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Operations with Numbers
Problems in this category can be solved using a combination of basic operations (addition, subtraction, multiplication, division). Problems requiring application of approximating skills (estimation, rounding) are also included in this category.

Problems that focus more specifically on each skill in this category can also be found in the following subcategories:

Related Resources
Interactive resources from our Math Tools project:
   Math 4: Operations with Numbers
The closest match in our Ask Dr. Math archives:
   Elementary Arithmetic
NCTM Standards:
   Number and Operations Standard for Grades 3-5

Access to these problems requires a Membership.

Across Australia - Lisa Lavelle
active problem Math Fundamentals, difficulty level 2. Help Mr. W figure out when he needs to start his trip in order to meet Mrs. W on time (requires a bit of map reading). ... more>>

Across the Netherlands - Maggie Hos-McGrane
teacher support active problem Math Fundamentals, difficulty level 2. Help sort out this bike trip through the Netherlands (requires a bit of map reading). Initially a two-week problem. ... more>>

Across Wisconsin - Jo Wenzler
teacher support active problem Math Fundamentals, difficulty level 2. Determine how long it will take this athletic math teacher to bike across Wisconsin (requires a little map reading). Initially a two-week problem. ... more>>

Aidan's Millimeter Measurements - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 1. Calculate Aidan's height and age based on his well-baby measurements at the doctor's office. ... more>>

Almond Cookie Bake - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 2. Convert this cookie recipe to feed the March Madness celebrators. ... more>>

Anderson's Pumpkin Patch - Teaching the Young Learner Group and Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 2. How many students are there in Ms. Juncos's fourth grade class? ... more>>

Anthony's Famous Butter Rolls - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 2. How many rolls will Anthony need to bake for the family's Thanksgiving feast? ... more>>

At the Movies - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Explore the changes in movie and theater prices. ... more>>

Back-to-School Shopping - Judy Ann Brown
teacher support active problem Math Fundamentals, difficulty level 2. Mrs. Bender noticed that the total of the items her children purchased was $155. Can you determine the cost of one pair of jeans? ... more>>

Back-to-school Supplies - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 2. Help calculate the total bill for these back-to-school supplies. ... more>>

Baseball Trivia - Judy Ann Brown
teacher support active problem Math Fundamentals, difficulty level 2. How many runs do the Phillies have to score before the base runners have covered a mile? ... more>>

Beautiful Borders - Lisa Lavelle
active problem Math Fundamentals, difficulty level 3. Help Abbie total the bill for sprucing up her room. ... more>>

The Big Balloon Blowup - Leon Roland & class
teacher support active problem Math Fundamentals, difficulty level 3. Help Ulrike and Lars determine the number of balloons in each bag. ... more>>

Birthday Beach Bash - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Help determine how many balloons were needed for party favors at the end of this celebration. ... more>>

Birthday Probability - Kristina Lasher & Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. What is the likelihood that someone is born on an even or odd day of the month? Are you more likely to be born on a prime number day or a multiple of 3? ... more>>

Building Bouquets - Amanda Knott and the Western Oregon University Mentors
teacher support active problem Math Fundamentals, difficulty level 2. Help Jana determine how to divide her extra flowers for the flower shop special. ... more>>

Building the Fence - Steve Risberg & Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 3. Herta is building a fence. How wide will the gaps between the pickets be so that everything is spaced evenly? ... more>>

Bunches of Basil - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Determine the maximum number of basil plants I will have after I finish thinning the garden. ... more>>

California Dreaming - Judy Ann Brown
teacher support active problem Math Fundamentals, difficulty level 3. Determine the length of time that will be needed to drive from Allentown, Pennsylvania, to Los Angeles, California. ... more>>

Can You Drink That Swimming Pool? - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 3. Estimating the amount of water in a pool. About how long would it take to drink that much water? ... more>>

Charlene Goes Shopping - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 2. Charlene needs to add some items to her winter collection. Help her determine where she should shop. ... more>>

The Chocolate Allergy Revelation - Antiquity (Steve Earth)
teacher support active problem Math Fundamentals, difficulty level 5. Use meta-reasoning to deduce the ages of three people based on a product, a sum, and a seemingly irrelevant third piece of information. ... more>>

Chocolate, Orange, Mega-mint Swirl - Fitzgerald's Spring 2000 Class C
teacher support active problem Math Fundamentals, difficulty level 4. How many half-gallon cartons of ice cream can fit in the freezer? ... more>>

Choose Your Challenge - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 2. Can Zak find a more precise measure of how much older his brother is than he is? ... more>>

Choosy Chooser's Choices - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Find out how many outfits Charlene can put together for a sunny day. ... more>>

Cicada Circus - Kristina Lasher and special thanks to John Cooley
teacher support active problem Math Fundamentals, difficulty level 2. Use the table of information about periodical cicadas to figure out when the next time is that there will be three years in a row without an emergence. ... more>>

Circles Around - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Use this exploration problem to discover the relation between circumference and diameter. ... more>>

Common Cents - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 2. How much money do Monique and Misty each contribute toward Mom's Valentine's candy? ... more>>

Cool Cubes - Heather Cool and Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Can Jackie really mark her cubes so that each sum from 1 to 36 is possible? ... more>>

Count the Discount - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 3. The jacket on the clearance rack is marked down 20% more each day. How much will it cost after 5 days? ... more>>

Crack the Code - Christi Sather and Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 2. Help Christi use the clues to figure out which code will unlock the vault. ... more>>

Cubic Changes - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Determine how the volume and surface area of a cube change when the edge length is changed. ... more>>

Cupcakes, Cupcakes! - Kristina Lasher & Terry Trotter
teacher support active problem Math Fundamentals, difficulty level 1. Andrei needs to put icing on the cupcakes and get out the door to catch the bus. Will he and his sister be able to get them all iced in time? ... more>>

Dad's Cookies - Diane Anderson's Teaching the Young Learner Class
teacher support active Math Fundamentals, difficulty level 3. Figure out how many cookies Dad baked for the family before they ate them all! ... more>>

A Dicey Situation - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 3. Determine the fairness of a game in which players score points according to the difference between the values of two rolled dice. ... more>>

Driving Decisions - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 4. Help the Downings decide which car rental is the best option for their trip to Denver. ... more>>

Elevator Weigh-in - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 2. Would Melissa's family and neigbors exceed the maximum weight allowance of their apartment building elevator? If not, how many more would fit? ... more>>

Erika's Rock Collection - Elisabeth and Stephen Baseman and Chamberlain
teacher support active problem Math Fundamentals, difficulty level 2. Find out how many rocks Erika has collected over the years. ... more>>

Expressions of One Hundred - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Find a way to express one hundred with the given digits. ... more>>

Feathers and Fur - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Determine the number of pigeons and puppies Xiao has. ... more>>

Filling the Freezer - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 4. How many cartons of ice cream can the Math Club fit in their freezer? ... more>>

Fish in a Barrel - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 3. Find out how many fish Jake, Herman and Luke each took home from their fishing trip. ... more>>

Five Digits of Fun - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Find a five-digit number based on these clues. ... more>>

Flying Time Zones - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Help me figure out what time my watch should show when I land in Denver. ... more>>

Football Fanfare - Suzanne Alejandre and Kristina Lasher
teacher support active Math Fundamentals, difficulty level 1. The students in the pep club are designing a "card stunt" for the halftime show for the next football game. What are the possible seating arrangements they can use? ... more>>

Four Playful Mathematicians - inspired by Maria Fung's class at Western Oregon
teacher support Math Fundamentals, difficulty level 2. Follow the clues to help the four playful mathematicians return the lost watch. ... more>>

Frog Farming - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 2. Help Farmer Mead build a rectangular pen that holds the greatest number of frogs. ... more>>

Frugal Flooring - Marita Paynter
teacher support active problem Math Fundamentals, difficulty level 2. Help Graeme determine how many tiles he needs to decorate his new bedroom and whether or not he can afford them. ... more>>

Frugal Freeda - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Help Freeda decide which store has the best buy. ... more>>

Funny Money - Lisa Lavelle (adapted)
teacher support active problem Math Fundamentals, difficulty level 2. Determine the amount of money Divya has in her bank. ... more>>

Garden Fresh Fruit - Shrawan Khanna's Ninth Grade Class
teacher support active problem Math Fundamentals, difficulty level 4. Help the poor farmer predict his revenue (if he can sell all his fruit). ... more>>

Giving with Grapefruit - Lisa Lavelle & Western Oregon University Students
teacher support active problem Math Fundamentals, difficulty level 1. How much will Cassie help raise for charity? ... more>>

Golf Anyone? - Phil Marchal
teacher support active problem Math Fundamentals, difficulty level 3. Kyle needs some help in figuring out how many buckets of golf balls were hit at the Hook and Slice Driving Range. ... more>>

Good Fences - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Design a fence that will keep the animals happy. ... more>>

Greta's Garden - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 2. Find out how much money Greta made from each of her vegetables at the Farmers's Market. ... more>>

Hauling Sand - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 2. How many tons of sand can Marty haul in his dump truck? ... more>>

Holiday Shopping and Surfing - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 2. Help Charlene calculate the change she'll have left for holiday card supplies after she completes her online shopping. ... more>>

Horton's Clover Hunt - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Find out how fast Horton had to work picking clovers. ... more>>

Hot Dog Day! - Jeffrey Mo
teacher support active problem Math Fundamentals, difficulty level 3. Determine how many large hot dogs have been ordered for this special day. ... more>>

How Old is Dad? - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 2. Use the clues to find out how old Dad is. ... more>>

I Get A Kick Out Of Soccer! - Judy Ann Brown
teacher support active problem Math Fundamentals, difficulty level 3. How many laps of the soccer field would a team member need to complete to run more than a mile? ... more>>

I Like to Palindrive! - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 3. How many palindromic numbers will appear on Kristina's odometer in October, 2003? ... more>>

Inching Along Down the Football Field - Terrel Trotter
teacher support active problem Math Fundamentals, difficulty level 3. Fred put his football down on a goal line of the 100-yard field. He then moved it forward half the field distance, over and over again. When did the distance first become less than one inch? ... more>>

Irish Specials - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Calculate the final bill for our St. Patrick's Day dinner last week. ... more>>

Is There Really a Discount? - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Determine which friend is correct about the final price on a sales item. ... more>>

Jellybean Rectangles - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Have fun figuring out strategy in the Jellybean Rectangle game. ... more>>

Jumping Rope - Leon Roland & class
teacher support active problem Math Fundamentals, difficulty level 2. Just how long was the rope with which we started? ... more>>

Lawn-Mowing Chore - Judy Ann Brown
teacher support active problem Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow. ... more>>

Let the Chips Fall . . . - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 3. Use clues about sums to determine which digits are on the reverse sides of three given chips. ... more>>

Lighting the Menorah - Lillian Ray and Claire Mead
teacher support active problem Math Fundamentals, difficulty level 1. How many candles are used during Chanukah? ... more>>

Lost in Space - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Figure out how big an error the engineers made when they mixed up their units. ... more>>

Lucky Lettuce Land - Kainoa Trotter, et al.
teacher support active problem Math Fundamentals, difficulty level 3. Help Farmer Lucky fence his lettuce land. ... more>>

Lunch Bunch Budgets - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 2. Determine the number of children needed for the lunch bunch budget to balance. ... more>>

Luscious Lemonade - Judy Ann Brown
teacher support active problem Math Fundamentals, difficulty level 3. The label on the lemon concentrate says that I need to mix 2 cups of concentrate with 3 cups of water. How much lemon concentrate should I buy to make 25 gallons of lemonade? ... more>>

The Mad Hatter's Gone! - Leanne Gater
teacher support active problem Math Fundamentals, difficulty level 4. Explore a coordinate plane and help the Cheshire Cat find his favorite cheese. ... more>>

Magic Square Jumble - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Help straighten out this magic square. ... more>>

March Madness! - Teaching the Young Learner Class
teacher support active problem Math Fundamentals, difficulty level 3. Given four clues, figure out which pair of friends won a basketball game. ... more>>

Math Club Lollipop Profits - Judy Ann Brown
teacher support active problem Math Fundamentals, difficulty level 3. The Math Club plans to sell lollipops. Help them to calculate their profit. ... more>>

The Math Teacher's Ties - Brentwood College School - Math 12(1)
teacher support active problem Math Fundamentals, difficulty level 3. Read the rhyme and determine the number of ties the math teacher has in his wardrobe. ... more>>

Mean Jellybeans - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Take a look at averages with Mr. Cal Q. Later and his class. ... more>>

Meters of Money - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 2. Help Ms. Juncos's class determine the amount of money they will raise with this metric project. ... more>>

A Million in Time - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 2. "Human beings can expect to live a million..." Use your conversion skills to determine which unit of time best completes this statement. ... more>>

Monmouth Mountain Bikes - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 1. How many mountain bikes will have the highest level of safety testing? ... more>>

More Mowing Madness - George Miller and Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Where should Matt and Georgette change places to evenly split their "Matt-mowing" work? ... more>>

Movie Line Madness - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Determine what time it will be when Odysseus and Penelope finish taking care of their movie customers. ... more>>

Ms. Newton's Secret - Jeanne Fitzgerald
teacher support active problem Math Fundamentals, difficulty level 2. Can you discover the secret of Ms. Newton's age? ... more>>

Multiplication Mystery - Ya. I. Perelman (translated from Russian by Valentina Sokolskaya)
active problem Math Fundamentals, difficulty level 3. Decipher this cryptic multiplication problem to uncover the final product. ... more>>

Mystery Numbers - CanSchoolNet - revised
teacher support active problem Math Fundamentals, difficulty level 2. Fill in the missing numbers on an ancient scroll. ... more>>

Neighborhood Watch - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. Find out how many trips will be made around the neighborhood in this watch program. ... more>>

Nova Scotia Quilt - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 3. Use the area of a rectangular bed quilt to determine its dimensions. ... more>>

Nuts in a Bowl - Claire Mead
teacher support active problem Math Fundamentals, difficulty level 3. Determine how many nuts are in five bowls using the given clues. ... more>>

Odds vs. Evens - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 3. Can Jerome and Kiya use what they know about probability to make their games fair? ... more>>

Oh, Brother! - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 1. Aidan is how many days younger than T.J.? ... more>>

Peanut Butter and Jelly - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 3. How many sandwiches can we make before using up a package of bread and jars of jelly and peanut butter at the same time? ... more>>

Penny Space - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Determine the space needed to store a million pennies. ... more>>

The Place Value Game - Kristina Lasher
teacher support active problem Math Fundamentals, difficulty level 2. Help Sylvia and Carina think about winning numbers in the Place Value Game. ... more>>

Pondering Palindromes - Mary DeYoung & class
teacher support active problem Math Fundamentals, difficulty level 1. Explore 4-digit palindromes and find something else they have in common. ... more>>

Pondering Prescriptions - Lisa Lavelle
teacher support active problem Math Fundamentals, difficulty level 4. Help calculate the amount of antibiotic in each dose of my prescription. ... more>>

Presidential Timepieces - Mary DeYoung & class
teacher support active problem Math Fundamentals, difficulty level 4. Develop a sense of time by exploring presidential events. ... more>>

Price Tag Repair - Teaching the Young Learner Group
teacher support active problem Math Fundamentals, difficulty level 2. Can you use the clues to help Cathy repair the price tags for the family yard sale? ... more>>

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