Math Forum - Problems Library - Pre-Algebra, Measurement

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Pre-Algebra
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Pre-Algebra
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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 6-8

Access to these problems requires a Membership.

Accuracy Please - Judy Ann Brown
Pre-Algebra, difficulty level 3. Considering precision, accuracy, and appropriateness in finding the volume of a cone. ... more>>

At Least a Mile - Suzanne Alejandre
Pre-Algebra, difficulty level 2. How many runs do the Phillies have to score before the base runners have covered a certain distance? ... more>>

Baking Blackberries - Annie Fetter
Pre-Algebra, difficulty level 1. Which rectangular baking dish should I use? ... more>>

Balancing Mobiles - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile. ... more>>

The Big Picture! - Judy Ann Brown
Pre-Algebra, difficulty level 3. A picture is enlarged to four times its area. ... more>>

Box of Boxes - Suzanne Alejandre
Pre-Algebra, 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. ... more>>

Building a Snow Statue - Judy Ann Brown
Pre-Algebra, difficulty level 3. Determine the height of a snow statue using the given information. ... more>>

Building Fences - Judy Ann Brown
Pre-Algebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36-yard fence. ... more>>

Building on Water - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building. ... more>>

Buying Cola - Leon Roland & class
Pre-Algebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy? ... more>>

Caliyah's Cart - Lillian Ray
Pre-Algebra, difficulty level 4. How many items did Caliyah decide to buy at the store? ... more>>

Canadian Soccer - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps. ... more>>

Chirp! Chirp! - Annie Fetter
Pre-Algebra, difficulty level 3. Find the temperature when a cricket chirps a certain number of times a minute. ... more>>

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

Citius, Altius, Fortius - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Would record-holding speed skaters and runners break the speed limit in a residential zone? ... more>>

Coast to Coast Driving Costs - Suzanne and Richard Alejandre
Pre-Algebra, 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? ... more>>

Cork Costs - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Find reasonable prices for the different sizes of cork. ... more>>

The Cost of Chocolate - Suzanne Alejandre
Pre-Algebra, difficulty level 2. How can I get the most chocolate for my $30.00? ... more>>

Cyndy's Curtains - Cynthia Paul, Suzanne Alejandre, Annie Fetter
Pre-Algebra, difficulty level 2. How many sets of shorter curtains can Cyndy make from the one set of extra-long curtains that she already has? ... more>>

Days on Other Planets - Cynthia Lanius, Suzanne Alejandre
Pre-Algebra, difficulty level 2. How old in Earth years would you be after spending time on another planet? ... more>>

Distance Driving - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Dividing Daffodils - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Help us plant our garden of daffodils. ... more>>

Downhill All the Way - Judy Ann Brown
Pre-Algebra, 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? ... more>>

Downloading Duel - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Whose downloading task should take longer? ... more>>

Ducky Promenade - Leon Roland & class (poetry by Annie Fetter)
Pre-Algebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem. ... more>>

Fences for Fido and Friends - Annie Fetter
Pre-Algebra, difficulty level 2. Find the area of each rectangular dog pen. ... more>>

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. ... more>>

Garden Grove - Steve Risberg & Stephen Weimar
Pre-Algebra, 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. ... more>>

Gas Guzzlers - Mai Sidawi and Lillian Ray
Pre-Algebra, difficulty level 2. Students are asked to decide which car model to replace to get the most savings in gas costs. ... more>>

Gearing Up - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Think about and explain the relationship between three different-sized gears. ... more>>

Geo in Jeopardy - Richard Tchen
Pre-Algebra, difficulty level 3. Find the dimensions of the three-dimensional phone booth. ... more>>

Golfing Luck? - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Work with probability on the practice hole of the golf course. ... more>>

The Good Samaritan - Piedmont High School 2nd- and 7th-period Geometry Classes
Pre-Algebra, difficulty level 4. Can the butler afford the paint needed to repair the sign? Did the butler do it? ... more>>

Graphing for Area - Judy Ann Brown
Pre-Algebra, difficulty level 2. Graph six points and find the area of the resulting hexagon. ... more>>

A Happy New Year Wish - Suzanne Alejandre, Ian Underwood
Pre-Algebra, difficulty level 2. Explain how time differences are calculated and understood using longitude. ... more>>

He Ate It All! - Mr. Marthinsen's Geometry Class
Pre-Algebra, difficulty level 3. The professor ate an entire pizza in 28 minutes. Figure out the size of the pizza. ... more>>

Heavy Hoisting - Math Forum Staff
Pre-Algebra, difficulty level 2. Using the information given in the problem, find the weight of an average human adult. ... more>>

How Wide Is My Garden? - Judy Ann Brown
Pre-Algebra, difficulty level 3. A scale drawing is used to determine the width and area of a garden. ... more>>

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? ... more>>

I'm a Groundhog? - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Using Suzanne's height, Phil's height, and Suzanne's shadow length, find Phil's shadow length. ... more>>

Inching Along Down the Football Field - Terrel Trotter
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>>

Lee's Lawn Chair - Lee & Suzanne Alejandre
Pre-Algebra, difficulty level 3. Using the measurements given in the problem, determine the scale factor used to create the larger chair. ... more>>

Lincoln's Top Hat - Suzanne Alejandre
Pre-Algebra, 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. ... more>>

Lost in Des Moines - Judy Ann Brown
Pre-Algebra, difficulty level 2. Calculate the speed of a car using given information. ... more>>

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? ... more>>

Measuring a Mountain Bike - Annie Fetter
Pre-Algebra, difficulty level 3. Help Annie determine the circumference of her bike tire so that she can accurately set up her new cyclometer. ... more>>

Milk Madness - Suzanne Alejandre
Pre-Algebra, difficulty level 4. Help Georgina find out how much milk is left using the number pattern she describes. ... more>>

Mirror Musing - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Using the information given in a picture of Hagrid and Baby Norbert, find out how tall each of them is. ... more>>

New Home for Fibonacci and Fractal - Judy Ann Brown
Pre-Algebra, difficulty level 2. Determine how long it will take Jimal and Leslie to fill the new 15-gallon aquarium. ... more>>

The Nutty Squirrel - Alice Miller
Pre-Algebra, difficulty level 3. How high could a human jump if she could jump with the power of a squirrel? ... more>>

Office Tile Choice - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the total cost of purchasing tiles for my office. ... more>>

Olympic Temperature - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Partial Area - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the area of the portion of the circle that is not included inside the inscribed square. ... more>>

Peanut's Back Yard - Jonathan Bauer
Pre-Algebra, 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? ... more>>

Photo Wall - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Find the dimensions of the large poster. ... more>>

Pi Day - Let's Eat Cake! - Judy Ann Brown
Pre-Algebra, difficulty level 3. In honor of Pi Day we will be comparing the volumes of slices taken from round and rectangular cakes. ... more>>

Pi Day Treats - Judy Ann Brown
Pre-Algebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration. ... more>>

Pizza Pie - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Pouring the Punch - Neil Bress
Pre-Algebra, difficulty level 3. The Refreshments Committee needs to pour exactly four liters of eggnog using only three-liter and five-liter measures. ... more>>

Power Outage - Jackson Geometry Class
Pre-Algebra, 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. ... more>>

Practicing for the Winter Olympics - Cynthia Paul
Pre-Algebra, difficulty level 2. What is the length of the semicircular path Sonya skates across the ice rink? ... more>>

Price Fluidity - Judy Ann Brown
Pre-Algebra, difficulty level 2. Compare the per-gallon cost of eleven different liquids, and put them in order from least to most expensive. ... more>>

Quilting Squares - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design. ... more>>

A Quilt Made of Squares - Annie Fetter
Pre-Algebra, difficulty level 3. Using the information given, will the finished quilt be in the shape of a square? ... more>>

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. ... more>>

Sailing Around the World - Leon Roland & class
Pre-Algebra, difficulty level 2. Determine the amounts of the supplies that Giuseppi Linguini will need to sail around the world. ... more>>

Saturday Bike Ride - Judy Ann Brown
Pre-Algebra, 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. ... more>>

Seesaw - Suzanne Alejandre
Pre-Algebra, difficulty level 3. How did the four friends balance on the seesaw? ... more>>

Shine On Harvest Moon - Judy Ann Brown
Pre-Algebra, difficulty level 2. Find the area of the largest circle that can be cut from a nine-inch by twelve-inch sheet of paper. ... more>>

The Silver Mile - Judy Ann Brown
Pre-Algebra, difficulty level 3. Determine the total value of the coins in a silver mile. ... more>>

Sizing Up Sequoias - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Compared to a given seed weight, find out how much an average mature sequoia weighs. ... more>>

Spring Garden Planning - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find the area as well as the length and width of my fractional garden. ... more>>

Stacking Wood - Annie Fetter
Pre-Algebra, difficulty level 2. Find how many cords of wood the woodshed will hold. ... more>>

A Stellar Garden - Bill Marthinsen
Pre-Algebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden. ... more>>

A Surfer's Tessellation - Mr. Marthinsen's First Period Class
Pre-Algebra, difficulty level 2. Shane is re-tiling his surf shack. How many of each kind of tile will he need, and what does a big tile cost? ... more>>

Tasty Tomato Salsa - Suzanne Alejandre
Pre-Algebra, 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? ... more>>

Temperature Change - Judy Ann Brown
Pre-Algebra, difficulty level 2. Use the given information to find the temperature. ... more>>

Thanksgiving Travel - Suzanne Alejandre & Maria Fung and her students
Pre-Algebra, difficulty level 3. Help Zach decide whether to take the PA Turnpike or the scenic route to see his parents for Thanksgiving. ... more>>

The World's Largest Popcorn Ball* - Annie Fetter
Pre-Algebra, difficulty level 1. How many boxes of microwave popcorn would it take to make a giant popcorn ball? ... more>>

Three-dimensional Television - Mr. Marthinsen's Geometry Class
Pre-Algebra, difficulty level 3. Help my friend find which TV will fit snugly into her TV nook. ... more>>

Tiling Tables - Suzanne Alejandre
Pre-Algebra, 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. ... more>>

Tiling Triangles - Suzanne Alejandre
Pre-Algebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it. ... more>>

Train Timetable - Suzanne Alejandre
Pre-Algebra, difficulty level 1. What is the minimum amount of time I can spend on the train commuting to and from work in one week? ... more>>

Train Travel - Annie Fetter & Ian Underwood
Pre-Algebra, difficulty level 2. At what time does the end of the train emerge from the tunnel? ... more>>

Valley Springs Snow Cream - Kelly Crisp
Pre-Algebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream. ... more>>

Val's Value - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Who has paid more for their jackets, Amir or Val? ... more>>

Volume Experiment - Judy Ann Brown
Math Fundamentals, difficulty level 2. Make a prediction, conduct an experiment, and report your findings. ... more>>

Watch Where You Step! - Suzanne Alejandre
Pre-Algebra, difficulty level 2. Using statistics about slugs, about how many might be in a certain sized yard? ... more>>

Wilda's Swamp Water - Judy Ann Brown
Pre-Algebra, difficulty level 3. Measure 8 quibits of swamp water using only 6-quibit and 10-quibit containers. ... more>>

Women's Walkway - Suzanne Alejandre
Pre-Algebra, difficulty level 2. How many bricks would it take to cover the full area of the pattern sample? What's the area? ... more>>

Wondering about Water - Annie Fetter
Pre-Algebra, difficulty level 3. Find the surface area of an Olympic-size ice hockey rink. ... more>>

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