Standard #: MA.1.AR.2.3


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Determine the unknown whole number in an addition or subtraction equation, relating three whole numbers, with the unknown in any position.


Examples


Example: 9+?=12

Example: begin mathsize 12px style 17 equals square plus 5 end style

Example: ?-4=8



Clarifications


Clarification 1: Instruction begins the development of algebraic thinking skills where the symbolic representation of the unknown uses any symbol other than a letter.

Clarification 2: Problems include the unknown on either side of the equal sign.

Clarification 3: Addition and subtraction are limited to sums within 20 and related subtraction facts. Refer to Situations Involving Operations with Numbers (Appendix A).



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 deepen their understanding of the equal sign and build relational thinking when looking at equations. In Kindergarten, students used objects or drawings to explain why addition or subtraction equations are true or false (MTR.5.1). 
  • Instruction includes helping students to begin to develop the algebraic skill of determining a number that makes an equation true. 
  • Within this benchmark, students are expected to understand the meaning of the equal sign and how equations are used to model mathematical situations and problems. 
  • Instruction includes an unknown value in any position (MTR.2.1). 
  • Instruction includes presenting equations in different forms such as a + b = c or c = a + b (MTR.2.1). 
  • Instruction may include the use of a balance scale representation or bar model to help students understand how to write equations (MTR.2.1, MTR.5.1). 
    • For example, a balance model and a “bar model” for 8 = 5 + 3 are shown below

a balance model and a bar model

 

Common Misconceptions or Errors

  • Students may not understand that they can use addition to figure out a subtraction equation or use a subtraction to figure out an addition equation. In these cases, ask students to find the related facts for a given problem.

 

Strategies to Support Tiered Instruction

  • Teacher provides opportunities to use number bonds to develop an understanding of fact families and inverse relationships. 
    • For example, students create a number bond for the number 9. Students then write the fact families for the number 9. Discussion should be focused on how the fact families are related and how knowing the addition facts can help the students solve a subtraction problem. 

a number bond for number 9

  • Teacher models solving problems that highlight the relationship between addition and subtraction using a linear ten frame. Then, students use two different colors to shade the addend on the ten frame. 
    • Example: 

a ten frame with two different colors

    • Students write the addition fact that is represented on the ten frame 5 + 3 = 8. 
    • Students then subtract 3 from 8 by folding under the three “orange” blocks. 

a linear five frame in blue color

    • Students are left with the 5 “blue” blocks, so 8 – 3 = 5. 
    • Students should practice with multiple addition facts. Discussion should be focused on the relationship between addition and subtraction.

 

Instructional Tasks

Instructional Task 1 (MTR.2.1) 

Annette says the missing number for 18 − __= 14 is 8. Jessica says the missing number is 4. Who is correct? Use numbers, pictures and/or words to show your thinking. 

 

Instructional Task 2 (MTR.2.1, MTR.4.1) 

Emelio needs to find the missing number in the following number sentence:__ − 7 = 9. Draw a picture to show Emelio how he could find the missing number. Then describe how you found the missing number.

 

Instructional Task 3 (MTR.3.1) 

What missing number would balance the equation 10 = 7 + __?

 

Instructional Items

Instructional Item 1 

Which of the following equations are true with an unknown value equal to 8? 
  • a.19− __=9 
  • b.18− __=10
  • c. __= 20 − 8 
  • d. __=2+6 
  • e. 4+5= __

 

Instructional Item 2 

What is the missing addend in the equation 15 = __ + 6? 
a. 15 
b. 10 
c. 9 
d. 5 

 

Instructional Item 3

What addition equation could help to determine the unknown in the equation 13 = __ − 4? 
a. 11+2=13 
b. 10+4=14 
c. 13+4=17 
d. 4+8=12 

 

*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.3 Determine the unknown whole number in an addition or subtraction equation, relating three whole numbers, with the result unknown (e.g., 8 − 2 = __, __ = 7 + 3). Sums may not exceed 10 and their related subtraction facts.


Related Resources

Formative Assessments

Name Description
Unknowns In Word Problems

Students are read a word problem and given an equation that matches the problem, and then asked to solve for the unknown in the equation.

What Is the Missing Number?

Students are given equations and asked to find missing numbers.

Unknowns In Equations

Students are asked to find the unknown in three different equations and explain their reasoning.

Find the Missing Number

Students are given equations with a missing number and asked to find the missing number.

Lesson Plans

Name Description
Mystery Bag to 12

This lesson deals with finding an unknown number in a subtraction equation by thinking addition and counting on. It utilizes the part-part-whole organizer and manipulatives to support the learning of students.

Cookie Subtraction

In this lesson, the teacher shares the book, "Mmm... Cookie Simple Subtraction". The students follow along by representing the problems in the book with cookie manipulatives and recording the equations for each problem. The lesson incorporates a variety of subtraction problem types.

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.

What's Missing?

In this lesson, students learn to solve addition equations that have a missing addend within 10.

Ladybug Missing Numbers

This lesson will introduce the concept of determining missing numbers in addition equations.

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 Task

Name Description
Find the Missing Number

This task asks students to solve addition and subtraction equations with different structures so that they are able to see the connections between addition and subtraction more easily. Examples should be presented with the the sum or difference on either side of the equal sign in order to dispel the notion that = means "compute."

Student Resources

Problem-Solving Task

Name Description
Find the Missing Number:

This task asks students to solve addition and subtraction equations with different structures so that they are able to see the connections between addition and subtraction more easily. Examples should be presented with the the sum or difference on either side of the equal sign in order to dispel the notion that = means "compute."



Parent Resources

Problem-Solving Task

Name Description
Find the Missing Number:

This task asks students to solve addition and subtraction equations with different structures so that they are able to see the connections between addition and subtraction more easily. Examples should be presented with the the sum or difference on either side of the equal sign in order to dispel the notion that = means "compute."



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