Standard 2 : Add, subtract, multiply and divide multi-digit numbers.



This document was generated on CPALMS - www.cpalms.org


General Information

Number: MA.5.NSO.2
Title: Add, subtract, multiply and divide multi-digit numbers.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 5
Strand: Number Sense and Operations

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.5.NSO.2.1: Multiply multi-digit whole numbers including using a standard algorithm with procedural fluency.
MA.5.NSO.2.2: Divide multi-digit whole numbers, up to five digits by two digits, including using a standard algorithm with procedural fluency. Represent remainders as fractions.
Clarifications:
Clarification 1: Within this benchmark, the expectation is not to use simplest form for fractions.
MA.5.NSO.2.3: Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency.
MA.5.NSO.2.4: Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value.
Clarifications:
Clarification 1: Estimating quotients builds the foundation for division using a standard algorithm.

Clarification 2: Instruction includes the use of models based on place value and the properties of operations.

MA.5.NSO.2.5: Multiply and divide a multi-digit number with decimals to the tenths by one-tenth and one-hundredth with procedural reliability.
Clarifications:
Clarification 1: Instruction focuses on the place value of the digit when multiplying or dividing.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MA.5.NSO.2.AP.1: Explore multiplication of two whole numbers, up to two digits by two digits.
MA.5.NSO.2.AP.2: Apply a strategy to divide two whole numbers up to two digits by one digit, including the possibility of whole number remainders.
MA.5.NSO.2.AP.3: Apply a strategy to add and subtract multi-digit numbers with decimals to the tenths (e.g., 3.3 + 0.5) and hundredths (e.g., 1.25 − 0.12). Multi-digit numbers not to exceed 9.99.
MA.5.NSO.2.AP.4: Explore the estimation of products and quotients of two multi-digit numbers with decimals to the tenths (e.g., 8.9 × 2.3 becomes 9 × 2 by rounding both factors to the nearest whole number). Multi-digit numbers not to exceed 9.9.
MA.5.NSO.2.AP.5: 5 Explore multiplying and dividing single-digit whole numbers by one-tenth and one-hundredth.


Related Resources

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

Original Student Tutorials

Name Description
Partying with Partial Quotients:

Join Party On Productions to solve whole number division problems with remainders using the partial quotient method in this interactive tutorial.

Sailing Through Subtracting Decimals:

Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.

Add Another Topping: Adding Decimals:

Learn to add decimals to the thousandths using a standard algorithm at the ice cream shop in this interactive tutorial. 

Designing Dog Playgrounds: Multiplying Decimals:

Help your town build a dog park by multiplying whole numbers by decimals to the tenths place in this interactive tutorial. 

Note: this is an introductory tutorial on multiplying whole numbers by decimals before students move on to multiplying decimals by decimals.

Let’s Get Buzzy: Multiplying Multi-digit Numbers Using the Standard Algorithm:

Learn how the standard algorithm for multiplying numbers works and practice your skills in this interactive tutorial.

Field Trip Frenzy (Part 4):

Learn when to write the remainder of a multi-step division process as a fraction or decimal in this interactive tutorial.

This is the final tutorial in the Field Trip Frenzy Series about remainders. Click below to open the other tutorials in this series.

Note: This tutorial extends beyond whole number quotients with whole number remainders to whole number quotients with fractional or decimal remainders.

Educational Games

Name Description
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.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

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.

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.

Change Maker:

This interactive applet gives students practice in making change in U.S. dollars and in four other currencies. Students are presented with a purchase amount and the amount paid, and they must enter the quantity of each denomination that make up the correct change. Students are rewarded for correct answers and are shown the correct change if they err. There are four levels of difficulty, ranging from amounts less than a dollar to amounts over $100.

Educational Software / Tool

Name Description
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

Name Description
Driving to Alaska:

Students are asked to solve a division word problem with a two-digit divisor using a strategy based on place value.

Complete The Multiplication Problem:

Students are asked to finish a multiplication problem that has already been started using the standard algorithm.

Running A Race:

Students are asked to solve a word problem that involves adding two decimals by using a strategy based on place value.

Tony’s Lunchbox:

Students are asked to solve a word problem that involves subtracting two decimals by using a strategy based on place value.

Analyzing and Applying 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.

Find the Multiplication Error:

Students are asked to find the error in a multiplication problem involving a three-digit and a two-digit number.

Multiplying Using the Standard Algorithm:

Students are asked to complete two multiplication problems using the standard algorithm.

More Multiplication Using the Standard Algorithm:

Students are asked to complete two multiplication problems using the standard algorithm.

Dividing Using an Area Model With Larger Divisors:

Students are asked to interpret a division problem with a two-digit divisor that has been completed using an area model. If the student is successful, he or she is asked to determine the solution to a division problem with a two-digit divisor using an area model.

Dividing Using Place Value With Larger Divisors:

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

Long Division - 1:

Students are asked to complete three long division problems (no remainders) to check for fluency with the standard division algorithm.

Long Division - 3:

Students are asked to complete three long division problems (each with a remainder) to check for fluency with the standard division algorithm.

Long Division - 2:

Students are asked to complete three long division problems (one with a remainder) to check for fluency with the standard long division algorithm.

Lesson Plans

Name Description
Catch Me If You Can: Engineering Design Challenge:

In this lesson, 5th grade students work in small groups on a STEM challenge that involves science and math standards related to the water cycle, as well as learning the engineering design process.

Weathering Weather:

This is a design challenge lesson allowing students to utilize their understanding of climate zones to design a tropical roof that would withstand the wind and water generated by a hurricane. This lesson also allows you to assess students understanding of operations with decimals to create their design under a given budget.

Icky, Icky, No More Slicky:

In this lesson, 5th grade students will build an engineering device to separate oil from water in a simulated oil spill. Students will have an opportunity to learn about the impact that humans can have on the environment, both positively and negatively.

This is an Engineering Design Challenge that is best used after a unit or lesson that is aligned to science standards on solving problems or materials which dissolve in water. This challenge provides students a means to use their knowledge of the way materials will or will not dissolve in water to create and design an oil spill removal tool while learning the Engineering Design Process and being exposed to the field of engineering. This lesson is not intended as an initial introduction to the standard and would be best utilized as a culmination lesson.

The Coasta with the Mosta:

Students will create an exciting and thrilling roller coaster model. Students will use their knowledge of forces to build a model of a roller coaster using foam insulation and a marble.

When the Wind Blows:

This is an engineering design process lesson that covers forces and motion. It is designed to engage students using hands-on problem solving strategies.

Bottling Rockets:

In this lesson, students will explore the concepts of force and motion as they use the engineering design process to create and test rockets. Students will demonstrate their understanding of familiar forces by creating and presenting a poster. Take students up, up, and away with this engaging lesson!

From Trash to Treasure - An Engineering Design Challenge:

This lesson gives students hands-on experience with sorting mixtures based on their properties. The students will relate these science standards to a real-world problem of eliminating trash in land fills. They will have to purchase the tools they use to create their assembly line to sort the garbage within the budget provided.

Bridge Over Troubled Waters:

In this engineering lesson, students will design and construct a bridge that will be free-standing and support a toy car.

Medic Mass Landing: Engineering Design Challenge:

In this lesson, 5th grade students work in small groups on a STEM challenge that involves science and math standards related to force, motion, and measurement, as well as learning the engineering design process.

How Much Did I Earn? Division with Decimals:

This lesson will introduce division of decimals using place value decomposition. Students will use base 10 blocks, division strategies and place value knowledge to divide decimals by whole numbers.

Where on Earth is (teacher name)?!:

Students practice converting metric and customary measurements, while helping their teacher travel on summer vacation in Europe.

Shopping for My Trip to the Beach:

This lesson will provide practice in adding/subtracting decimals in money form.  Student will model with base-ten blocks and then using the standard algorithm, through the hundredths place. This is not an introductory lesson. Students should already have conceptual knowledge and practice adding four-digit numbers using manipulatives or other methods.

Area Models to Algorithms:

Students will investigate the standard algorithm of two-digit by two-digit multiplication and how it connects and relates to the area model. This will provide an introduction to the standard algorithm.

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.  

Make a Funny Partial Quotient Division Story:

This lesson introduces students to the area model and the partial quotient model to solve division problems with 2-digit divisors. Students are asked to apply both strategies to solve funny division problems that they help create by inserting information that is left blank in the story problems.

Multiplying Decimals: Finding Part of a Whole:

This is an introductory lesson for this concept.   Students will use area models to show that multiplying a whole number by a decimal creates a product that is only part of the original whole.

Deft Drawings for Decimal Division:

In this lesson, students divide decimals to hundredths in real-world word problems by drawing illustrations based on place value and explaining the reasoning used.

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.

Blessings in a Bag!!:

In this MEA, the students will help a charitable organization select 5 snack items from a list to provide nutritious snacks for children in low-income communities.  Students will practice using the four operations to solve real-world problems and use decimal notation to make calculations involving money.  Additionally, they will be asked to compare multi-digit numbers to the thousandths.

Getting the Top Mini-Fridge not a Small Deal:

In this MEA, students will create a procedure to rank five mini-refrigerators to determine which one should be purchased for the school by the PTA based on size, type, features, energy usage, and cost.  In the process, students will solve real-world problems involving the multiplication of multi-digit numbers with decimals to the hundredths, including using money.  Students will also determine the volume of a rectangular prism using a formula.

Workouts That Work:

Students will create a rating system for workout DVD's according to weight loss, muscle toning, and increased physical condition.

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.

Keeping Your Cool With Your Lunch Bag:

On this MEA activity, students will create a procedure to rank five lunch bags as to which one is the best in keeping food and drinks at a safe temperature and appealing to the taste, while keeping design and price on target.

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.

Evan's Family Vacation:

Evan needs your help convincing his parents to rent a car for their family's vacation to Washington D.C. His parents are thinking of traveling in the family's old SUV that has no air and horrible gas mileage. Students will be asked to estimate each rental car's gas costs along with the weekly rental fee to rank the choices. In the twist, the students will be given safety information and 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. Click here to learn more about MEAs and how they can transform your classroom.

To Oregon by Wagon:

Students work in teams to plan the contents of a covered wagon for a family relocating from Missouri to Oregon. Students must calculate the weight and cost of the wagon by adding, subtracting, and multiplying with decimals.

Museum Dilemma:

In this MEA, students evaluate the contributions of various explorers to help a museum select the subject who provided the most impact on Western development for a new exhibit. Students will need to convert units to have the necessary information to help come up with a solution to the problem.

Out to Lunch: Decimal Operations with a Menu:

In this lesson students work toward fluency with decimal operations by using a snack bar menu and going "Out to Lunch" with a friend.

Cracking the Code: A Division Challenge:

In this lesson, students will use their knowledge of division and division strategies to solve problems that have been written in a code where numbers are replaced with symbols. The students are challenged to find out how the traditional algorithm strategy works and how it compares to other strategies they already know. Students are also charged with creating a list of mathematical tools that help make solving division problems easier.

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.

Currency Craze!:

If I travel to Italy, can I buy a raspberry gelato with a $5.00 bill? Students will understand that other countries use currencies different from the United States, and that when visiting those countries, exchange rates are used to determine the value of the United States dollar (USD). This lesson integrates Mathematics with Social Studies as the students apply their knowledge of decimals and basic operations with their passports for a real-world application.

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.

Balls Galore: Evaluating Playground Ball Companies:

This MEA gives the students the opportunity to evaluate and rank several playground ball companies based on their use in a summer camp program. Students should use multiplication to determine the total cost of the balls for each company.

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.

Estimating Decimal Products:

In this lesson, students will learn to estimate decimal products using different strategies to arrive at compatible numbers. They will learn that estimates will vary depending on the strategy chosen and that the closer the compatible numbers are to the actual factors, the closer the estimate will be to the exact answer. Students will also learn that estimation is used to solve problems that don't require exact answers and to check exact answers for reasonableness.

Easy as Pie Division!:

This is a hands-on lesson to show the relationship between division and multiplication. It provides a different method for solving long division that my students love.

Better Buy: 75 fl oz or 150 fl oz?:

The students will clip out advertisements or use the attached PowerPoint to determine the better buy between small quantities and large quantities. The students will answer the question, "Which item costs less per unit?" and demonstrate fluency in dividing with decimals.

The Mystery of Decimals:

This lesson reviews all four operations (adding, subtracting, multiplying, and dividing) with decimals. It is designed to easily provide differentiated instruction for students. The culmination of the lesson is a computer-based assessment which provides a fun change from a typical pencil and paper test.

Diving deeper into division:

This lesson introduces students to dividing with 2 digit divisors.  Students are asked to apply strategies that they learned in dividing with 1 digit divisors such as partial quotients or breaking numbers apart using the distributive property.

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.

Banana County Public School-Painters MEA:

This Model Eliciting Activity (MEA) is written at a 4th grade level.

This activity allows students to think critically using information provided. Students will write a procedure on how they determined which painting company would be suitable for the client.

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.

Dividing Decimals Investigations:

In this introductory lesson, students test how the basic operations performed on the dividend and divisor affect the quotient of a pair of numbers. Students then conclude whether the results of their trials can be applied to solve problems with a decimal divisor.

“Dinner with Friends”:

The students will determine what to order at a dinner with friends yet stay within a budget. The students will try to maximize their budgets and order as much food as they possibly can with their given amount of money.

Wallpaper Woes Money Math: Lessons for Life:

Students hear a story about a middle-school student who wants to redecorate his bedroom. They measure the classroom wall dimensions, draw a scale model, and incorporate measurements for windows and doors to determine the area that could be covered by wallpaper. Students then hear more about the student's redecorating adventure and learn about expenses, budget constraints, and tradeoffs.

Race to Fill the Whole!:

In this engaging lesson, students will play a game using base ten blocks to add decimals to the hundredths.

Sunshine Beach Restaurant:

This Model Eliciting Activity (MEA) asks students to develop a procedure to select a hurricane shutter company based on several data points.

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

The 20 Second Game:

This is a game students will love to play to improve their understanding of estimating decimal products and increase speed when finding these estimations. The game can be modified to practice estimating products of whole numbers, quotients of whole numbers, and quotients of decimals.

Perspectives Video: Experts

Name Description
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.

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.

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.

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. maththematics benchmarks in this Expert Perspectives video.

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.

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.

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.

Perspectives Video: Teaching Ideas

Name Description
Representing Remainders as Fractions:

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

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.

Estimating Decimal Multiplication:

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

Precision of Measurement:

Classroom activities that teach students precision of measurement.

Problem-Solving Tasks

Name Description
Reasoning about Multiplication and Division and Place Value, Part 2:

Students are asked to reason about and explain the placement of decimals in quotients.

What is 23 ÷ 5?:

When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them.

Minutes and Days:

This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Interpreting a Division Computation:

The purpose of this task is to use the computation shown below to find the products. Understanding of place value is necessary for successful completion.

Tutorials

Name Description
Multiplying a Decimal by a Power of 10:

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

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.

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.

Adding and Subtracting with Decimals:

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.



Student Resources

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

Original Student Tutorials

Title Description
Partying with Partial Quotients:

Join Party On Productions to solve whole number division problems with remainders using the partial quotient method in this interactive tutorial.

Sailing Through Subtracting Decimals:

Sail through subtracting decimals to the thousandths place using a standard algorithm in this interactive tutorial.

Add Another Topping: Adding Decimals:

Learn to add decimals to the thousandths using a standard algorithm at the ice cream shop in this interactive tutorial. 

Designing Dog Playgrounds: Multiplying Decimals:

Help your town build a dog park by multiplying whole numbers by decimals to the tenths place in this interactive tutorial. 

Note: this is an introductory tutorial on multiplying whole numbers by decimals before students move on to multiplying decimals by decimals.

Let’s Get Buzzy: Multiplying Multi-digit Numbers Using the Standard Algorithm:

Learn how the standard algorithm for multiplying numbers works and practice your skills in this interactive tutorial.

Field Trip Frenzy (Part 4):

Learn when to write the remainder of a multi-step division process as a fraction or decimal in this interactive tutorial.

This is the final tutorial in the Field Trip Frenzy Series about remainders. Click below to open the other tutorials in this series.

Note: This tutorial extends beyond whole number quotients with whole number remainders to whole number quotients with fractional or decimal remainders.

Educational Games

Title Description
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.

Addition/Subtraction: The addition and subtraction of whole numbers, the addition and subtraction of decimals.

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.

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.

Change Maker:

This interactive applet gives students practice in making change in U.S. dollars and in four other currencies. Students are presented with a purchase amount and the amount paid, and they must enter the quantity of each denomination that make up the correct change. Students are rewarded for correct answers and are shown the correct change if they err. There are four levels of difficulty, ranging from amounts less than a dollar to amounts over $100.

Educational Software / Tool

Title Description
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.

Problem-Solving Tasks

Title Description
Reasoning about Multiplication and Division and Place Value, Part 2:

Students are asked to reason about and explain the placement of decimals in quotients.

What is 23 ÷ 5?:

When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them.

Minutes and Days:

This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Tutorials

Title Description
Multiplying a Decimal by a Power of 10:

This Khan Academy tutorial video explains patterns in the placement of the decimal point, when a decimal is multiplied by a power of 10.  Exponents are NOT discussed.

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.

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.

Adding and Subtracting with Decimals:

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.



Parent Resources

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

Problem-Solving Tasks

Title Description
Reasoning about Multiplication and Division and Place Value, Part 2:

Students are asked to reason about and explain the placement of decimals in quotients.

What is 23 ÷ 5?:

When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as with Part (b)) or a mixed number/decimal (as with Part (c)). Part (a) presents two variations on a context that require these two different responses to highlight the distinction between them.

Minutes and Days:

This task requires division of multi-digit numbers in the context of changing units. In addition, the conversion problem requires two steps since 2011 minutes needs to be converted first to hours and minutes and then to days, hours, and minutes.

Tutorials

Title Description
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.

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.

Adding and Subtracting with Decimals:

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.