# MA.4.NSO.2.2

Multiply two whole numbers, up to three digits by up to two digits, with procedural reliability.

### Clarifications

Clarification 1: Instruction focuses on helping a student choose a method they can use reliably.

Clarification 2: Instruction includes the use of models or equations based on place value and the distributive property.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (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.4.NSO.2.AP.2: Explore multiplication of two whole numbers, up to two digits by one digit.

## Related Resources

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

## 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

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

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

New Puppy's Pen:

The purpose of this lesson is to help students find the missing side's length for rectangular area problems, when the total area and one side's length is given. The use of square tiles, then graph paper and equations are used throughout the lesson to help students progress from conceptual to procedural knowledge.

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.Â  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.Â  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.Â

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.Â The goal is to help students understand multiplication, not force them into using every strategy.Â

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

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

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

Fourth graders will help Cookies and Treats find cost-effective and eco-friendly packaging for its cookies. Students will organize data and compare prices using decimal notation in order to develop a procedure for choosing packaging for cookies.Â  Students will use multiplication and division of whole numbers to plan for how many packages to order.

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

## 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

## STEM Lessons - Model Eliciting Activity

Fourth graders will help Cookies and Treats find cost-effective and eco-friendly packaging for its cookies. Students will organize data and compare prices using decimal notation in order to develop a procedure for choosing packaging for cookies.Â  Students will use multiplication and division of whole numbers to plan for how many packages to order.

## 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.

## 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 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

## 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