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M.S. Problems
Middle School
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Middle School: Area
In grades 6-8, students explore the relations among similar objects,
solving problems that link length, perimeter, area, and volume.
To do so, students learn to calculate the surface area of a variety
of objects.
Problems that allow middle-school students to practice finding the
area of two- and three-dimensional objects are listed below. They address the
NCTM Geometry
Standard for Grades 6-8 expectation that students will be able to
analyze characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about geometric
relationships.
For background information elsewhere on our site, explore the
Middle School Geometry
area of the Ask Dr. Math archives. For relevant sites on the Web, browse
and search Euclidean Plane Geometry
in our Internet Mathematics Library; to find middle-school sites, go
to the bottom of the page, set the searcher for middle school (6-8),
and press the Search button.
Access to these problems requires a Membership.
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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.
... more>>
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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.
... more>>
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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.
... more>>
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Chamique the Archer
- Mr. Marthinsen's Geometry Class
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Pre-Algebra, difficulty level 3. Chamique wants to know the probability of hitting a bull's-eye with a randomly shot arrow.
... more>>
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Cubic Changes
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Determine how the volume and surface area of a cube change when the edge length is changed.
... more>>
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Dividing Daffodils
- Suzanne Alejandre
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Pre-Algebra, difficulty level 4. Help us plant our garden of daffodils.
... more>>
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Exploring Area
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method.
... more>>
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Frugal Flooring
- Marita Paynter
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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.
... more>>
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Funny Ducks
- Ethel Breuche
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Algebra, difficulty level 4. These funny ducks always walk exactly three feet from the lily pond. What is the area of the region bounded by their path?
... more>>
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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.
... more>>
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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?
... more>>
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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.
... more>>
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Green Pastures
- Carol Dormuth
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Trig/Calc, difficulty level 1. Find the area of the cow's grazing pasture.
... more>>
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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.
... more>>
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How Large is the Patio?
- Judy Ann Brown
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Middle School, difficulty level 2. The Smiths are putting new flagstone on their patio. How many square feet will the patio cover?
... more>>
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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.
... more>>
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Lawn-Mowing Chore
- Judy Ann Brown
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Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow.
... more>>
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Lost in Space
- Lisa Lavelle
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Math Fundamentals, difficulty level 4. Figure out how big an error the engineers made when they mixed up their units.
... more>>
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The New Rug
- Lisa Lavelle
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Elementary, difficulty level 3. Find the number of squares needed to cover the Reading area.
... more>>
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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.
... more>>
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One Area - Many Solutions
- Leigh Nataro
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Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices.
... more>>
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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.
... more>>
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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.
... more>>
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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.
... more>>
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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.
... more>>
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Rabbit's Run
- Lisa Lavelle
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Math Fundamentals, difficulty level 1. Help Regina develop options for building her rabbit's run.
... more>>
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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.
... more>>
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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.
... more>>
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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.
... more>>
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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?
... more>>
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