# Standard 2: Add and subtract multi-digit whole numbers. Build an understanding of multiplication and division operations. Export Print
General Information
Number: MA.3.NSO.2
Title: Add and subtract multi-digit whole numbers. Build an understanding of multiplication and division operations.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.3.NSO.2.AP.1
Apply a strategy to add and subtract two two-digit whole numbers.
MA.3.NSO.2.AP.2
Explore the concept of multiplication of two single-digit whole numbers using objects.
MA.3.NSO.2.AP.3
Explore multiplying a one-digit whole number by 10.
MA.3.NSO.2.AP.4
Explore the relationship between multiplication and division in order to multiply and divide. Multiplication may not exceed two single-digit whole numbers and their related division facts.

## Related Resources

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

## Educational Games

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.

Type: Educational Game

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.

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

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

Type: Formative Assessment

Kate and Her Doll:

Students are given a context for a multiplicative comparison and asked to explain the comparison.

Type: Formative Assessment

Pet Snakes:

Students discuss the relationship between the lengths of two snakes in a multiplicative comparison problem that includes an equation.

Type: Formative Assessment

Writing an Equation to Match a Word Problem:

Students write an equation to match a given word problem.

Type: Formative Assessment

Animal Photographs:

Students read a multiplicative comparison word problem and are asked to write an equation that matches the problem.

Type: Formative Assessment

Fill In The Missing Number:

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

Type: Formative Assessment

Packages of 50:

Students consider the solution to a multiplication problem and explain their thinking.

Type: Formative Assessment

Multiplying by Multiples of Ten:

Students are asked to explain how the knowing the product of nine and three can help in finding the product of nine and 30.

Type: Formative Assessment

Explaining Multiplication Using Multiples of Ten:

Students are asked to explain why, when multiplying by a power of 10, the product has a zero in the ones place.

Type: Formative Assessment

How Are These Two Problems Related?:

Students are asked to consider how using an easier, known fact could help them solve a related multiplication problem with a multiple of 10.

Type: Formative Assessment

Using A Number Line to Solve a Division Problem:

Students are asked to explain how to use a number line for dividing, in the context of a word problem.

Type: Formative Assessment

Interpreting Division:

Students are asked to illustrate a division problem and write a corresponding equation.

Type: Formative Assessment

What Does the Six Mean?:

Students are given division word problem and asked to determine how it might have been solved and what the quotient means.

Type: Formative Assessment

Fluency with Multiplication:

Students are assessed for fluency with multiplication.

Type: Formative Assessment

Fluency with Division:

Students are assessed for fluency with division.

Type: Formative Assessment

Using Flexible Strategies:

Students are asked to describe two different ways to find the product of two numbers.

Type: Formative Assessment

Fluency with Basic Multiplication Facts:

Students are assessed on their fluency with multiplication facts for the products of two one-digit numbers.

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

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

Type: Formative Assessment

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

Type: Formative Assessment

Writing Multiplication Word Problems:

Students are asked to write multiplication word problems prompted by pictures and then to write both an addition and a multiplication expression that can be used to solve the problem.

Type: Formative Assessment

What does the 21 mean?:

Students are given a context for a multiplication problem and asked to determine how to solve it and what the product means.

Type: Formative Assessment

Multiplication on the Number Line:

Students are asked to explain how to use a number line for multiplying, in the context of a word problem.

Type: Formative Assessment

Interpreting Multiplication:

Students are asked to explain what 5 x 7 means and to provide a real-world context for 5 x 7.

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

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

In this model-eliciting activity (MEA), students will work together to determine the best bus for a class trip.  Students will be able to decide between several buses with varying capabilities and costs while practicing their application of multiplying one-digit whole numbers by a multiple of ten.

Type: Lesson Plan

In this MEA, students will work in groups to rank books using the following criteria: price, genre, number of pages, reading level and a summary provided for each book. The students must calculate the price for a class set of each book by multiplying each price by 20 students. There is a budget of \$100. Students are then given a new budget and a new criteria and asked to re-evaluate their decision.

Type: Lesson Plan

Peace Love Baseball:

Batter Up!!! Help the Peace Love Baseball Championship find a home!!! In this interactive Model-Eliciting Activity (MEA), the students will successfully multiply one digit whole numbers by multiples of 10. The students will also work collaboratively to express their opinions, while considering those of their peers.

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

Zero on a Hero (Exploring the Zero Property of Multiplication):

Students will explore the Zero Property of Multiplication using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication facts, and identify patterns in a set of multiplication facts to develop understanding of the Zero Property of Multiplication.

Type: Lesson Plan

One with a Bun (Exploring the Multiplicative Identity Property of 1):

In this lesson students will explore the Multiplicative Identity Property of 1, using array and equal-group models for multiplication. Students will model story problems, translate problems into multiplication equations, and identify patterns in a set of multiplication facts to develop understanding of the Multiplicative Identity Property of 1.

Type: Lesson Plan

Let's Multiply using Groups and Arrays:

In this lesson, students will use pictures in arrays and groups to write multiplication story problems, write an equation, solve the problem, and identify the factors and products.

Type: Lesson Plan

Product Productions:

The lesson uses a movie making theme to teach the characteristics and purpose of arrays, as well as the vocabulary, factor and product.

Type: Lesson Plan

Just Group It:

Students will be able to use counters to create equal groups and write multiplication equations to represent these representations.

Type: Lesson Plan

Multiply by Multiples of 10 with Number Cubes:

In this lesson students will use various strategies to multiply one-digit numbers by multiples of 10 within the range of 10-90. The strategies will encompass the Distributive, Commutative, and Associative properties, place value, number lines, base-ten blocks, diagrams, hundreds chart. Students will play a game with number cubes to practice this multiplication.

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.

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

Arrays Show the Way to the Multiplication Chart:

This is an introductory lesson to explore the use of arrays to solve multiplication problems. Students build arrays and save the arrays in a class Multiplication Chart. They learn to use arrays to find products and factors, and by placing them in the Multiplication Chart, they learn how to read the chart. They learn how to write equations to represent situations that are modeled with arrays. An overall theme is the organization of the multiplication chart and how it includes arrays within.

Type: Lesson Plan

Hungry Zero:

The definition of the Zero Property of Multiplication will be analyzed, modeled and practiced.

Type: Lesson Plan

Giddy Up, Round Up: Relating Division to Multiplication:

In this lesson, students will learn to solve division problems by relating them to multiplication facts. Practice materials focus on the 6's and 8's multiplication facts.

Type: Lesson Plan

Efficient Multiplication:

Students will engage with questions to evaluate the students' abilities to select and apply multiplication strategies with fluency and efficiency. The focus of the lesson is decomposing numbers to multiply using the Distributive property and understanding and applying the Commutative property. Then, students will reinforce decomposing of factors while playing Decomposition of Factors. The lesson concludes with a real world application problem on an Exit Slip.

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

Pet Store Partitive Division:

In this lesson students will model partitive division through the real-world activity of a pet store owner.

Type: Lesson Plan

Chip Chip Array!:

Students work together to create arrays to represent given numbers.

Type: Lesson Plan

Array to Multiply:

In this lesson, students will understand the concept of arrays and will be able to create/draw an array for multiplication sentences. Engaging center game is used to help students with concrete visual representation of multiplication sentences.

Type: Lesson Plan

Tasty Algebra: Using toasted O cereal to find the missing factor in a multiplication equation.:

In this lesson students will use Cheerios to solve multiplication equations relating 3 whole numbers from word problems that include missing factors ranging from one through ten. Students will also argue the validity of multiplication equations that include missing factors and products with corresponding word problems.

Type: Lesson Plan

Amazing Arrays:

This is a hands-on lesson for introducing and practicing building arrays to create models that represent the distributive property of multiplication, and then using those arrays to draw models of the equations they represent.

Type: Lesson Plan

Apples, Oranges, and Bananas of Math?:

In this lesson, the students will work in independently or in small groups to write equations to represent situations as well as their own math riddles around the concepts of multiplication. The teacher will use the book, The Grapes of Math by Greg Tang, to support this lesson.

Type: Lesson Plan

Area Isn't Just for Squares:

This lesson helps students make the connections between area and multiplication using square tiles.

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

How Many Seeds in a Pumpkin?:

In this hands-on math exploration, students will use knowledge of estimation and multiplication to develop strategies for estimating how many seeds are in a medium-sized pumpkin.

Type: Lesson Plan

Magnificent, Amazing Multiplication Arrays!:

In this lesson students will be creating, describing, and analyzing arrays as they relate to multiplication. In addition, they will be working on hands on activities that allow them to justify their answers and prove their reasoning.

Type: Lesson Plan

Way Too Much!:

In this lesson, students will learn that in some word problems too much information is given. They will learn to identify what information is needed to solve a single digit multiplication problem and what is "additional information" or way too much! With this information, they will represent their answers using arrays and explain their thinking. This is a good lesson to use after students have become comfortable with multiplication and prior to introducing multi-step problems.

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

Birthday at Home: Multiplication & Division Fluency Part 2:

Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Birthday at Home: Multiplication & Division Fluency Part 1:

Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Monkeying Around with Multiplication :

Come play with Marty the monkey as he teaches you how to understand the concept of multiplication in this interactive tutorial.

Type: Original Student Tutorial

Multiplying By Multiples of Ten: Part 2 :

Learn to multiply by multiples of ten, in this interactive tutorial!

This is the second tutorial in a two-part series. .

Type: Original Student Tutorial

Multiply By Multiples of Ten: Part 1 :

Learn how to multiply a 1-digit number by ten using a pattern to help you. This interactive tutorial is Part 1 in a two-part series about multiplying by multiples of ten.

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

Be Fair When You Share:

Allie learns to be fair when she shares and she learns more about division in this interactive tutorial.

Type: Original Student Tutorial

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.

## 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

## Student Resources

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

## 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

Birthday at Home: Multiplication & Division Fluency Part 2:

Help Jaliah continue to plan her birthday party and be fluent in her math facts using helpful facts she already knows, and the relationship between multiplication and division in Part 2 of this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Birthday at Home: Multiplication & Division Fluency Part 1:

Jaliah is ready to celebrate her birthday and use strategies of doubling and halving and relating multiplication and division for building fluency with multiplication and division facts in this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Monkeying Around with Multiplication :

Come play with Marty the monkey as he teaches you how to understand the concept of multiplication in this interactive tutorial.

Type: Original Student Tutorial

Multiplying By Multiples of Ten: Part 2 :

Learn to multiply by multiples of ten, in this interactive tutorial!

This is the second tutorial in a two-part series. .

Type: Original Student Tutorial

Multiply By Multiples of Ten: Part 1 :

Learn how to multiply a 1-digit number by ten using a pattern to help you. This interactive tutorial is Part 1 in a two-part series about multiplying by multiples of ten.

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

Be Fair When You Share:

Allie learns to be fair when she shares and she learns more about division in this interactive tutorial.

Type: Original Student Tutorial

## Educational Games

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.

Type: Educational Game

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.

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

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.

## 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 topic.

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.

## 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