 # Standard 2 : Use place value understanding and properties of operations to perform multi-digit arithmetic. (Major Cluster) (Archived)

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Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

### General Information

Number: MAFS.4.NBT.2
Title: Use place value understanding and properties of operations to perform multi-digit arithmetic. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Number and Operations in Base Ten

#### Related Standards

This cluster includes the following benchmarks
Code Description
MAFS.4.NBT.2.4: Fluently add and subtract multi-digit whole numbers using the standard algorithm.
 Clarifications:Fluency Expectations or Examples of Culminating Standards Students’ work with decimals (4.NF.3.5–3.7) depends to some extent on concepts of fraction
MAFS.4.NBT.2.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 Clarifications:Examples of Opportunities for In-Depth Focus When students work toward meeting this standard, they combine prior understanding of multiplication with deepening understanding of the base-ten system of units to express the product of two multi-digit numbers as another multi-digit number. This work will continue in grade 5 and culminate in fluency with the standard algorithms in grade 6.
MAFS.4.NBT.2.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
 Clarifications:Examples of Opportunities for In-Depth Focus When students work toward meeting this standard, they combine prior understanding of multiplication and division with deepening understanding of the base-ten system of units to find whole-number quotients and remainders with up to four-digit dividends and one- digit divisors. This work will develop further in grade 5 and culminate in fluency with the standard algorithms in grade 6.

#### Related Access Points

This cluster includes the following access points.

#### Access Points

 Access Point Number Access Point Title MAFS.4.NBT.2.AP.5a: Solve a two-digit by one-digit whole number multiplication problem using two different strategies. MAFS.4.NBT.2.AP.4a: Solve multi-digit addition and subtraction problems within 1,000. MAFS.4.NBT.2.AP.6a: Find whole-number quotients and remainders with up to three-digit dividends and one-digit divisors, using two different strategies.

#### Related Resources

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

#### Original Student Tutorials

 Name Description CPALMS Aquarium: Part 3 Division with Larger Numbers: Learn more about division with larger numbers in this aquarium-themed, interactive tutorial.  This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division. CPALMS Aquarium Part 2: Division Strategies: Learn to solve division challenges using the partial quotients strategy with this interactive tutorial. This is the second tutorial is a series on division strategies. CPALMS Aquarium: Connecting Multiplication and Division: Part 1: Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.   This is part 1 of a two-part series. Click to open Part 2, Division Strategies. Multi-Digit Multiplication Magic Part 3: Recording Partial Products: Calculate the product of multi-digit factors by decomposing factors and recording partial products in this interactive tutorial. This is part 3 in a 3-part series. Click below to open the other tutorials in the series. Multi-Digit Multiplication Magic Part 1: Arrays Multi-Digit Multiplication Magic Part 2: Area Models Multi-Digit Multiplication Magic Part 3: Recording Partial Products (current tutorial) Multi-Digit Multiplication Area Models: Part 2: See the magical power of area models when multiplying multi-digit numbers in this interactive tutorial.   This is part 2 in a 3-part series. Click below to open the other tutorials in the series. Multi-Digit Multiplication Magic Part 1: Arrays Multi-Digit Multiplication Magic Part 2: Area Models (Current Tutorial) Multi-Digit Multiplication Magic Part 3: Recording Partial Products Multi-Digit Multiplication Magic Part 1: Arrays: Learn to use arrays to solve multi-digit multiplication problems in this interactive tutorial. This is part 1 in a 3-part series. Click below to open the other tutorials in the series. Adding It All Up with a Standard Algorithm: Learn to add multi-digit numbers using a standard algorithm in this interactive tutorial.

#### Educational Games

 Name Description Estimator Four: In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). 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. 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. Arithmetic Workout: This interactive Flash applet offers three ways for students to practice basic fact skills related to multiplication and division. Users control the challenge level by choosing the size of the blank multiplication grid displayed by the applet. In Multiply mode users type in the product that completes a multiplication sentence. In Factor mode users click a grid cell that matches a given product. In Divide mode users type in a missing factor in the displayed multiplication sentence. A sound effect and timing feature are optional. Who Wants to be a Mathionaire?: This online game replicates the popular "Who Wants to be a Millionaire?" format, using multiplication facts. It's a fun way for kids to practice multiplication!

#### Educational Software / Tool

 Name Description 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.

#### Formative Assessments

 Name Description The Produce Shop: Students are asked to multiply a pair of two-digit numbers using a strategy based on place value. Reading Challenge: Students are asked to multiply a four-digit number by a one-digit number using a strategy based on place value. Partial Products: Students are asked to solve two multiplication problems using a partial products strategy. Multiplying Using An Array or Area Model: Students are asked to multiply a four-digit number by a one-digit number and two, two-digit numbers using an array or area model. Dividing Using an Area Model: Students are asked to interpret a division problem with a one-digit divisor that has been completed using an area model. If the student is successful, he or she is asked to complete a division problem with a one-digit divisor using an area model. Subtracting Using the Standard Algorithm: Students are asked to solve two 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. Addition Using the Standard Algorithm: Students are asked to solve two addition problems using the standard algorithm. Book Drive: Students are asked to solve a division problem using a strategy based on place value. Interpreting Division: Students are asked to analyze and explain another student’s division work in terms of a partial quotients strategy and to apply this strategy to another division problem. Dividing Using Place Value: Students are asked to complete a division problem using place value. Fill In The Missing Number: Students are asked to complete subtraction problems using the standard algorithm.

#### Lesson Plans

 Name Description 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. Comparing Money Raised: The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. Comparing Products: The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. It builds on applying properties of operations as strategies to multiply and divide and interpreting a multiplication equation as a comparison.

#### Teaching Idea

 Name Description Hand Spans, A Lesson for Third and Fourth Graders (Division and Measurement): A measurement activity to give students experience with the grouping model of division and practice with rulers and tape measures.

#### Tutorials

 Name Description Division: The importance of place value: In this video tutorial from Khan Academy, learn about the importance of place value when dividing. The tutorial uses place value up to thousands to help students think about division. Division: Intro to remainders: In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders. Multiplying: how to use the area model: In this video tutorial from Khan Academy, view a demonstration of how to set-up an area model for multiplying a two-digit number by a two-digit number on graph or grid paper and then link this to the standard algorithm. Multiplying: 2-digit number times a 2-digit number (area model): In this tutorial video from Khan Academy, view an example of how to multiply a two-digit number by a two-digit number using the area model. The video makes a connection between partial products and the area model. Multiplying: 2-digit number times 2-digit number (using distributive property): In this video tutorial from Khan Academy, view an example and a description of how the distributive property can be used to multiply a two-digit number by a two-digit number. The second example uses the area model with the distributive property. Multiplying: 4-digits times 1-digit (using expanded form): In this Khan Academy video tutorial, view an example of multiplying a 4-digit number by a 1-digit number by expanding the 4-digit number and multiplying by each digit individually in an area model. This video will help to build an understanding before teaching the standard algorithm.  Multiplying with a 4-digit factor is larger than some standards which limit factors to 3-digits. Multiplying: 2-digit number times a 2-digit number (standard algorithm): In this tutorial video from Khan Academy, view an example of how to multiply a 2-digit number by another 2-digit number. Be sure to stick around for the second example! The key is understanding the value of each digit! Multiplying: 3 digits times 1 digit (standard algorithm): In this video tutorial from Khan Academy, view an example of how to solve a problem in which a 3-digit number is being multiplied by a 1-digit number using the standard algorithm. Multiplying: 2 digits times 1 digit (standard algorithm): In this video tutorial from Khan Academy, view an example of how to solve a multiplication problem with a two-digit number multiplied by a one-digit number using the standard algorithm. 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. 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. Subtraction by Regrouping: This 8-minute video demonstrates how to perform subtraction with regrouping. The presenter uses base-10 blocks to explain the rationale and to make a visual connection with the standard algorithm. The examples involve 2-digit and 3-digit numbers.

#### Student Resources

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

#### Original Student Tutorials

 Title Description CPALMS Aquarium: Part 3 Division with Larger Numbers: Learn more about division with larger numbers in this aquarium-themed, interactive tutorial.  This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division. CPALMS Aquarium Part 2: Division Strategies: Learn to solve division challenges using the partial quotients strategy with this interactive tutorial. This is the second tutorial is a series on division strategies. CPALMS Aquarium: Connecting Multiplication and Division: Part 1: Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.   This is part 1 of a two-part series. Click to open Part 2, Division Strategies. Multi-Digit Multiplication Magic Part 3: Recording Partial Products: Calculate the product of multi-digit factors by decomposing factors and recording partial products in this interactive tutorial. This is part 3 in a 3-part series. Click below to open the other tutorials in the series. Multi-Digit Multiplication Magic Part 1: Arrays Multi-Digit Multiplication Magic Part 2: Area Models Multi-Digit Multiplication Magic Part 3: Recording Partial Products (current tutorial) Multi-Digit Multiplication Area Models: Part 2: See the magical power of area models when multiplying multi-digit numbers in this interactive tutorial.   This is part 2 in a 3-part series. Click below to open the other tutorials in the series. Multi-Digit Multiplication Magic Part 1: Arrays Multi-Digit Multiplication Magic Part 2: Area Models (Current Tutorial) Multi-Digit Multiplication Magic Part 3: Recording Partial Products Multi-Digit Multiplication Magic Part 1: Arrays: Learn to use arrays to solve multi-digit multiplication problems in this interactive tutorial. This is part 1 in a 3-part series. Click below to open the other tutorials in the series. Adding It All Up with a Standard Algorithm: Learn to add multi-digit numbers using a standard algorithm in this interactive tutorial.

#### Educational Games

 Title Description Estimator Four: In this activity, students play a game of connect four, but to place a piece on the board they have to correctly estimate an addition, multiplication, or percentage problem. Students can adjust the difficulty of the problems as well as how close the estimate has to be to the actual result. This activity allows students to practice estimating addition, multiplication, and percentages of large numbers (100s). 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. 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.

#### Educational Software / Tool

 Title Description 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.

 Title Description 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. Comparing Money Raised: The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. Comparing Products: The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. It builds on applying properties of operations as strategies to multiply and divide and interpreting a multiplication equation as a comparison.

#### Tutorials

 Title Description Division: The importance of place value: In this video tutorial from Khan Academy, learn about the importance of place value when dividing. The tutorial uses place value up to thousands to help students think about division. Division: Intro to remainders: In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders. Multiplying: how to use the area model: In this video tutorial from Khan Academy, view a demonstration of how to set-up an area model for multiplying a two-digit number by a two-digit number on graph or grid paper and then link this to the standard algorithm. Multiplying: 2-digit number times a 2-digit number (area model): In this tutorial video from Khan Academy, view an example of how to multiply a two-digit number by a two-digit number using the area model. The video makes a connection between partial products and the area model. Multiplying: 2-digit number times 2-digit number (using distributive property): In this video tutorial from Khan Academy, view an example and a description of how the distributive property can be used to multiply a two-digit number by a two-digit number. The second example uses the area model with the distributive property. Multiplying: 4-digits times 1-digit (using expanded form): In this Khan Academy video tutorial, view an example of multiplying a 4-digit number by a 1-digit number by expanding the 4-digit number and multiplying by each digit individually in an area model. This video will help to build an understanding before teaching the standard algorithm.  Multiplying with a 4-digit factor is larger than some standards which limit factors to 3-digits. Multiplying: 2-digit number times a 2-digit number (standard algorithm): In this tutorial video from Khan Academy, view an example of how to multiply a 2-digit number by another 2-digit number. Be sure to stick around for the second example! The key is understanding the value of each digit! Multiplying: 3 digits times 1 digit (standard algorithm): In this video tutorial from Khan Academy, view an example of how to solve a problem in which a 3-digit number is being multiplied by a 1-digit number using the standard algorithm. Multiplying: 2 digits times 1 digit (standard algorithm): In this video tutorial from Khan Academy, view an example of how to solve a multiplication problem with a two-digit number multiplied by a one-digit number using the standard algorithm. 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. 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.

#### Parent Resources

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