with cubes

 

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 + ___ 

two sets of number cards

  • 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 Tasks

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

Course Number1111 Course Title222
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

Access Point Number Access Point Title
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

Formative Assessments

Name Description
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.

Does It Work For Subtraction?

Students discuss if the Commutative Property holds for subtraction.

True or Not True

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

Equality

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

Equal or Not Equal

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

Lesson Plans

Name Description
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.

Weigh your options!

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.

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.

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.

Original Student Tutorial

Name Description
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.

Perspectives Video: Teaching Idea

Name Description
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.

Problem-Solving Tasks

Name Description
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

Name Description
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.

Student Resources

Original Student Tutorial

Name Description
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.

Problem-Solving Tasks

Name Description
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

Name Description
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.



Parent Resources

Problem-Solving Tasks

Name Description
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.



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