MA.3.NSO.2.1

Add and subtract multi-digit whole numbers including using a standard algorithm with procedural fluency.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 3
Strand: Number Sense and Operations
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

Terms from the K-12 Glossary

  • Expression
  • Equation 
  • Whole Number

Vertical Alignment

Previous Benchmarks

Next Benchmarks

Purpose and Instructional Strategies

The purpose of this benchmark is for students to add and subtract multi-digit whole numbers with procedural fluency. Students use skills from the procedural reliability stage in Grade 2 to become fluent with efficient and accurate procedures, including standard algorithms for addition and subtraction. 
  • A standard algorithm is defined as any efficient and accurate procedure that allows students to add and subtract whole numbers. Students’ choices of standard algorithms for addition and subtraction do not need to be the same (MTR.5.1). 
  • Students should be able to justify their use of a standard algorithm for adding and subtracting by explaining the steps mathematically. Each student should be able to explain if and when regrouping is needed, and how regrouping is computed using their chosen algorithm. During instruction, teachers and students should work together to relate place value understanding to algorithms (MTR.3.1, MTR.4.1, MTR.5.1). 
  • Problems should include both vertical and horizontal forms, including opportunities for students to apply the commutative and associative properties. 
  • Instruction of this benchmark should be taught with MA.3.NSO.1.4. Students should use rounding as a means to estimate reasonable solutions of sums and differences before calculating (MTR.6.1).

Common Misconceptions or Errors

  • Students who learn a standard algorithm without being able to explain why it works using place value understanding often make computational errors and/or cannot determine if their solutions are reasonable. To assist students with this misconception, teachers should expect students to justify the algorithm they choose.

Strategies to Support Tiered Instruction

  • Instruction includes guiding students through the process of estimating reasonable values for sums and differences using an understanding of place value, addition, and subtraction. 
    • For example, students make reasonable estimates for the sum of 174 + 253. Instruction includes a prompt such as “Before using an algorithm, we will estimate the sum to make sure that we are using the algorithm correctly and our answer is reasonable. The first addend of 174 is close to the benchmark number 200 and the second addend of 253 is close to the benchmark number 250. So, we can use 200 + 250 = 450 to estimate that our sum should be close to 450.” 
  • Instruction includes guiding students through the process of explaining and justifying the chosen algorithm and determining if an algorithm was used correctly by reviewing the reasonableness of solutions. 
    • For example, students use a standard algorithm to solve 174 + 253 and explain their thinking using a place value visual representation. Instruction includes a prompt such as “Begin by adding in the one's place. 4 ones plus 3 ones is 7 ones. Because the total number of ones is less than 10, it is not necessary to regroup. Next, add in the tens place. 7 tens plus 5 tens is 12 tens. Because I have more than 10 tens it is necessary to regroup the 10 tens to make one hundred. After composing a group of 10 tens there are 2 tens remaining. Finally, add 1 hundred plus 2 hundreds. Add the 1 hundred that was regrouped from the tens place. The sum is 427. Our sum of 427 is close to our estimate of 450, this helps us determine that our answer is reasonable” 

  • For example, students use a standard algorithm to solve 327 − 174 and explain their thinking using a place value visual representation. Instruction includes prompts such as “ Begin subtracting 174 starting in the one's place. 7 ones minus 4 ones are 3 ones. There are not enough tens to subtract 7 tens from 2 tens. It is necessary to decompose one hundred into 10 tens. Now there are 12 tens, and there is enough to subtract 7 tens. 12 tens minus 7 tens equals 5 tens. Finally, subtract the hundreds: 3 hundreds minus 1 hundred equals 2 hundreds. The difference is 253.” 

a standard algorithm to solve 327 - 174

  • For example, students use a standard algorithm and base-ten blocks to solve 62 − 37 and explain their thinking using a place value visual representation. Instruction includes a prompt such as “Begin subtracting 37 starting in the one's place. There are not enough ones to subtract 7 ones from 2 ones. It is necessary to decompose one ten into 10 ones. Now there are 12 ones and there is enough to subtract 7 ones. 12 ones take away 7 ones equals 5 ones. Finally, subtract the tens: 5 tens minus 3 tens is 2 tens. The difference is 25.” 

a standard algorithm and base-ten blocks to solve 62 - 37

  • Teacher provides guidance on using strategies based on place value to add and subtract. 
    • For example, students use strategies based on place value to solve 174 + 253.

strategies based on place value to solve 174 + 253

Instructional Tasks

Instructional Task 1 

  • Miranda finds 492 seashells during her vacation. She now has 1,045 seashells in her collection. How many seashells did she have in her collection before vacation? 
    • Part A. Solve using a standard algorithm. 
    • Part B. Indicate one step where you needed to regroup while solving and show how you did it using words or a pictorial model.

Instructional Items

Instructional Item 1 

  • What is the sum of 1,432 and 2,981? 

Instructional Item 2

  • What is the difference of 8,000 and 1,432? 
*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.
5012050: Grade Three Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712040: Access Mathematics Grade 3 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.3.NSO.2.AP.1: Apply a strategy to add and subtract two two-digit whole numbers.

Related Resources

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

Educational Games

Ice Ice Maybe: An Operations Estimation Game:


This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

Estimator Quiz:

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

Educational Software / Tool

Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

Formative Assessments

Subtracting Using the Standard Algorithm:

Students are asked to solve two subtraction problems using the standard algorithm.

Type: Formative Assessment

Find the Error:

Students are asked to find the error in a partially completed subtraction problem using the standard algorithm and to solve the problem correctly.

Type: Formative Assessment

Addition Using the Standard Algorithm:

Students are asked to solve two addition problems using the standard algorithm.

Type: Formative Assessment

Fill In The Missing Number:

Students are asked to complete subtraction problems using the standard algorithm.

Type: Formative Assessment

Andy's Book:

Students add four two-digit numbers within the context of a word problem.

Type: Formative Assessment

Adding Two Digit Numbers Using Properties of Operations:

Students are asked to add four two digit numbers by considering how another student added "friendly" numbers first.

Type: Formative Assessment

Wanda's Method:

The student is encouraged to use compensation to efficiently add multi-digit numbers.

Type: Formative Assessment

Subtraction Within 1000:

Students are asked to complete four subtraction problems (within 1000) using strategies of their own choosing.

Type: Formative Assessment

Adding and Subtracting Using Properties:

Students are asked to complete addition and subtraction problems that can be done more easily by using properties.

Type: Formative Assessment

Addition Within 1000:

Students are asked to add four different pairs of numbers (within 1000) using strategies of their own choosing.

Type: Formative Assessment

Adding Two Digit Numbers Using Place Value:

Students are asked to add four two digit numbers using place value.

Type: Formative Assessment

Adding Four Two-Digit Numbers:

Students add four two-digit numbers without the context of a word problem.

Type: Formative Assessment

Lesson Plans

Food Drive:

A data table is given listing class donations to a food drive. Students interpret the data and answer questions using addition and subtraction. Students discuss the importance of, volunteerism and ways that they can help their community. 

Type: Lesson Plan

Rampin' It Up:

Students will use their knowledge of properties of materials and measurement of length to determine how the properties of different surfaces affect the distance traveled by a toy car.

Type: Lesson Plan

DOLO - Dinosaurs Only Live Once?:

During this activity, students will create an incubator to save the last dinosaur eggs. Students will use their knowledge of energy to develop a strategy and choose which materials would be best for their dinosaur egg incubator.

Type: Lesson Plan

"Amazing Race-Elapsed Time":

In this lesson, which focuses specifically on the elapsed time portion of the standard, students work in small groups in a "race" to solve real world problems involving time.

Type: Lesson Plan

Let's Think in Small Units:

In this lesson students will make and complete tables to express larger unit measurements in terms of a smaller unit within one system of units. They will use the chart to make comparisons and explain their reasoning.

Type: Lesson Plan

Dining Dilemma!:

The students will compare different nutritional content of chicken nuggets from many restaurants. They will factor in the calories, the total fat, saturated fat, and sodium levels in the nuggets to rank the nuggets from healthiest to least healthy.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Kites for Education MEA:

Kites for Education is a Modeling Eliciting Activity which presents students with an engineering challenge in which they must analyze data sets and develop a procedure for ranking different kite models. The product ranked as best by the students will hypothetically be sold to customers and the profit used to purchase school textbooks and supplies for school age children impacted by Haiti's devastating earthquake.

Type: Lesson Plan

Jumping Beans: Adding with Open Number Lines:

Students will use the open number line as a strategy to add within 1,000. The lesson begins with a formative assessment that evaluates students' strategies for efficiently solving addition sentences within 1,000. In order for students to have practice reinforcing the skill, students will complete the guided practice with open number lines, as well as playing the game, Jumping Beans. To conclude the lesson, students will evaluate a solution to an open number line problem.

Type: Lesson Plan

Subtraction Attraction:

In this lesson, students will demonstrate fluency in using a standard algorithm to complete story problems involving subtraction with regrouping using multi-digit whole numbers.

Type: Lesson Plan

Rip and Regroup to Add:

Students will learn how to transpose a horizontal addition equation with two-digit addends using a specialized vertical place value work mat. Students will "rip and regroup" to help understand how to regroup ten ones as one ten and move toward using a standard algorithm for addition.

Type: Lesson Plan

Decoding Decomposing {Adding two 3-digit Numbers}:

Students will add 3-digit numbers by decomposing them by place value.  It is a useful lesson to reinforce place value concepts when adding.

Type: Lesson Plan

Original Student Tutorials

Responsibility to Vote Part 2: Graphing Data:

Learn how to use a bar graph to summarize voting results at school in this interactive tutorial. 

This is part 2 in a two-part series. Click HERE to open Part 1.

Type: Original Student Tutorial

Responsibility to Vote Part 1:

United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project. 

Type: Original Student Tutorial

Adding It All Up with a Standard Algorithm:

Learn to add multi-digit numbers using a standard algorithm in this interactive tutorial.

Type: Original Student Tutorial

Speedy Sam:

Help Speedy Sam add and subtract as quickly as possible by using the properties of addition and subtraction in this interactive tutorial. 

Type: Original Student Tutorial

Perspectives Video: Experts

Fluency vs. Automaticity:

How are fluency and automaticity defined? Dr. Lawrence Gray explains fluency and automaticity in the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

The Role of Procedures in Fluency:

What are the components to a good procedure? Dr. Lawrence Gray discusses the role of procedures in the path to fluency in this Expert Perspectives video.

Type: Perspectives Video: Expert

That's Not How I Learned it: Why today's math may look different:

Why do students need "a" good procedure for the arithmetic operations? Dr. Lawrence explains why math may look different than in the past in this Expert Perspectives video.

Type: Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

Why Isn't Getting the "Right" Answer Good Enough?:

Why is it important to look beyond whether a student gets the right answer? Dr. Lawrence Gray explores the importance of understanding why we perform certain steps or what those steps mean, and the impact this understanding can have on our ability to solve more complex problems and address them in the context of real life in this Expert Perspectives video.

Type: Perspectives Video: Expert

A Standard Algorithm:

Ever wonder why the benchmarks say, “a standard algorithm,” instead of, “the standard algorithm?" Dr. Lawrence Gray explores the role that standard algorithms can play in building and exhibiting procedural fluency through this Expert Perspectives video.

Type: Perspectives Video: Expert

Problem-Solving Task

To regroup or not to regroup:

This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping. This way students have to recognize the pattern and not just follow a memorized algorithm--in other words, they have to think about what happens in the subtraction process when we regroup. This task is appropriate to use after students have learned the standard US algorithm.

Type: Problem-Solving Task

Tutorials

Subtracting: regrouping twice:

In this video tutorial from Khan Academy, learn how to subtract in situations that require regrouping twice using the expanded forms of numbers, as well as the standard algorithm.

Type: Tutorial

Mental technique for subtraction without regrouping:

In this Khan Academy video tutorial, consider an alternate algorithm for subtracting multi-digit numbers mentally. This video is best for students that are already comfortable with using regrouping to subtract using the standard algorithm.

Type: Tutorial

STEM Lessons - Model Eliciting Activity

Dining Dilemma!:

The students will compare different nutritional content of chicken nuggets from many restaurants. They will factor in the calories, the total fat, saturated fat, and sodium levels in the nuggets to rank the nuggets from healthiest to least healthy.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Kites for Education MEA:

Kites for Education is a Modeling Eliciting Activity which presents students with an engineering challenge in which they must analyze data sets and develop a procedure for ranking different kite models. The product ranked as best by the students will hypothetically be sold to customers and the profit used to purchase school textbooks and supplies for school age children impacted by Haiti's devastating earthquake.

MFAS Formative Assessments

Adding and Subtracting Using Properties:

Students are asked to complete addition and subtraction problems that can be done more easily by using properties.

Adding Four Two-Digit Numbers:

Students add four two-digit numbers without the context of a word problem.

Adding Two Digit Numbers Using Place Value:

Students are asked to add four two digit numbers using place value.

Adding Two Digit Numbers Using Properties of Operations:

Students are asked to add four two digit numbers by considering how another student added "friendly" numbers first.

Addition Using the Standard Algorithm:

Students are asked to solve two addition problems using the standard algorithm.

Addition Within 1000:

Students are asked to add four different pairs of numbers (within 1000) using strategies of their own choosing.

Andy's Book:

Students add four two-digit numbers within the context of a word problem.

Fill In The Missing Number:

Students are asked to complete subtraction problems using the standard algorithm.

Find the Error:

Students are asked to find the error in a partially completed subtraction problem using the standard algorithm and to solve the problem correctly.

Subtracting Using the Standard Algorithm:

Students are asked to solve two subtraction problems using the standard algorithm.

Subtraction Within 1000:

Students are asked to complete four subtraction problems (within 1000) using strategies of their own choosing.

Wanda's Method:

The student is encouraged to use compensation to efficiently add multi-digit numbers.

Original Student Tutorials Mathematics - Grades K-5

Adding It All Up with a Standard Algorithm:

Learn to add multi-digit numbers using a standard algorithm in this interactive tutorial.

Speedy Sam:

Help Speedy Sam add and subtract as quickly as possible by using the properties of addition and subtraction in this interactive tutorial. 

STEM Civics Tutorials and Videos - Grades K-12

Responsibility to Vote Part 1:

United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project. 

Responsibility to Vote Part 2: Graphing Data:

Learn how to use a bar graph to summarize voting results at school in this interactive tutorial. 

This is part 2 in a two-part series. Click HERE to open Part 1.

Student Resources

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

Original Student Tutorials

Responsibility to Vote Part 2: Graphing Data:

Learn how to use a bar graph to summarize voting results at school in this interactive tutorial. 

This is part 2 in a two-part series. Click HERE to open Part 1.

Type: Original Student Tutorial

Responsibility to Vote Part 1:

United States citizens have a responsibility to vote. In this integrated civics and math tutorial, a class collects voting data to display in a table showing the students' and teachers' choices for a new school project. 

Type: Original Student Tutorial

Adding It All Up with a Standard Algorithm:

Learn to add multi-digit numbers using a standard algorithm in this interactive tutorial.

Type: Original Student Tutorial

Speedy Sam:

Help Speedy Sam add and subtract as quickly as possible by using the properties of addition and subtraction in this interactive tutorial. 

Type: Original Student Tutorial

Educational Games

Ice Ice Maybe: An Operations Estimation Game:


This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

Type: Educational Game

Estimator Quiz:

In this activity, students are quizzed on their ability to estimate sums, products, and percentages. The student can adjust the difficulty of the problems and how close they have to be to the actual answer. This activity allows students to practice estimating addition, multiplication, or percentages of large numbers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Game

Educational Software / Tool

Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

Problem-Solving Task

To regroup or not to regroup:

This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping. This way students have to recognize the pattern and not just follow a memorized algorithm--in other words, they have to think about what happens in the subtraction process when we regroup. This task is appropriate to use after students have learned the standard US algorithm.

Type: Problem-Solving Task

Tutorials

Subtracting: regrouping twice:

In this video tutorial from Khan Academy, learn how to subtract in situations that require regrouping twice using the expanded forms of numbers, as well as the standard algorithm.

Type: Tutorial

Mental technique for subtraction without regrouping:

In this Khan Academy video tutorial, consider an alternate algorithm for subtracting multi-digit numbers mentally. This video is best for students that are already comfortable with using regrouping to subtract using the standard algorithm.

Type: Tutorial

Parent Resources

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

Problem-Solving Task

To regroup or not to regroup:

This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping. This way students have to recognize the pattern and not just follow a memorized algorithm--in other words, they have to think about what happens in the subtraction process when we regroup. This task is appropriate to use after students have learned the standard US algorithm.

Type: Problem-Solving Task

Tutorials

Subtracting: regrouping twice:

In this video tutorial from Khan Academy, learn how to subtract in situations that require regrouping twice using the expanded forms of numbers, as well as the standard algorithm.

Type: Tutorial

Mental technique for subtraction without regrouping:

In this Khan Academy video tutorial, consider an alternate algorithm for subtracting multi-digit numbers mentally. This video is best for students that are already comfortable with using regrouping to subtract using the standard algorithm.

Type: Tutorial