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parts of wholes
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Parts of Wholes

The problems in this category build on a developing understanding of fractions, decimals, and percentages as parts of unit wholes, parts of a collection, locations on the number line, and as divisions of whole numbers. Problems may require understanding the effects of arithmetic operations on these numbers, as well as understanding the relationship between them.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 4: Fractions
Math 4: Percentages
The closest match in our Ask Dr. Math archives:
Elementary Fractions/Decimals
NCTM Standards:
Number and Operations Standard for Grades 35
Access to these problems requires a Membership.

Across Wisconsin
 Jo Wenzler

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 twoweek problem.
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A Pound of Tea
 Claire Mead

Math Fundamentals, difficulty level 3. Find out how long a pound of tea would last Hazel if she were alone.
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BacktoSchool Shopping
 Judy Ann Brown

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?
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Backtoschool Supplies
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Help calculate the total bill for these backtoschool supplies.
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Baseball Trivia
 Judy Ann Brown

Math Fundamentals, difficulty level 2. How many runs do the Phillies have to score before the base runners have covered a mile?
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Birthday Beach Bash
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Help determine how many balloons were needed for party favors at the end of this celebration.
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Birthday Pictures
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Join Ms. Juncos's fourthgrade team in a comparison of seasons of birthdays.
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Birthday Trip
 Kristina Lasher

Math Fundamentals, difficulty level 3. Just how far is the trip to Aunt Mazie's house?
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Building Barns *
 Claire Mead

Math Fundamentals, difficulty level 3. How long will it take Amy's crew to build a barn?
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Building the Fence
 Steve Risberg & Kristina Lasher

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?
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California Dreaming
 Judy Ann Brown

Math Fundamentals, difficulty level 3. Determine the length of time that will be needed to drive from Allentown, Pennsylvania, to Los Angeles, California.
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Campers' Cider
 Elizabeth Gardner (Western Oregon University) & Math Forum Staff

Math Fundamentals, difficulty level 2. How much cider did the campers press for the evening festivities?
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Catching Up!
 Kristina Lasher

Math Fundamentals, difficulty level 3. Marika is catching up to her father's age. How can that be?
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Cat Walk
 Math Olympiad Problem (revised)

Elementary, difficulty level 2. Using the ratio of dog steps to cat steps and the length of a dog step, calculate the number of feet a cat walks in 24 steps.
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Change You Can't Count On
 Claire Mead

Math Fundamentals, difficulty level 2. What is the greatest amount of money I can have in my pocket?
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Charlene Goes Shopping
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Charlene needs to add some items to her winter collection. Help her determine where she should shop.
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Circles Around
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Use this exploration problem to discover the relation between circumference and diameter.
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Common Cents
 Claire Mead

Math Fundamentals, difficulty level 2. How much money do Monique and Misty each contribute toward Mom's Valentine's candy?
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Count the Discount
 Kristina Lasher

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?
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Dad's Cookies
 Diane Anderson's Teaching the Young Learner Class

Math Fundamentals, difficulty level 3. Figure out how many cookies Dad baked for the family before they ate them all!
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Filling Beauty's Seats
 Kristina Lasher and Claire Mead

Math Fundamentals, difficulty level 3. Use fractions to find out how many seats are still available for the
school play and how
much money the show will earn.
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Filling the Freezer
 Kristina Lasher

Math Fundamentals, difficulty level 4. How many cartons of ice cream can the Math Club fit in their freezer?
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Fish in a Barrel
 Claire Mead

Math Fundamentals, difficulty level 3. Find out how many fish Jake, Herman and Luke each took home from their
fishing trip.
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Flying Time Zones
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Help me figure out what time my watch should show when I land in Denver.
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Frugal Freeda
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Help Freeda decide which store has the best buy.
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Garden Fresh Fruit
 Shrawan Khanna's Ninth Grade Class

Math Fundamentals, difficulty level 4. Help the poor farmer predict his revenue (if he can sell all his fruit).
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Giving with Grapefruit
 Lisa Lavelle & Western Oregon University Students

Math Fundamentals, difficulty level 1. How much will Cassie help raise for charity?
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Good Fences
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Design a fence that will keep the animals happy.
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Greta's Garden
 Claire Mead

Math Fundamentals, difficulty level 2. Find out how much money Greta made from each of her vegetables at the
Farmers's Market.
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Holiday Shopping and Surfing
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Help Charlene calculate the change she'll have left for holiday card supplies after she completes her online shopping.
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Horton's Clover Hunt
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Find out how fast Horton had to work picking clovers.
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How Many Actors?
 Kristina Lasher and Lisa Lavelle

Math Fundamentals, difficulty level 3. Can you help the director of the spring musical check to see if Madera spoke with each actor about costumes?
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How Old is Dad?
 Claire Mead

Math Fundamentals, difficulty level 2. Use the clues to find out how old Dad is.
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How Old is Mia?
 Claire Mead

Math Fundamentals, difficulty level 3. Use Mia's clues to find how old she is.
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How Old is Santa Claus?
 Claire Mead

Math Fundamentals, difficulty level 4. Use your knowledge of fractions to discover how old Santa is.
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Inching Along Down the Football Field
 Terrel Trotter

Math Fundamentals, difficulty level 3. Fred put his football down on a goal line of the 100yard field. He then moved it forward half the field distance, over and over again. When did the distance first become less than one inch?
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Irish Specials
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Calculate the final bill for our St. Patrick's Day dinner last week.
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Is There Really a Discount?
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Determine which friend is correct about the final price on a sales item.
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A Jar of Coins
 Claire Mead

Math Fundamentals, difficulty level 2. Use fraction clues to discover how many pennies, nickels, dimes and quarters I have in my
jar.
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Jellybean Fractions
 Lisa Lavelle

Elementary, difficulty level 2. Determine good and bad choices in playing the Jellybean Fractions Game.
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Jumping Rope
 Leon Roland & class

Math Fundamentals, difficulty level 2. Just how long was the rope with which we started?
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Lost in Space
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Figure out how big an error the engineers made when they mixed up their units.
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The Mad Hatter's Gone!
 Leanne Gater

Math Fundamentals, difficulty level 4. Explore a coordinate plane and help the Cheshire Cat find his favorite cheese.
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Math Club Lollipop Profits
 Judy Ann Brown

Math Fundamentals, difficulty level 3. The Math Club plans to sell lollipops. Help them to calculate their profit.
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Meters of Money
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Help Ms. Juncos's class determine the amount of money they will raise with this metric project.
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More Balloons
 Lisa Lavelle

Math Fundamentals, difficulty level 5. Here's a more difficult problem based on our balloon color preferences.
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More Recess
 Kristina Lasher

Math Fundamentals, difficulty level 3. Camilla checks out a kickball while Patrick brings his handball. How
much more recess does Patrick save?
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PennyPinching Pretzel Company
 Kristina Lasher

Math Fundamentals, difficulty level 2. If a pretzel company reduces the amount of pretzels in a bag by 25%
and then later increases that new amount by 25%, do the changes break
even?
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Penny Space
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Determine the space needed to store a million pennies.
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Pizza Dough
 Claire Mead

Math Fundamentals, difficulty level 2. How much water does Mario need to use to make enough pizza dough for
him and his
friends?
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Pondering Prescriptions
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Help calculate the amount of antibiotic in each dose of my prescription.
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Pumpkin Pride
 Claire Mead

Math Fundamentals, difficulty level 2. Find the mean average diameter of jacko'lanterns lined up on planks
and also the number
of miles the planks would cover if laid end to end.
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Raisin Nut Cookies
 Marsha May

Math Fundamentals, difficulty level 4. Sarah needs to convert her cookie recipe for her cousin.
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School, Who Has Time?
 Lisa Lavelle (old remembered puzzle)

Math Fundamentals, difficulty level 3. Given all the time we spend doing other things, how do we have time for school?
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Sharing Smelt
 Claire Mead

Math Fundamentals, difficulty level 3. Find out how many smelt Larry caught Saturday morning.
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Sheila's Shelves
 Claire Mead

Math Fundamentals, difficulty level 2. How much space will Sheila have on her new book shelves?
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Sprinkler Spray
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Compare the radii of three sprinklers in Lily's garden.
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Stained Glass Window
 Jackson First Year Algebra Class

Elementary, difficulty level 5. Find the size of a stained glass window for my front door.
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Subway Subtotals
 Kristina Lasher

Math Fundamentals, difficulty level 2. When people ride the subway, they can pay with money, tokens, or transit cards. How did the people in my subway car pay their fare this morning?
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Subway Tokens
 Annie Fetter and Claire Mead

Math Fundamentals, difficulty level 2. How did Samantha know the subway token machine didn't behave as advertised?
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Summer at Sweet Tooth
 Ross Shelter & Carrie Shankweiler

Math Fundamentals, difficulty level 2. Calculate Kate's earnings during her summer waitressing job.
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Super Deal Salsa
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Determine how much money was saved by buying salsa in bulk.
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Timber!!!
 Lisa and Judy Gardner

Math Fundamentals, difficulty level 3. Determine the lengths of two pieces of a damaged redwood tree.
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Toys To Go
 Claire Mead

Math Fundamentals, difficulty level 2. Help Sam determine the sale price of scooters at the toy store.
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The Twelve Percents of Christmas
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Calculate the percentages of the total gifts received on each of the twelve days of Christmas.
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Video Viewing
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Just how much television will Frank and Lisa watch?
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Water Park Adventure
 Leon Roland & class

Math Fundamentals, difficulty level 2. How much does each member of the class need to earn to fund the field trip?
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What a Move!
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Determine the number of hours it took the movers to move the Lavelles to their new home, as well as the number of manhours.
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What Percentage?
 Claire Mead

Math Fundamentals, difficulty level 4. Students are asked to find the percentage of numbers from 1 to 100
which meet several
given criteria.
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Wheels R Us
 Claire Mead

Math Fundamentals, difficulty level 2. How many bicycles does Danielle have in her cycle shop?
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