# Standard 2: Build an understanding of operations with multi-digit numbers including decimals.

General Information
Number: MA.4.NSO.2
Title: Build an understanding of operations with multi-digit numbers including decimals.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.4.NSO.2.AP.1
Recall multiplication facts of one-digit whole numbers multiplied by 1, 2, 5 and 10.
MA.4.NSO.2.AP.2
Explore multiplication of two whole numbers, up to two digits by one digit.
MA.4.NSO.2.AP.3
Apply a strategy to multiply two whole numbers up to two digits by one digit.
MA.4.NSO.2.AP.4
Explore division of two whole numbers up to two digits by one digit with and without remainders. Represent remainders as whole numbers.
MA.4.NSO.2.AP.5
Explore the estimation of products and quotients of two whole numbers up to two digits by one digit.
MA.4.NSO.2.AP.6
Identify the number that is one-tenth more and one-tenth less than a given number (i.e., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9).
MA.4.NSO.2.AP.7
Explore the addition and subtraction of decimals less than one to the tenths (e.g., 0.3 + 0.5) and hundredths (e.g., 0.25 − 0.12).

## Related Resources

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

## Educational Games

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.

Type: Educational Game

Ice Ice Maybe: An Operations Estimation Game:

This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

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

## 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

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.

Type: Formative Assessment

Book Drive:

Students are asked to solve a division problem using a strategy based on place value.

Type: Formative Assessment

Interpreting Division:

Students are asked to analyze and explain another studentâ€™s division work in terms of a partial quotients strategy and to apply this strategy to another division problem.

Type: Formative Assessment

Dividing Using Place Value:

Students are asked to complete a division problem using place value.

Type: Formative Assessment

Estimating the Solution:

Students are asked to use a mental estimation strategy to evaluate the solution of a multistep word problem.

Type: Formative Assessment

## Lesson Plans

Making Cents of Taxes Part 1:

In this lesson plan, students will apply addition and subtraction skills with decimal values and multiplication of whole numbers to explore how taxes may impact citizens’ daily lives.

Type: Lesson Plan

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

3-COURSE Meal Mini Lesson Money Matter Part 3:

This lesson aims to enhance students' problem-solving skills while fostering their understanding of how public issues impact citizens' daily lives. Students will use a grocery store ad and purchase multiple items to complete a 3-course meal for them and a few friends. Students will be challenged to stay within a budget to complete the task. They will add and subtract decimals to the hundredth, applying place value strategies while using money in this integrated lesson plan.

Type: Lesson Plan

3-COURSE MEAL Mini Unit Money Matters Part 2 :

In this lesson students purchased supplies to build a bird house and had to stick to a budget when doing so

Type: Lesson Plan

3-Course Meal Mini Unit Money Matters Part 1:

In this lesson of the unit students will learn how to add and subtract decimals to the tenth and hundredth place value. Students will apply place value strategies while using money in this integrated math/civis 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

Volunteering with the Mayor Part 2:

Volunteering is vital to keeping any community safe, inviting, and running smoothly! In this lesson, students will work together to plan a volunteer project they would like to see happen in their community; as well as, create a budget for their project.

Type: Lesson Plan

Volunteering with the Mayor:

The mayor wants to build a new park in town! Volunteer your time and help the mayor design an expense report with a given budget for the new park in this lesson.

Type: Lesson Plan

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.

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

Making Sense of Multiplication to Build Fluency of 6's, 7's, 8's, and 9's:

This lesson will help students multiply numbers with factors of 6, 7, 8, or 9 through decomposing numbers in an array and applying the distributive property. Many times, these factors are difficult for students to recall from memory. Teaching students how to use an array can give them a visual representation of the final product. This visual can also help students to make the connection that multiplying whole numbers is a sum of equal groups. Decomposing the numbers and using the distributive property is a strategy for students to use who are having trouble solving these higher factor multiplication facts.

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

Dividing for Equal Groups:

This lesson is meant to help solidify division understanding before teaching the standard algorithm.Â  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.Â Â

Type: Lesson Plan

I Love Leftovers!:

In this lesson, students will explore situational problems that address the different ways to interpret the remainder.

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

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.

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

Factor Word Challenges:

Students will apply multiplication, division and factor knowledge to word problems.

Type: Lesson Plan

Shopping for Groceries:

In this lesson, students will use grocery ads to take the role of a shopper and a cashier and will purchase several items. Students will be able to add and subtract decimals to hundredths, using strategies based on models, illustrations, and place value.

Type: Lesson Plan

Slither Not in the Everglades! Python MEA:

This MEA will ask students to work in teams to help their client, The Florida Fish and Wildlife Conservation Commission, to decide which Burmese python traps manufacturing company to buy traps from. The traps will be placed along the Florida Keys and the Everglades to help prevent the growth of invasive Burmese Python population. The students will implement their knowledge of how plants, animals, and humans impact the environment, use mathematical and analytical problem-solving strategies, and be able report their finding in an organized, descriptive manner.

Type: Lesson Plan

Where Will We Stay?:

In this lesson, students explore lodging options for their dream family vacation. Students will plan a vacation for a family of four. With a budget of \$5,000 students will prepare a budget to include the cost of transportation, lodging, and attractions. In this lesson, students will focus on preparing the budget for hotel costs. In lesson 1 of this unit lesson, students prepared a budget for transportation. In the subsequent lesson to this one, students will prepare a budget for the entertainment/attractions costs portion of their vacation. Teachers can choose to do one, some, or all lessons as they can be completed independently of one another.

Type: Lesson Plan

Cupid's Carnival Rides:

In this Model Eliciting Activity, MEA students will analyze different carnival rides to determine which ride would make the most profit by looking at factors such as number of tickets per ride, the cost per ticket, the length of the ride, the number of hours the ride is open, and the cost to operate the ride. Students will need to use different operations in order to solve the tasks and will be required to do multi-steps.

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

The Dock at Lake Wonder MEA:

In this Model Eliciting Activity, MEA, students will be asked to rank and choose from the potential docks the Lake Wonder Camp could purchase before next summer based on the data given. In the process, students will need to find area and perimeter as part of their criteria for ranking. The data provided is: dock dimensions, price per square foot for materials, warranty, and material quality. In the twist, students will be asked to calculate the cost of adding a safety bumper around each dock (after finding the perimeter) and calculate the total cost of each dock with the price of the safety bumper added. They must also stay within a \$5,000 budget. Students must decide how to change their procedure with the new information.

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

A Tasty Treat:

In this lesson, students will be given a list of ingredients and prices they must use to create their own snack mix. Students will have to add, subtract, multiply, and divide decimal numbers. The closure of the lesson focuses specifically on the division strategies students used to solve the problem.

Type: Lesson Plan

Fun with Factors:

This is an introductory lesson addressing factors for number 1-20. Factoring will lead students to discover differences and similarities between prime and composite numbers. Students will also discuss five claims about factors, prime, and composite numbers and create support from examples and non-examples to determine whether these claims are valid or invalid.

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

Lizard Lights:

Students will use a real-world problem solving situation to determine the best types of light bulbs to maintain an appropriate environment for a captive lizard.Â

Type: Lesson Plan

Patty's Party Planning:

In this Model Eliciting Activity, MEA, students will help a party planner determine which party location is the best one to use. They will calculate the cost of the banquet hall rental based on the number of people, number of tables and hourly rental of the location by using division and multiplication.

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

Playground Protection:

In this Model Eliciting Activity, MEA students will decide which type of protective surface should be put in under a new playground unit. They will consider many factors before ranking their decisions about the best surface.

Type: Lesson Plan

The Toy Shop:

This is an interactive and collaborative activity where the students will have the opportunity to play the roles of a customer and cashier at a "toy shop". This activity will provide your students with real-world examples involving money while using decimal notation appropriately. This could be a great activity to complete in one day, or throughout the week, depending on your students' needs!

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

Share and Share Alike:

This lesson is an introduction to divisionÂ and does not include a procedural recording for division.Â 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.Â

Â

Type: Lesson Plan

What Are They Thinking? Understanding Division:

This lesson uses a discovery approach to exploring the meaning of division. The students will utilize math practice standards as they analyze math solutions and explain their own solutions. Since the lesson analyzes division, it is a sound lesson to use to check student understanding before introducing efficient division algorithms.

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.

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

## Original Student Tutorials

Making Cents of Taxes:

Learn about sales tax as Malik tries to buy his favorite candy from the store in this short video.

Type: Original Student Tutorial

CPALMS Aquarium: Part 3 Division with Larger Numbers:

This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division.

Type: Original Student Tutorial

Topsy-Turvy Playground: Subtracting Decimals:

Learn to subtract decimals to the hundredths place using place-value models and written expressions as you fix the topsy-turvy playground in this interactive tutorial.

Type: Original Student Tutorial

CPALMS Aquarium Part 2: Division Strategies:

Learn to solve division challenges using the partial quotients strategy with this interactive tutorial.

This is the second tutorial is a series on division strategies.

Type: Original Student Tutorial

Sweet Treats Factory Invasion: Adding Decimals:

Help these aliens clean up the Sweet Treats Factory by learning to add decimals in this interactive mathematics tutorial.

Type: Original Student Tutorial

CPALMS Aquarium: Connecting Multiplication and Division: Part 1:

Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.

This is part 1 of a two-part series. Click to open Part 2, Division Strategies.

Type: Original Student Tutorial

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: Experts

Fluency vs. Automaticity:

How are fluency and automaticity defined? Dr. Lawrence Gray explains fluency and automaticity in the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

The Role of Procedures in Fluency:

What are the components to a good procedure? Dr. Lawrence Gray discusses the role of procedures in the path to fluency in this Expert Perspectives video.

Type: Perspectives Video: Expert

That's Not How I Learned it: Why today's math may look different:

Why do students need "a" good procedure for the arithmetic operations? Dr. Lawrence Gray explains why math may look different than in the past in this Expert Perspectives video.

Type: Perspectives Video: Expert

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. mathematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

What is Fluency?:

What is fluency? What are the ingredients required to become procedurally fluent in mathematics? Dr. Lawrence Gray explores what it means for students to be fluent in mathematics in this Expert Perspectives video.

Type: Perspectives Video: Expert

What is Automaticity?:

What does automaticity look like? What is the role of automaticity in mathematics? Dr. Lawrence Gray explores what it means for students to have automaticity with basic mathematics facts in this Expert Perspectives video.

Type: Perspectives Video: Expert

Why Isn't Getting the "Right" Answer Good Enough?:

Why is it important to look beyond whether a student gets the right answer? Dr. Lawrence Gray explores the importance of understanding why we perform certain steps or what those steps mean, and the impact this understanding can have on our ability to solve more complex problems and address them in the context of real life in this Expert Perspectives video.

Type: Perspectives Video: Expert

A Standard Algorithm:

Ever wonder why the benchmarks say, “a standard algorithm,” instead of, “the standard algorithm?" Dr. Lawrence Gray explores the role that standard algorithms can play in building and exhibiting procedural fluency through this Expert Perspectives video.

Type: Perspectives Video: Expert

## Perspectives Video: Teaching Ideas

Representing Remainders as Fractions:

Unlock an effective teaching strategy for representing remainders as fractions in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

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

The Van de Walle Dot Matrix: A tool to support concepts from counting to multiplying polynomials:

Unlock an effective teaching tool that can help students all the way from basic counting principles to multiplying polynomials.

Dot Matrix sheet is available for dowload here.

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

Estimating Decimal Multiplication:

Unlock an effective teaching strategy for teaching decimal multiplication in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

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.

Bowling for Numbers:

The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Students eager to knock down all of the pins quickly develop patterns in their expressions. They may re-use parts of an expression, perhaps changing just the final operation.

## Teaching Idea

A Square of Numbers (problem to solve using addition, subtraction, multiplication, division):

A problem for students to solve using students' understanding of the operations of addition, subtraction, multiplication, and division. The problem presents an opportunity for students to appreciate the value of approaching a solution in a systematic way using what they know about the structure of operations.

Type: 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.

Type: Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

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

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting with decimals. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

## Student Resources

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

## Original Student Tutorials

Making Cents of Taxes:

Learn about sales tax as Malik tries to buy his favorite candy from the store in this short video.

Type: Original Student Tutorial

CPALMS Aquarium: Part 3 Division with Larger Numbers:

This is part 3 of in a three-part series. Click below to learn different strategies to help you become more efficient with division.

Type: Original Student Tutorial

Topsy-Turvy Playground: Subtracting Decimals:

Learn to subtract decimals to the hundredths place using place-value models and written expressions as you fix the topsy-turvy playground in this interactive tutorial.

Type: Original Student Tutorial

CPALMS Aquarium Part 2: Division Strategies:

Learn to solve division challenges using the partial quotients strategy with this interactive tutorial.

This is the second tutorial is a series on division strategies.

Type: Original Student Tutorial

Sweet Treats Factory Invasion: Adding Decimals:

Help these aliens clean up the Sweet Treats Factory by learning to add decimals in this interactive mathematics tutorial.

Type: Original Student Tutorial

CPALMS Aquarium: Connecting Multiplication and Division: Part 1:

Learn how multiplication connects to division to help understand what division is in this aquarium-themed, interactive tutorial.

This is part 1 of a two-part series. Click to open Part 2, Division Strategies.

Type: Original Student Tutorial

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

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.

Type: Educational Game

Ice Ice Maybe: An Operations Estimation Game:

This fun and interactive game helps practice estimation skills, using various operations of choice, including addition, subtraction, multiplication, division, using decimals, fractions, and percents.

Various levels of difficulty make this game appropriate for multiple age and ability levels.

Multiplication/Division: The multiplication and addition of whole numbers.

Percentages: Identify the percentage of a whole number.

Fractions: Multiply and divide a whole number by a fraction, as well as apply properties of operations.

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

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.

Type: Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

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

This tutorial for student audiences will assist learners with a further understanding of the rules for adding and subtracting with decimals. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer turning orange and a wrong answer dissolving.

Type: Tutorial

## Parent Resources

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

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.

Bowling for Numbers:

The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Students eager to knock down all of the pins quickly develop patterns in their expressions. They may re-use parts of an expression, perhaps changing just the final operation.

## 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.

Type: Tutorial

Division: Intro to remainders:

In this video tutorial from Khan Academy, you will get an introduction to the meaning of remainders.

Type: Tutorial

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