# 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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Number and Operations in Base Ten
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Use place value understanding and properties of operations to perform multi-digit arithmetic. (Major Cluster) -

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.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Items may require multiplying: four digits by one digit, three digits by one digit, two digits by one digit, or two digits by two digits.
• Calculator :

No

• Context :

No context

Sample Test Items (2)

• Test Item #: Sample Item 2
• Question:

This question has two parts.

Two numbers are multiplied using the area model shown.

Part A. What is the value of the missing number in the area model?

Part B. What is the product of the two numbers represented by the area model?

• Difficulty: N/A
• Type: EE: Equation Editor

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.4.NBT.2.AP.5a: Solve a two-digit by one-digit whole number multiplication problem using two different strategies.

## Related Resources

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

## Assessments

Sample 4 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 3 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 2 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 1 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

## Educational Games

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.

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

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.

Type: Educational Game

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!

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

The Produce Shop:

Students are asked to multiply a pair of two-digit numbers using a strategy based on place value.

Type: Formative Assessment

Students are asked to multiply a four-digit number by a one-digit number using a strategy based on place value.

Type: Formative Assessment

Partial Products:

Students are asked to solve two multiplication problems using a partial products strategy.

Type: Formative Assessment

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.

Type: Formative Assessment

## Lesson Plans

The Playground Project:

Students will enjoy designing their "dream" playground while applying math and science skills in this engineering design challenge lesson. Students will find the area and perimeter of their playground designs. They will also use a budget sheet to make decisions about what to include in their playground, considering the physical properties of the materials they "purchase."

Type: Lesson Plan

Model Multiplication:

This concept based, hands-on lesson is intended to help you assess how well your students understand and can use a variety of strategies and representations of 2 two-digit multiplication.

Type: Lesson Plan

Modeling Multiplication for Mastery:

In this lesson, students will work to multiply multi-digit numbers using various strategies. The lesson begins with a review of single x single digit numbers and progresses to two-digit x two-digit numbers.  Students will use arrays, array frames with base ten blocks, and area models to explore and justify their solutions.

Type: Lesson Plan

Multi-digit Multiplication Using Array Frames:

This is an introductory lesson and is limited to multiplication of two-digit by one-digit numbers.  The students will work with base ten blocks to model their multiplication.

Type: Lesson Plan

Draw a blueprint of your dream house floor plan.:

This lesson will help your students learn about area and perimeter while imagining and drawing a blueprint of their dream house floor plan. They will have so much fun drawing and creating their blueprint they will forget that they are actually learning how to find area and perimeter.

Type: Lesson Plan

Hooray for arrays!:

Students will identify prime and composite numbers through arrays. The lesson begins with a fun situational story.

Type: Lesson Plan

Oops! What did I do?:

This lesson uses a discovery approach to exploring different errors in various strategies of multiplication. The goal is to help students understand multiplication, not force them into using every strategy.

Type: Lesson Plan

Multiplying Around the Block:

The students will build upon their understanding of the place-value system and multiplying using base-ten models to build their understanding of multiplying with two-digit by two-digit numbers using area models. They will work with partners during the learning process to help them develop the usage of mathematical language when explaining their thinking and calculations to others.

Type: Lesson Plan

Aaron and Anya's Quilt Challenge: Problem Solving and Interpreting Remainders:

In this situational story, Aaron and Anya find a large piece of brightly colored fabric. They decide to cut it into squares to make a quilt. Students will find the area of the fabric by multiplying two digits by two digits. They will explore factors as they figure out the largest quilt square that can be cut for 25 students. There will be fabric left over; students will have to determine and justify remainders based on several different scenarios. Finally, students will create their own quilt square using grid paper.

Type: Lesson Plan

Kudos for Kicks - MEA:

In this MEA, students will work in collaborative groups to solve multi-step problems with whole numbers and decimals by using different mathematical operations of addition, subtraction, and multiplication. The students will be asked to assist a discount shoe store owner, who is planning a one day sale promotion, to choose a famous brand sneaker to feature for the one day sale. Students will determine which one will bring in more customers, as well as provide the most profit. Students will need to read a data table, rank the famous brand sneakers from 1-6, calculate the total profit margin per pair, and the total sales potential profit margin determined by the number of sneakers in stock. A twist is added to the problem when additional stock items are added, plus one of the brands is removed and two new brands are added.

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

2-Digit Array Multiplication:

This lesson explores a conceptual approach to multiplying two 2-digit numbers. Students will create, explore, describe and record arrays built with place value pieces. The lesson supplies the understanding that will make multiplying multidigit numbers easy to do.

Type: Lesson Plan

Amazing Arrays 3X1 or 1X3:

This lesson is the third lesson in a unit beginning with Amazing Arrays and Amazing Arrays 2X1.

In this lesson students solve a multiplication problem by drawing arrays and segment the areas in several ways to solve the problem. Students will also apply the distributive property, explore rotations of area models to demonstrate the commutative property of multiplication, and match a word problem with its array.

Type: Lesson Plan

Chance Product:

Are you trying to deepen your students understanding of 2-digit by 2-digit multiplication? Then this is the game for you. This game allows students to demonstrate their abilities in multiplication and reasoning. Students will place numbers drawn onto a recording sheet in order to create the largest product possible.

Type: Lesson Plan

Loaning Out Laptops:

This engaging MEA introduces students to a company named "Loaning Out Laptops" that needs their help in choosing the best laptops for students to do their schoolwork.

Type: Lesson Plan

Tennis Lessons:

This MEA asks students to take on the job of a tennis pro and decide which factors are most important in choosing a facility to take tennis lessons. Students will perform math calculations, create a two-column table for hours and minutes, develop a procedure to rank facilities, and provide written feedback through letters to a parent whose child needs group tennis lessons and writes letters to ask for advice. They will rank their choices from "best to worst" tennis lesson facilities. Students will provide a detailed written explanation for how they decided to rank factors and their solution for rating tennis lesson facilities.

Type: Lesson Plan

Boxing Math - Using the Area Model for Multiplication:

A common mistake students make when learning to multiply is treating multiplication like addition, and multiplying ones by ones and tens by tens. In this lesson, your students will avoid that mistake as they learn to use the area model to do double digit multiplication. After group practice, students are taught a game to reinforce their learning.

Type: Lesson Plan

Hotels: Where to Stay:

This MEA allows students to explore the creation of a model to rank hotels. Students are presented with the first part of the problem and the data which includes cost, meals served, pet friendly, and closeness to highway. They will determine which hotel will receive their highest recommendation. The second part of the task adds two hotels and additional data related to discounts. Students need to apply and test their model and make modifications as needed. All findings are submitted to the client in writing. Students may use this information to plan a family vacation researching which hotels they might stay in as they travel.

Type: Lesson Plan

Amazing Arrays 2X1:

This is a hands-on lesson for extending and practicing drawing arrays using area models that show a 2-digit number times a 1-digit number. Students are also required to use the distributive property of multiplication and the equations they represent.

Type: Lesson Plan

Array for Charity!:

Students will use array frames to find out how many pennies each of the classes in their school collected for a charity drive. Students will demonstrate and explain the array frame as well as determining how many pennies will go to each of the seven charities for which they have collected pennies. This lesson may be used as part of an introduction to multiplying 2-digit x 2-digit numbers.

Type: Lesson Plan

Party Entertainment:

In this MEA, students will decide which entertainer an owner of an entertainment company should hire. They will base their decisions on information provided on resumes. Students will calculate the cost of hiring the entertainer (multiplication of whole numbers) as well as compare the statistics of their talent competitions and attendance turn-out (comparing fractions). Students will write letters to the owner of the entertainment company ranking the entertainers and providing explanation and justification of their strategy for doing so.

Type: Lesson Plan

## Original Student Tutorials

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.

Type: Original Student 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.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

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

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.

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial

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!

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial

## STEM Lessons - Model Eliciting Activity

Hotels: Where to Stay:

This MEA allows students to explore the creation of a model to rank hotels. Students are presented with the first part of the problem and the data which includes cost, meals served, pet friendly, and closeness to highway. They will determine which hotel will receive their highest recommendation. The second part of the task adds two hotels and additional data related to discounts. Students need to apply and test their model and make modifications as needed. All findings are submitted to the client in writing. Students may use this information to plan a family vacation researching which hotels they might stay in as they travel.

Kudos for Kicks - MEA:

In this MEA, students will work in collaborative groups to solve multi-step problems with whole numbers and decimals by using different mathematical operations of addition, subtraction, and multiplication. The students will be asked to assist a discount shoe store owner, who is planning a one day sale promotion, to choose a famous brand sneaker to feature for the one day sale. Students will determine which one will bring in more customers, as well as provide the most profit. Students will need to read a data table, rank the famous brand sneakers from 1-6, calculate the total profit margin per pair, and the total sales potential profit margin determined by the number of sneakers in stock. A twist is added to the problem when additional stock items are added, plus one of the brands is removed and two new brands are added.

Loaning Out Laptops:

This engaging MEA introduces students to a company named "Loaning Out Laptops" that needs their help in choosing the best laptops for students to do their schoolwork.

Party Entertainment:

In this MEA, students will decide which entertainer an owner of an entertainment company should hire. They will base their decisions on information provided on resumes. Students will calculate the cost of hiring the entertainer (multiplication of whole numbers) as well as compare the statistics of their talent competitions and attendance turn-out (comparing fractions). Students will write letters to the owner of the entertainment company ranking the entertainers and providing explanation and justification of their strategy for doing so.

Tennis Lessons:

This MEA asks students to take on the job of a tennis pro and decide which factors are most important in choosing a facility to take tennis lessons. Students will perform math calculations, create a two-column table for hours and minutes, develop a procedure to rank facilities, and provide written feedback through letters to a parent whose child needs group tennis lessons and writes letters to ask for advice. They will rank their choices from "best to worst" tennis lesson facilities. Students will provide a detailed written explanation for how they decided to rank factors and their solution for rating tennis lesson facilities.

## MFAS Formative Assessments

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.

Partial Products:

Students are asked to solve two multiplication problems using a partial products strategy.

Students are asked to multiply a four-digit number by a one-digit number using a strategy based on place value.

The Produce Shop:

Students are asked to multiply a pair of two-digit numbers using a strategy based on place value.

## Original Student Tutorials Mathematics - Grades K-5

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:

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.

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.

## Student Resources

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

## Original Student Tutorials

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.

Type: Original Student 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.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

## Educational Games

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.

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

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

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.

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial

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!

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial

## Parent Resources

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

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

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.

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial

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!

Type: Tutorial

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.

Type: Tutorial

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.

Type: Tutorial