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Measurement/Units

These problems require students to manipulate and calculate different types of measurements. They include geometric measurements, as well as the concepts of money and time.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 4: Measurement
The closest match in our Ask Dr. Math archives:
Elementary Measurement
NCTM Standards:
Measurement Standard for Grades 35
Access to these problems requires a Membership.

Across the Netherlands
 Maggie HosMcGrane

Math Fundamentals, difficulty level 5. Help sort out this bike trip through the Netherlands (requires a bit of map reading). Initially a twoweek problem.
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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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After School Snacks
 Claire Mead

Math Fundamentals, difficulty level 3. How much money is Shawn spending on after school snacks? How long will
it take him to
save enough for a new calculator?
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Aidan's Millimeter Measurements
 Lisa Lavelle

Math Fundamentals, difficulty level 1. Calculate Aidan's height and age based on his wellbaby measurements at the doctor's office.
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All Aboard!
 Claire Mead

Math Fundamentals, difficulty level 3. How long will Sasha's train trip from Washington to Chicago take?
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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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At the Movies
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Explore the changes in movie and theater prices.
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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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The Big Balloon Blowup
 Leon Roland & class

Math Fundamentals, difficulty level 3. Help Ulrike and Lars determine the number of balloons in each bag.
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Birthday Probability
 Kristina Lasher & Lisa Lavelle

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?
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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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Bunches of Basil
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Determine the maximum number of basil plants I will have after I finish thinning the garden.
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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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Can You Drink That Swimming Pool?
 Kristina Lasher

Math Fundamentals, difficulty level 3. Estimating the amount of water in a pool. About how long would it take
to drink that much water?
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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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Choose Your Challenge
 Kristina Lasher

Math Fundamentals, difficulty level 2. Can Zak find a more precise measure of how much older his brother is than he is?
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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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Clock Work
 Claire Mead

Math Fundamentals, difficulty level 2. How did Maria and Sammy arrange their pencils on the clock face?
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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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Cubic Changes
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Determine how the volume and surface area of a cube change when the edge length is changed.
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Cupcakes, Cupcakes!
 Kristina Lasher & Terry Trotter

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?
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Dragons and Tigers and Hares, Oh My!
 Claire Mead

Math Fundamentals, difficulty level 3. Use clues about the Chinese calendar to determine when Lin's greatgrandfather was born
and how old he is.
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Driving Decisions
 Kristina Lasher

Math Fundamentals, difficulty level 4. Help the Downings decide which car rental is the best option for their trip to Denver.
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Elevator Weighin
 Kristina Lasher

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?
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The Farmer in the Dilemma
 Claire Mead

Math Fundamentals, difficulty level 3. Help Farmer Mead spend exactly $100 buying exactly 100 sheep, cows and
horses.
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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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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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Football Fanfare
 Suzanne Alejandre and Kristina Lasher

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?
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Four Dates
 Claire Mead

Math Fundamentals, difficulty level 2. Anthony explores number patterns on a calendar.
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Frequent Flier Figuring
 Judy Ann Brown

Math Fundamentals, difficulty level 2. Use Web resources to help plan the shortest route from Allentown, Pennsylvania, to New Orleans, Louisiana.
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Frog Farming
 Claire Mead

Math Fundamentals, difficulty level 2. Help Farmer Mead build a rectangular pen that holds the greatest
number of frogs.
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Frugal Flooring
 Marita Paynter

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.
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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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Funny Money
 Lisa Lavelle (adapted)

Math Fundamentals, difficulty level 2. Determine the amount of money Divya has in her bank.
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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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Georg Tricks the Troll
 Terry Trotter

Elementary, difficulty level 3. Georg decides to tangle with the troll and see if he can make some money.
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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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Golden Gate Bridge *
 Claire Mead

Math Fundamentals, difficulty level 2. Find out how much wire was used in the two main cables of the Golden
Gate Bridge.
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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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Hauling Sand
 Claire Mead

Math Fundamentals, difficulty level 2. How many tons of sand can Marty haul in his dump truck?
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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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Horsin' Around
 Claire Mead

Math Fundamentals, difficulty level 2. How long does it take Zachary to complete his journey on horseback and
on foot?
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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 Does Your Garden Grow?
 Team 7 Red Math Students  Highland Middle School

Elementary, difficulty level 4. Help the HMS students find out how many ways they can arrange their schoolyard garden.
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I Get A Kick Out Of Soccer!
 Judy Ann Brown

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?
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I Like to Palindrive!
 Kristina Lasher

Math Fundamentals, difficulty level 3. How many palindromic numbers will appear on Kristina's odometer in October, 2003?
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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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It's Summer in Melbourne
 Claire Mead

Math Fundamentals, difficulty level 2. How many hours of sunlight does Melbourne, Australia, have on its
longest day of the year?
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Jason's Piggy Bank
 Claire Mead

Math Fundamentals, difficulty level 2. How many nickels did Jason find in his piggy bank?
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Jellybean Rectangles
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Have fun figuring out strategy in the Jellybean Rectangle 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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A Larger Garden
 Kristina Lasher

Math Fundamentals, difficulty level 2. Can you increase the area of a garden but use less fencing to protect
it from the deer?
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LawnMowing Chore
 Judy Ann Brown

Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow.
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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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Lucky Lettuce Land
 Kainoa Trotter, et al.

Math Fundamentals, difficulty level 3. Help Farmer Lucky fence his lettuce land.
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Lunch Bunch Budgets
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Determine the number of children needed for the lunch bunch budget to balance.
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Luscious Lemonade
 Judy Ann Brown

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?
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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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A Million in Time
 Lisa Lavelle

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.
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MiniMall Measurements
 Claire Mead

Math Fundamentals, difficulty level 2. Use given measurements of the stores in the minimall to find the area
and dimensions of
other stores.
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Moons, by Jove!
 Claire Mead

Math Fundamentals, difficulty level 3. Find out how long it will take these 3 moons to return to a position
of alignment with their
planet.
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More Mowing Madness
 George Miller and Lisa Lavelle

Math Fundamentals, difficulty level 4. Where should Matt and Georgette change places to evenly split their "Mattmowing" work?
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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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Movie Line Madness
 Lisa Lavelle

Math Fundamentals, difficulty level 4. Determine what time it will be when Odysseus and Penelope finish taking care of their movie customers.
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Mowing Madness
 George Miller and Lisa Lavelle

Math Fundamentals, difficulty level 2. Using a special "Mattmowing" technique, find the dimensions of the last rectangle to be mowed in a 48 ft. by 64 ft. yard.
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Mr. W. Goes Across Australia
 Lisa Lavelle

Math Fundamentals, difficulty level 5. 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).
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Neighborhood Watch
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Find out how many trips will be made around the neighborhood in this watch program.
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Nova Scotia Quilt
 Claire Mead

Math Fundamentals, difficulty level 3. Use the area of a rectangular bed quilt to determine its dimensions.
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Odd (and Even) Dates
 Lisa Lavelle

Math Fundamentals, difficulty level 1. Can you figure out these curious dates?
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Oh, Brother!
 Lisa Lavelle

Math Fundamentals, difficulty level 1. Aidan is how many days younger than T.J.?
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Pauline the Plumber
 Claire Mead

Math Fundamentals, difficulty level 2. Use the clues to find out how many widgets Pauline purchased.
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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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Pig Pens
 Claire Mead

Math Fundamentals, difficulty level 2. Find the rectangle of least perimeter which encloses 36 sq meters of area.
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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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Pocket Change
 Claire Mead

Math Fundamentals, difficulty level 1. How many dimes do I have in my pocket?
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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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Pooling Tips
 Claire Mead

Math Fundamentals, difficulty level 2. How much should Fran and Gloria each give Ethan so that they all have an equal amount?
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Presidential Timepieces
 Mary DeYoung & class

Math Fundamentals, difficulty level 4. Develop a sense of time by exploring presidential events.
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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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Pushing Pennies
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Estimate the number of pennies that you can fit on a sheet of paper, then evaluate your estimate.
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Puzzling Puzzle Pieces
 Lisa Lavelle

Math Fundamentals, difficulty level 2. Explore the ways 108 puzzle pieces can be arranged.
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Rabbit's Run
 Lisa Lavelle

Math Fundamentals, difficulty level 1. Help Regina develop options for building her rabbit's run.
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Railroad Crossing
 Lisa Lavelle

Math Fundamentals, difficulty level 3. Determine how far apart Division Junction and Logarithm Square are, based on the time Emily and Edward Engineer cross paths.
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Rounding Mountains
 Judy Ann Brown

Math Fundamentals, difficulty level 2. Use estimated figures to determine the maximum and minimum differences between the heights of two mountains.
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Sacagawea Cheerios
 Stephen Maurer

Math Fundamentals, difficulty level 3. Determine how many Sacagawea coins the government will give away during this Cheerios promotion.
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School Spirit
 Kristina Lasher

Math Fundamentals, difficulty level 1. Do a little estimating to determine how much money is needed to buy school spirit items.
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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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