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Measurement

Problems in this category expect students to use metric or customary systems of measurement, understand relations among units, and be able to convert between units and/or systems of measurement. They may require measuring angles, perimeter, area, surface area, volume, time, temperature or weight.
Some of these problems are also in the following subcategories:
 Related Resources

Interactive resources from our Math Tools project:
Math 7: Measurement
The closest match in our Ask Dr. Math archives:
Middle School: Measurement
NCTM Standards:
Measurement Standard for Grades 68
Access to these problems requires a Membership.

Accuracy Please
 Judy Ann Brown

PreAlgebra, difficulty level 3. Considering precision, accuracy, and appropriateness in finding the volume of a cone.
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At Least a Mile
 Suzanne Alejandre

PreAlgebra, difficulty level 2. How many runs do the Phillies have to score before the base runners have covered a certain distance?
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Baking Blackberries
 Annie Fetter

PreAlgebra, difficulty level 1. Which rectangular baking dish should I use?
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Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
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The Big Picture!
 Judy Ann Brown

PreAlgebra, difficulty level 3. A picture is enlarged to four times its area.
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Box of Boxes
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Given information about the surface area, find the dimensions of the
large box. Also, find
how many small boxes fit inside the large box.
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Building a Snow Statue
 Judy Ann Brown

PreAlgebra, difficulty level 3. Determine the height of a snow statue using the given information.
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Building Fences
 Judy Ann Brown

PreAlgebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36yard fence.
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Building on Water
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building.
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Buying Cola
 Leon Roland & class

PreAlgebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy?
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Caliyah's Cart
 Lillian Ray

PreAlgebra, difficulty level 4. How many items did Caliyah decide to buy at the store?
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Canadian Soccer
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps.
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Chirp! Chirp!
 Annie Fetter

PreAlgebra, difficulty level 3. Find the temperature when a cricket chirps a certain number of times a minute.
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Chocolate, Orange, Megamint Swirl
 Fitzgerald's Spring 2000 Class C

PreAlgebra, difficulty level 4. How many halfgallon cartons of ice cream can fit in the freezer?
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Citius, Altius, Fortius
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Would recordholding speed skaters and runners break the speed limit in a residential zone?
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Coast to Coast Driving Costs
 Suzanne and Richard Alejandre

PreAlgebra, difficulty level 2. If the price of gas has increased 61% in the five years since we took
our first coast to coast
trip in October 2000, what would it cost per mile to make the same
trip in October of 2005?
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Cork Costs
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Find reasonable prices for the different sizes of cork.
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The Cost of Chocolate
 Suzanne Alejandre

PreAlgebra, difficulty level 2. How can I get the most chocolate for my $30.00?
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Cyndy's Curtains
 Cynthia Paul, Suzanne Alejandre, Annie Fetter

PreAlgebra, difficulty level 2. How many sets of shorter curtains can Cyndy make from the one set of
extralong curtains
that she already has?
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Days on Other Planets
 Cynthia Lanius, Suzanne Alejandre

PreAlgebra, difficulty level 2. How old in Earth years would you be after spending time on another planet?
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Distance Driving
 Judy Ann Brown

PreAlgebra, difficulty level 3. Write an expression that will help you determine how long it will take the car to travel any given number of kilometers.
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Dividing Daffodils
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Help us plant our garden of daffodils.
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Downhill All the Way
 Judy Ann Brown

PreAlgebra, difficulty level 2. Starting at 10,000 feet above sea level, descending a 6% grade followed by a 4% grade will put a car how many feet above sea level?
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Downloading Duel
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Whose downloading task should take longer?
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Ducky Promenade
 Leon Roland & class (poetry by Annie Fetter)

PreAlgebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem.
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Fences for Fido and Friends
 Annie Fetter

PreAlgebra, difficulty level 2. Find the area of each rectangular dog pen.
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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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Garden Grove
 Steve Risberg & Stephen Weimar

PreAlgebra, difficulty level 3. Determine the amount of dirt and the amount of peat moss needed to have the correct ratio of dirt to peat moss for the garden.
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Gas Guzzlers
 Mai Sidawi and Lillian Ray

PreAlgebra, difficulty level 2. Students are asked to decide which car model to replace to get the
most savings in gas costs.
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Gearing Up
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Think about and explain the relationship between three differentsized gears.
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Geo in Jeopardy
 Richard Tchen

PreAlgebra, difficulty level 3. Find the dimensions of the threedimensional phone booth.
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Golfing Luck?
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Work with probability on the practice hole of the golf course.
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The Good Samaritan
 Piedmont High School 2nd and 7thperiod Geometry Classes

PreAlgebra, difficulty level 4. Can the butler afford the paint needed to repair the sign? Did the butler do it?
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Graphing for Area
 Judy Ann Brown

PreAlgebra, difficulty level 2. Graph six points and find the area of the resulting hexagon.
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A Happy New Year Wish
 Suzanne Alejandre, Ian Underwood

PreAlgebra, difficulty level 2. Explain how time differences are calculated and understood using
longitude.
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He Ate It All!
 Mr. Marthinsen's Geometry Class

PreAlgebra, difficulty level 3. The professor ate an entire pizza in 28 minutes. Figure out the size of the pizza.
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Heavy Hoisting
 Math Forum Staff

PreAlgebra, difficulty level 2. Using the information given in the problem, find the weight of an
average human adult.
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How Wide Is My Garden?
 Judy Ann Brown

PreAlgebra, difficulty level 3. A scale drawing is used to determine the width and area of a 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'm a Groundhog?
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Using Suzanne's height, Phil's height, and Suzanne's shadow length, find Phil's shadow length.
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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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Lee's Lawn Chair
 Lee & Suzanne Alejandre

PreAlgebra, difficulty level 3. Using the measurements given in the problem, determine the scale
factor used to create the larger chair.
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Lincoln's Top Hat
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Find the dimensions of a rectangular sheet of paper used to make a paper top hat that has width and height the same.
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Lost in Des Moines
 Judy Ann Brown

PreAlgebra, difficulty level 2. Calculate the speed of a car using given information.
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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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Measuring a Mountain Bike
 Annie Fetter

PreAlgebra, difficulty level 3. Help Annie determine the circumference of her bike tire so that she
can accurately set up her
new cyclometer.
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Milk Madness
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes.
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Mirror Musing
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is.
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New Home for Fibonacci and Fractal
 Judy Ann Brown

PreAlgebra, difficulty level 2. Determine how long it will take Jimal and Leslie to fill the new 15gallon aquarium.
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The Nutty Squirrel
 Alice Miller

PreAlgebra, difficulty level 3. How high could a human jump if she could jump with the power of a squirrel?
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Office Tile Choice
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the total cost of purchasing tiles for my office.
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Olympic Temperature
 Judy Ann Brown

PreAlgebra, difficulty level 3. Compare the difference in temperatures between Sydney, Australia at 14 degrees Celsius and Swarthmore, Pennsylvania, U.S.A. at 63 degrees Fahrenheit.
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Partial Area
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square.
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Peanut's Back Yard
 Jonathan Bauer

PreAlgebra, difficulty level 3. Peanut, the overexcited dog, makes 40 laps around a stake and travels a total distance of 1 mile. If his bowl of water is 20 feet away from the stake, can he get a drink?
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Photo Wall
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Find the dimensions of the large poster.
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Pi Day  Let's Eat Cake!
 Judy Ann Brown

PreAlgebra, difficulty level 3. In honor of Pi Day we will be comparing the volumes of slices taken from round and rectangular cakes.
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Pi Day Treats
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration.
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Pizza Pie
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use the given information to decide how many slices of the small pizza would be equal to or greater than 3 slices from the large pizza.
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Pouring the Punch
 Neil Bress

PreAlgebra, difficulty level 3. The Refreshments Committee needs to pour exactly four liters of eggnog using only threeliter and fiveliter measures.
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Power Outage
 Jackson Geometry Class

PreAlgebra, difficulty level 3. The power went out. Use the current reading on the clocks to determine when the power went out, and for how long.
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Practicing for the Winter Olympics
 Cynthia Paul

PreAlgebra, difficulty level 2. What is the length of the semicircular path Sonya skates across the
ice rink?
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Price Fluidity
 Judy Ann Brown

PreAlgebra, difficulty level 2. Compare the pergallon cost of eleven different liquids, and put them in order from least to most expensive.
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Quilting Squares
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design.
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A Quilt Made of Squares
 Annie Fetter

PreAlgebra, difficulty level 3. Using the information given, will the finished quilt be in the shape of a
square?
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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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Sailing Around the World
 Leon Roland & class

PreAlgebra, difficulty level 2. Determine the amounts of the supplies that Giuseppi Linguini will need to sail around the world.
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Saturday Bike Ride
 Judy Ann Brown

PreAlgebra, difficulty level 2. Now that spring has arrived, Ali and Maya decide to dust off their bikes and go for a Saturday ride. Help find what time they will meet.
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Seesaw
 Suzanne Alejandre

PreAlgebra, difficulty level 3. How did the four friends balance on the seesaw?
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Shine On Harvest Moon
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the area of the largest circle that can be cut from a nineinch by twelveinch sheet of paper.
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The Silver Mile
 Judy Ann Brown

PreAlgebra, difficulty level 3. Determine the total value of the coins in a silver mile.
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Sizing Up Sequoias
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Compared to a given seed weight, find out how much an average mature sequoia weighs.
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Spring Garden Planning
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find the area as well as the length and width of my fractional garden.
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Stacking Wood
 Annie Fetter

PreAlgebra, difficulty level 2. Find how many cords of wood the woodshed will hold.
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A Stellar Garden
 Bill Marthinsen

PreAlgebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden.
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A Surfer's Tessellation
 Mr. Marthinsen's First Period Class

PreAlgebra, difficulty level 2. Shane is retiling his surf shack. How many of each kind of tile will he need, and what does a big tile cost?
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Tasty Tomato Salsa
 Suzanne Alejandre

PreAlgebra, difficulty level 2. If I use all of the olives, how many grams of tomatoes should I use to
keep the same proportions in my salsa recipe?
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Temperature Change
 Judy Ann Brown

PreAlgebra, difficulty level 2. Use the given information to find the temperature.
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Thanksgiving Travel
 Suzanne Alejandre & Maria Fung and her students

PreAlgebra, difficulty level 3. Help Zach decide whether to take the PA Turnpike or the scenic route to see his parents for Thanksgiving.
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The World's Largest Popcorn Ball*
 Annie Fetter

PreAlgebra, difficulty level 1. How many boxes of microwave popcorn would it take to make a giant
popcorn ball?
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Threedimensional Television
 Mr. Marthinsen's Geometry Class

PreAlgebra, difficulty level 3. Help my friend find which TV will fit snugly into her TV nook.
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Tiling Tables
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Find a method to quickly calculate the dimensions of a rectangular table top with a given area so that it has the smallest possible perimeter.
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Tiling Triangles
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it.
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Train Timetable
 Suzanne Alejandre

PreAlgebra, difficulty level 1. What is the minimum amount of time I can spend on the train commuting
to and from work in one week?
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Train Travel
 Annie Fetter & Ian Underwood

PreAlgebra, difficulty level 2. At what time does the end of the train emerge from the tunnel?
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Valley Springs Snow Cream
 Kelly Crisp

PreAlgebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream.
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Val's Value
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Who has paid more for their jackets, Amir or Val?
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Volume Experiment
 Judy Ann Brown

Math Fundamentals, difficulty level 2. Make a prediction, conduct an experiment, and report your findings.
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Watch Where You Step!
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Using statistics about slugs, about how many might be in a certain sized yard?
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Wilda's Swamp Water
 Judy Ann Brown

PreAlgebra, difficulty level 3. Measure 8 quibits of swamp water using only 6quibit and 10quibit containers.
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Women's Walkway
 Suzanne Alejandre

PreAlgebra, difficulty level 2. How many bricks would it take to cover the full area of the pattern
sample? What's the
area?
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Wondering about Water
 Annie Fetter

PreAlgebra, difficulty level 3. Find the surface area of an Olympicsize ice hockey rink.
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