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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.

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

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MAFS.4.NBT.2.4 : Fluently add and subtract multi-digit whole numbers using the standard algorithm.
  • 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.
  • 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.
Cluster 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
Grade:
4
Domain-Subdomain
Number and Operations in Base Ten
Cluster Access Points

This cluster includes the following Access Points.

  • 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.
Cluster Resources

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

Original Student Tutorials
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.

  • 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
  • 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
  • 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
  • Making Cents of Taxes Part 2: In this lesson plan, students will apply addition and subtraction skills with decimal values while exploring how taxes may impact citizen’s daily lives.

  • 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."

  • "Life's a Breeze!": In this Engineering Design Challenge, students must design a vessel that will carry passengers safely and quickly across a body of water by harnessing the power of the wind. Students will be given the opportunity to test and improve their vessels as they apply various math and science skills.

  • Heating Up the Neighborhood: This Engineering Design Challenge is intended to help students apply the concepts of heat insulators as they build a model house and test different materials to use as insulators, stopping the warm air from escaping and keeping the cool air out. Students will also have an opportunity to use technology in their exploration of heat energy.

  • Sound Vibrations Using the Engineering Design Process: This lesson uses the engineering design process to guide students through the exploration of sound energy and pitch. The design challenge is to produce a low-pitch tone by using different containers and liquids. Students must also create a budget to purchase supplies.

  • Set Sail with STEM: Exploring Wind and Water Movement as Energy with Sailboats: Come sail away with this STEM activity! Students will use hands-on inquiry to find out more about wind and its effect on sails. Through trial and error and based on data collected, students will design, build, and race their own vessel or "sailboat" across the boundless waters of a kiddie pool. Students should gain a better understanding of how moving water and air are sources of energy and can propel objects forward at varying rates of speed.

  • 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.

  • 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.

  • 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.

  • Dividing for Equal Groups: This lesson is meant to help solidify division understanding before teaching the standard algorithm.  Given a situational story, students will use base 10 blocks to model division in order to solve problems. It may be used for 4th or 5th grade depending on the size of the divisor.  

  • I Love Leftovers!: In this lesson, students will explore situational problems that address the different ways to interpret the remainder.

  • 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. 

  • Hooray for arrays!: Students will identify prime and composite numbers through arrays. The lesson begins with a fun situational story.

  • 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. 

  • I See! Division with the Distributive Property: In this lesson, students will use visual models to represent division using the distributive property as a strategy. Students will have an understanding of how to decompose numbers in the context of division problems using an area model.

  • 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.

  • Factor Word Challenges: Students will apply multiplication, division and factor knowledge to word problems.

  • Replaced Pitcher: The students will use mathematical skills and problem solving skills to recommend which current starting pitcher will be replaced once one of the pitchers is back on the active roster for the Miami Marlins. They will write a letter on the computer and print it out to respond to the assistant coach's letter.

    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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

  • Kudos for Kicks - MEA: In this Model Eliciting Activity, MEA, 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 shoe 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, calculate the total profit margin per pair, and the total sales potential profit margin determined by the number of sneakers in stock. Students will also need to consider comfort, durability, and specific details about each brand. 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.

    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

  • 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.

  • 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.

  • 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.

  • 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.

  • Loaning Out Laptops: In this Model Eliciting Activity, MEA, students will create a procedure for ranking laptops for students for a company named "Loaning Out Laptops." Students must consider ergonomics, portability, memory, and cost.

    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

  • Let's Make a Movie: In this Model Eliciting Activity, MEA, students will add, subtract, and compare multi-digit numbers in order to help a new movie production company decide which genre they should make for their first movie.

    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

  • 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.

    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 processes. 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 MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

  • 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.

  • 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.

    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

  • Subtraction Attraction: In this lesson, students will demonstrate fluency in using a standard algorithm to complete story problems involving subtraction with regrouping using multi-digit whole numbers.

  • Share and Share Alike: This lesson is an introduction to division and does not include a procedural recording for division. The student will be able to physically model the division of 2-, 3-, and 4-digit dividends with 1-digit divisors using objects and base ten blocks and explain the meaning of a remainder. 

     

  • 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.

  • 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.

  • 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.

    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

Problem-Solving Tasks
  • 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
Tutorials
  • 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.