# Cluster 2: Perform operations with multi-digit whole numbers and with decimals to hundredths. (Major Cluster)Archived

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.

General Information
Number: MAFS.5.NBT.2
Title: Perform operations with multi-digit whole numbers and with decimals to hundredths. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Number and Operations in Base Ten

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.5.NBT.2.AP.6a
Find whole number quotients up to two dividends and two divisors.
MAFS.5.NBT.2.AP.6b
Find whole number quotients of whole numbers with up to two-digit dividends and two-digit divisors.
MAFS.5.NBT.2.AP.7a
Solve one-step problems using decimals.
MAFS.5.NBT.2.AP.5a
Fluently multiply two-digit numbers.

## Related Resources

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

## Educational Games

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 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.

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

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.

Type: Educational Game

## Educational Software / Tool

Arithmetic Quiz:

In this activity, students solve arithmetic problems involving whole numbers, integers, addition, subtraction, multiplication, and division. This activity allows students to track their progress in learning how to perform arithmetic on whole numbers and integers. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Educational Software / Tool

## Formative Assessments

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

Type: Formative Assessment

Complete The Multiplication Problem:

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

Type: Formative Assessment

Running A Race:

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

Type: Formative Assessment

Tony’s Lunchbox:

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

Type: Formative Assessment

Students are asked to solve a word problem involving multiplication of a decimal by a whole number using a model or drawing or a strategy based on place value, the relationship between multiplication and division, or properties of operations.

Type: Formative Assessment

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.

Type: Formative Assessment

Running:

Students are asked to solve a word problem involving division of a whole number by a decimal using a model or drawing, a strategy based on place value, the relationship between multiplication and division, or properties of operations.

Type: Formative Assessment

Find the Multiplication Error:

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

Type: Formative Assessment

Multiplying Using the Standard Algorithm:

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

Type: Formative Assessment

More Multiplication Using the Standard Algorithm:

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

Type: Formative Assessment

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.

Type: Formative Assessment

Dividing Using Place Value With Larger Divisors:

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

Type: Formative Assessment

## Lesson Plans

Electric Energy & Temperature:

This lesson introduces how electrical devices transform electrical energy to thermal energy to alter the temperature of a substance resulting in the freezing, melting, or boiling of the substance. Each electrical device produces thermal energy as a byproduct that is conducted from a source like an electrical socket or battery; this lesson discusses how that energy is transferred while also comparing and contrasting the states of matter of different substances.

This is lesson 1 in a Unit on Detecting Thermal & Electrical Energy.

Type: Lesson Plan

Florida Food Round Up!:

Most families must buy food and household items that they will need every few weeks. Instead of randomly throwing things into a shopping cart and paying whatever the total is, many families must stick carefully to a predetermined budget to buy all of the items they need. A helpful way to make sure that you are able to buy everything needed is to use a list that is written before going shopping. Families must also determine, if they will purchase "name brand" or "store brand" products. Today, students will practice using a grocery list with a predetermined budget as they add and subtract decimals.

Type: Lesson Plan

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.

Type: Lesson Plan

Hoverama:

In this lesson students will create a model hovercraft. The challenge is to lift the most mass. Students will use their knowledge of forces and how increased mass interacts with motion. They will need to follow a budget in order to purchase building material for their hovercraft. While budgeting, students will apply real world mathematical (money) problem solving. Students will use iPads to record and document the process of the engineering and building of their model hovercrafts.

Type: Lesson Plan

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.

Type: Lesson Plan

Marbelous Pool Noodle Ramps:

In this lesson, students will build a ramp out of a pool noodle and use it to launch a marble across the room. Students will investigate by adjusting the height and slope of the ramp and record their findings on a data sheet. Students will practice collecting and analyzing data and will investigate the importance of performing repeated experimental trials. Students will practice converting metric units of distance as well as the addition and division of decimals to find the mean of a small data set.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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!

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Where on Earth is (teacher name)?!:

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

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

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

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.

Type: Lesson Plan

Not that Hot Anymore:

The students will rank companies offering canopies to a school for their Physical Education field.

Type: Lesson Plan

Bakery Boxes in the Mail:

Students need to make decisions about the correct bakery box to send cookies through the mail to fill orders. Students need to consider the capacity, dimensions, and volume of the boxes in terms of how many cookies each box will hold.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Workouts That Work:

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

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

This is a Model Eliciting Activity in which students are asked to assist a toy company in ranking several cities for them to consider where they will open their next store. They also read data and apply multiplication skills.

Type: Lesson Plan

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.

Type: Lesson Plan

Textbook Predicament:

This 5th grade MEA is designed to have students do math computations and compare information to provide best answer to the problem based on calculations and information given.

Type: Lesson Plan

Beach on a Budget:

Topic Overview:This 5th grade MEA asks students to work in teams to determine from which store they will buy beach equipment for a new beach rental business, after considering several criteria. After the students have created a proposal based on given data, a twist is added which may vary their results.

Type: Lesson Plan

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.

Type: Lesson Plan

Supermarket Sweep!:

In this lesson, students will use a grocery store ad to select items for purchase, working within the constraint of making their purchases with a \$50 gift card. After their initial plan, they have some emergency expenses that change the amount of the gift card unexpectedly, and they must alter their list and re-compute how much money would remain on their gift card after their planned purchases are made.

Type: Lesson Plan

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.

Type: Lesson Plan

Which Sweets for the Bakery?:

This MEA gives students the opportunity to use real world data to rank proposed product lines from most likely to be profitable to least likely to be profitable. There are two sequential tasks; the second task adds a component of complexity to the original task. Students will apply multiplication and division skills in problem solving, write a procedure with grade-appropriate organization and conventions, and participate in group collaboration to complete this task.

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

The Dazzling Painting Co.:

ResourceID: 49826

Type: Lesson Plan

Tablets for Mrs. Tomlinson's Class:

Students' love of technology will hook them on this MEA that also applies their knowledge of multiplication, estimation, and rounding. And that's just the beginning!

Type: Lesson Plan

Field Day Fun:

In this MEA, students will choose their top choices of field day activities given the cost, number of adult supervisors needed, the area required for event, safety concerns, clean up required, number of students that can play at a time, and peer comments about the activity. Students will need to make trade-offs in cost when the "twist" provides budget restrictions. Students will calculate area and multiply whole numbers and decimal numbers.

Type: Lesson Plan

Patty's Party Planning:

Students will help a party planner determine which party location is the best one to use for this situation. 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.

Type: Lesson Plan

Are You Ready for a Hurricane?:

This activity allows students to determine the types of items that should be in a hurricane survival kit, use a budget and calculations to determine the items to include in the kit and gain an understanding of hurricanes and the need to prepare for them.

Type: Lesson Plan

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.

Type: Lesson Plan

Stand Up and Cheer:

This MEA asks the students to compare items to be given to fans attending a college homecoming football game.

Students will use multi-digit multiplication and measurement conversion while comparing data on the items. They will also take into account fan reviews of the items which should create interesting student discussions.

Type: Lesson Plan

Blow Me Away:

This MEA asks the students to decide which hand dryer model would be the "best and the worst" for Blow Me Away Incorporated to sell.

The students will consider company's cost; selling price; whether hand dryer turns on when hands are placed near it; whether hand dryer stays on when hands are near it; whether hand dryer turns of when hands are moved away; appearance and energy efficiency.

Students will provide "top choice" to Blow Me Away Incorporated and explain how they arrived at the solution.

LEGO Education WeDo Robotics extension activity can follow should a school have the WeDo program.

Type: Lesson Plan

In this open-ended MEA, students will work in teams to determine a procedure for ranking recycling companies. Students will need to calculate their return on recycling, make decisions based on a table of data, and write a letter to the client providing evidence for their decisions.

Type: Lesson Plan

How Many Gigabytes Does Lathan Really Need?:

Students will be comparing quantitative and qualitative aspects of technology devices in order to rank them for a particular student's needs.

Type: Lesson Plan

Cameras on Campus:

This MEA uses technology and real world problem solving to hook the students.

Type: Lesson Plan

Fast Food Decision:

Students will rank fast food restaurants from best to worst based on their nutrition, price, and distance to sport field. Students will need to be able to add, subtract, and multiply decimal numbers. Given the first data set, students will come up with a procedure for ranking restaurants based on the prices and nutrition information given. Students will need to consider what is more important, price or nutrition. They will also need to determine what nutritional elements are more important to consider (fat, calories, sodium). Because some ties can occur, students will have to make tradeoffs for nutrition or price. Given the second data set, students have to reconsider their procedure when given price and coupon information along with distance to the restaurant and budget.

Type: Lesson Plan

Come Sail Away!:

In teams, students will determine which sailboat the Leeward Family should purchase. They will use their knowledge of multiplying decimals to assist in their problem solving. The criteria will be based on air conditioning, swim out, auto helm, recent bottom job, condition of sails, condition of upholstery, and other twists!

Type: Lesson Plan

Black Out in an Ice Cream Shop!:

This Model Eliciting Activity (MEA) asks students to develop a procedure for choosing a back-up energy source (generator) for an ice cream shop. Students will need to consider Cost of unit, wattage output, size of fuel container, length of time this machine will run, auto turn on, and the number of outlets it can receive. In the second portion of the problem statement, the students will need to prepare and compare the cost of use for 24 hour period. They will need to determine if they have still made the correct choices while adding three more generators for consideration, and make a cost analysis for 24 hours of use. In the culminating activity, the students will write a proposal for the client for the generator of their choice and include the 24 hours cost analysis.

Type: Lesson Plan

Pick A Pet:

This Model Eliciting Activity (MEA) asks students to develop a procedure for choosing a reptile or amphibian to place in a school reception area. Students will need to consider safety, price of animal, cost by week to feed animal, size and cost of the enclosure, and the life span of the animals they are considering. In the second portion of the problem statement, the students will need to prepare a budget and cost analysis for the year to consider if they have still made the correct choices while adding three more animals for consideration. The culminating activity for this MEA will have the student write a proposal for the Principal to state their choice of animal, give a year's budget for cost and care for the animal.

Type: Lesson Plan

Oak Tree Engineers:

This Model Eliciting Activity (MEA) is written at a 5th grade level. In this open-ended problem, students are presented with a variety of steps. Based on the data table given for student review, students must decide which simple machines they want to assemble and rank the stores in order starting with the one they would like to order from. Moreover, students are given special characteristics that they need to consider before describing their reasoning and procedures implemented in reaching their answers.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Getting Dry:

This MEA asks the students to compare hand drying products based on: initial cost, replacement cost and absorbency. Students will provide the "top choice" to the principal of the school and explain how they arrived at the solution. In the twist, students will be asked to consider the environmental impact of the products and reevaluate their conclusions.

Type: Lesson Plan

New Frozen Yogurt Store:

This MEA asks students to decide which factors are important in developing a successful frozen yogurt (froyo) store in order to compete with and become the best store in the area. Students will provide feedback to an entrepreneur who is looking to open a frozen yogurt store. They will rank order their choices of the most successful to least successful store. Students will provide a detailed written explanation for how they decided to rank factors and their solution rating existing stores from best to worst.

Type: Lesson Plan

New Snack Shack Snack:

This MEA asks the students to decide which snack food would be the best for introduction in the school Snack Shack. Students are asked to compare nutritional value per ounce of food based on calories, fat, sodium, cholesterol, protein, and sugar.

Type: Lesson Plan

Rank Our Pressure Cleaners:

This MEA asks the students to decide on a pressure cleaning machine that will provide the Sidewalks and Roof Cleaning Services Incorporated company with the best value for their money. Students are asked to rank order of pressure cleaning machines in term of consumer rating, gallons per minute (GPS), pounds per square inch (PSI), cleaning units (CU), whether it is gasoline or electric operated, price, and amount of time the pressure cleaner takes to clean 10 square feet of surface area. Students must provide a "Best Value" pressure cleaner to the company owner and explain how they arrived at their solution.

Type: Lesson Plan

Shopping on a Budget:

This lesson reinforces multiplication of money by a whole number. Students will be presented with real-world items such as cans of soup, etc to investigate the concept of multiplying decimals. The culminating activity of the lesson is for students to create a school supply order for their classroom utilizing school supply catalogs.

Type: Lesson Plan

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.

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

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.

Type: Lesson Plan

“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.

Type: Lesson Plan

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.

Type: Lesson Plan

Race to Fill the Whole!:

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

Type: Lesson Plan

Sunshine Beach Hotel MEA:

This Model Eliciting Activity (MEA) asks students to develop a procedure to select a hurricane shutter company.

Type: Lesson Plan

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.

Type: Lesson Plan

Vending Machine Snacks:

In this MEA, students are challenged to choose the snacks that will be in a vending machine in a school. Students will need to multiply and divide whole numbers and decimal numbers as well as compare fractions and decimal numbers. Students will work in groups to solve the problem and write a letter to the client explaining their thinking.

Type: Lesson Plan

## Original Student Tutorials

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.

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

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

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.

Type: Original Student Tutorial

Carnival Tickets:

The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases.

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

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

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

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.

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

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

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.

Type: Original Student Tutorial

## Educational Games

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 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.

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

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.

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

Carnival Tickets:

The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases.

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

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

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.

Carnival Tickets:

The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation. Inflation is a sustained increase in the average price level. In this task, students can see that if the price level increases and people’s incomes do not increase, they aren’t able to purchase as many goods and services; in other words, their purchasing power decreases.

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

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

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