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Pre-Algebra
Problems
Pre-Algebra
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Measurement
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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
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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.
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Accuracy Please
- Judy Ann Brown
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 1. Which rectangular baking dish should I use?
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Balancing Mobiles
- Suzanne Alejandre
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. A picture is enlarged to four times its area.
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Box of Boxes
- Suzanne Alejandre
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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.
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Building a Snow Statue
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Determine the height of a snow statue using the given information.
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Building Fences
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36-yard fence.
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Building on Water
- Judy Ann Brown
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 4. How many items did Caliyah decide to buy at the store?
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Canadian Soccer
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps.
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Chirp! Chirp!
- Annie Fetter
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Pre-Algebra, difficulty level 3. Find the temperature when a cricket chirps a certain number of times a minute.
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Chocolate, Orange, Mega-mint Swirl
- Fitzgerald's Spring 2000 Class C
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Pre-Algebra, difficulty level 4. How many half-gallon cartons of ice cream can fit in the freezer?
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Citius, Altius, Fortius
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Would record-holding 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
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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?
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Cork Costs
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Find reasonable prices for the different sizes of cork.
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The Cost of Chocolate
- Suzanne Alejandre
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Pre-Algebra, 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
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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?
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Days on Other Planets
- Cynthia Lanius, Suzanne Alejandre
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Pre-Algebra, 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
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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.
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Dividing Daffodils
- Suzanne Alejandre
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Pre-Algebra, difficulty level 4. Help us plant our garden of daffodils.
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Downhill All the Way
- Judy Ann Brown
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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?
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Downloading Duel
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Whose downloading task should take longer?
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Ducky Promenade
- Leon Roland & class (poetry by Annie Fetter)
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 2. Find the area of each rectangular dog pen.
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Frequent Flier Figuring
- Judy Ann Brown
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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
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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.
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Gas Guzzlers
- Mai Sidawi and Lillian Ray
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Think about and explain the relationship between three different-sized gears.
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Geo in Jeopardy
- Richard Tchen
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Pre-Algebra, difficulty level 3. Find the dimensions of the three-dimensional phone booth.
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Golfing Luck?
- Suzanne Alejandre
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Pre-Algebra, 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 7th-period Geometry Classes
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, 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
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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
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Pre-Algebra, 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
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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?
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Lee's Lawn Chair
- Lee & Suzanne Alejandre
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Pre-Algebra, 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
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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.
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Lost in Des Moines
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Calculate the speed of a car using given information.
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Luscious Lemonade
- Judy Ann Brown
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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
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Pre-Algebra, 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
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Pre-Algebra, 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
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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.
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New Home for Fibonacci and Fractal
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Determine how long it will take Jimal and Leslie to fill the new 15-gallon aquarium.
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The Nutty Squirrel
- Alice Miller
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Find the total cost of purchasing tiles for my office.
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Olympic Temperature
- Judy Ann Brown
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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.
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Partial Area
- Judy Ann Brown
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Pre-Algebra, 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
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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?
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Photo Wall
- Suzanne Alejandre
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Pre-Algebra, difficulty level 3. Find the dimensions of the large poster.
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Pi Day - Let's Eat Cake!
- Judy Ann Brown
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration.
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Pizza Pie
- Judy Ann Brown
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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.
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Pouring the Punch
- Neil Bress
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Pre-Algebra, difficulty level 3. The Refreshments Committee needs to pour exactly four liters of eggnog using only three-liter and five-liter measures.
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Power Outage
- Jackson Geometry Class
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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.
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Practicing for the Winter Olympics
- Cynthia Paul
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 2. Compare the per-gallon cost of eleven different liquids, and put them in order from least to most expensive.
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Quilting Squares
- Suzanne Alejandre
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Pre-Algebra, 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
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Pre-Algebra, 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
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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
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Pre-Algebra, 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
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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.
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Seesaw
- Suzanne Alejandre
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Pre-Algebra, difficulty level 3. How did the four friends balance on the seesaw?
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Shine On Harvest Moon
- Judy Ann Brown
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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.
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The Silver Mile
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Determine the total value of the coins in a silver mile.
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Sizing Up Sequoias
- Suzanne Alejandre
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Pre-Algebra, 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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 2. Find how many cords of wood the woodshed will hold.
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A Stellar Garden
- Bill Marthinsen
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Pre-Algebra, 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
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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?
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Tasty Tomato Salsa
- Suzanne Alejandre
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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?
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Temperature Change
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Use the given information to find the temperature.
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Thanksgiving Travel
- Suzanne Alejandre & Maria Fung and her students
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 1. How many boxes of microwave popcorn would it take to make a giant
popcorn ball?
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Three-dimensional Television
- Mr. Marthinsen's Geometry Class
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Pre-Algebra, difficulty level 3. Help my friend find which TV will fit snugly into her TV nook.
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Tiling Tables
- Suzanne Alejandre
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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.
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Tiling Triangles
- Suzanne Alejandre
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Pre-Algebra, 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
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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?
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Train Travel
- Annie Fetter & Ian Underwood
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream.
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Val's Value
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Who has paid more for their jackets, Amir or Val?
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Volume Experiment
- Judy Ann Brown
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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
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Measure 8 quibits of swamp water using only 6-quibit and 10-quibit containers.
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Women's Walkway
- Suzanne Alejandre
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Pre-Algebra, 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
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Pre-Algebra, difficulty level 3. Find the surface area of an Olympic-size ice hockey rink.
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