MA.4.NSO.2.2

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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.)
Grade: 4
Strand: Number Sense and Operations
Standard: Build an understanding of operations with multi-digit numbers including decimals.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Distributive Property
  • Expression 
  • Equation
  • Factor

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

  • The purpose of this benchmark is for students to choose a reliable method for multiplying 3 digit numbers by 2 digit numbers. It builds on the understanding developed in grade 3 (MA.3.NSO.2.2, MA.3.NSO.2.3, MA.3.NSO.2.4), builds on automaticity (MA.4.NSO.2.1) and prepares for procedural fluency (MA.4.NSO.2.3 and MA.5.NSO.2.1).
  • For instruction, students may use a variety of strategies when multiplying whole numbers and use words and diagrams to explain their thinking (MTR.2.1). Strategies can include using base-ten blocks, area models, partitioning, compensation strategies and a standard algorithm.
  • Using place value strategies enables students to develop procedural reliability with multiplication and transfer that understanding to division. Procedural reliability expects students to utilize skills from the exploration stage to develop an accurate, reliable method that aligns with their understanding and learning style. 
  • The area model shows students how they can use place value strategies and the distributive property to find products with multi-digit factors.

 

Common Misconceptions or Errors

  • Students that are taught a standard algorithm without any conceptual understanding will often make mistakes. For students to understand a standard algorithm or any other method, they need to be able to explain the process of the method they chose and why it works. This explanation may include pictures, properties of multiplication, decomposition, etc.

 

Strategies to Support Tiered Instruction

  • Instruction includes explaining mathematical reasoning while solving multiplication problems. Instruction also includes determining if a method was used correctly by reviewing the reasonableness of solutions. 
  • For example, students determine 5 × 137 using an area model and place value understanding.
an area model
  • For example, students solve 5 × 137 using partitioning and place value understanding.

  • For example, students determine 4 × 43 using base-ten blocks and place value understanding. 
base ten blocks
  • For example, students determine 4 × 43 using partitioning and place value understanding.

 

Instructional Tasks

Instructional Task 1 

Paul orders tomatoes for The Produce Shop. Each box has 24 tomatoes in it. If Paul orders 32 boxes of tomatoes, how many tomatoes will The Produce Shop have to sell? Use a strategy of your choice to find the number of tomatoes The Produce Shop has to sell. Explain your thinking and why your method works.

 

Instructional Items

Instructional Item 1 

 The product of 57 and 92 is ____. 
  • a. 627 
  • b. 4,644 
  • c. 5,234 
  • d. 5,244 

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
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

Reading Challenge:

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

Order_in_the_School_Zone_Part_3:

Students will work in pairs or small groups. They will be provided with a “school district” and zones. The groups will be tasked with assigning each zone to a school, while respecting the school's enrollment caps and the zone's proximity to the school.  Once the zones are assigned, the students will calculate the approximate busing costs.  Then, the groups will pair off and compare how they determined zoning for each school.

Type: Lesson Plan

Order_in_the_School_Zone_Part_2:

Students will determine the number of students from each zone that would need buses to get to their new schools. Then they will determine the total cost of transportation per week, per month and per school year. Students will discuss the possibility of adding portable classrooms instead of rezoning and comparing the cost. They will discuss how this cost increase could affect the school budgets and how the students and families could work with the school board on alternative solutions, in this integrated lesson plan.

Type: Lesson Plan

Emergency Savings:

Students will use their multiplication skills to explore the importance of taxes and how the government uses tax revenues to save for unforeseen emergencies, in this integrated lesson plan.

Type: Lesson Plan

Plastic Footprint Lesson Plan:

Students explore the problem of marine debris and ways that citizens can work alongside government to reduce the impact of plastic pollution.  They calculate their plastic footprint by estimating the number of common single-use plastics they use in one year, then calculate how much plastic waste could be eliminated by cutting down on their use of single-use plastics in this integrated lesson plan.

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

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.  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

Robotics on a Budget:

The P.T.A. President at ABC Elementary needs your students' help in selecting a robotics model that fits the needs of the students and the after school enrichment program. There is a budget of $2,000 that the students must adhere to. Students will be asked rank 4 models based on criteria given to them and the budget. Students will be given a data set to help them develop a procedure for doing so. In their teams they will write a letter to the P.T.A President giving their procedures and explanation of the strategy they used. Students will practice adding, subtracting and multiplying numbers to the thousands in order to calculate the amount of models that can be bought of a certain model without going over the budget. Rubrics are included to help grade students.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

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

Cookies and Treats:

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.  Students will use multiplication and division of whole numbers to plan for how many packages to order.

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

Type: Lesson Plan

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

Perspectives Video: Teaching Ideas

Making Connections with the Area Model:

Unlock an effective teaching strategy for making connections in area models in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Multiplying Multi-digit Numbers:

Unlock an effective teaching strategy for teaching multiplying multi-digit numbers using ten frames in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Comparing Money Raised:

The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. 

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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

Cookies and Treats:

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.  Students will use multiplication and division of whole numbers to plan for how many packages to order.

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

Robotics on a Budget:

The P.T.A. President at ABC Elementary needs your students' help in selecting a robotics model that fits the needs of the students and the after school enrichment program. There is a budget of $2,000 that the students must adhere to. Students will be asked rank 4 models based on criteria given to them and the budget. Students will be given a data set to help them develop a procedure for doing so. In their teams they will write a letter to the P.T.A President giving their procedures and explanation of the strategy they used. Students will practice adding, subtracting and multiplying numbers to the thousands in order to calculate the amount of models that can be bought of a certain model without going over the budget. Rubrics are included to help grade students.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

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.

Reading Challenge:

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

Problem-Solving Tasks

Comparing Money Raised:

The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. 

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Problem-Solving Tasks

Comparing Money Raised:

The purpose of this task is to give students a better understanding of multiplicative comparison word problems with money. 

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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