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M.S. Problems
Middle School
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Middle School: Area
In grades 68, 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 middleschool students to practice finding the
area of two and threedimensional objects are listed below. They address the
NCTM Geometry
Standard for Grades 68 expectation that students will be able to
analyze characteristics and properties of two and threedimensional
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 middleschool sites, go
to the bottom of the page, set the searcher for middle school (68),
and press the Search button.
Access to these problems requires a Membership.

The Big Picture!
 Judy Ann Brown

PreAlgebra, difficulty level 3. A picture is enlarged to four times its area.
... more>>

Building Fences
 Judy Ann Brown

PreAlgebra, difficulty level 3. Plan a garden so as to maximize the area surrounded by a 36yard fence.
... more>>

Building on Water
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find the area of a circular pond not covered by a rectangular building.
... more>>

Chamique the Archer
 Mr. Marthinsen's Geometry Class

PreAlgebra, difficulty level 3. Chamique wants to know the probability of hitting a bull'seye with a randomly shot arrow.
... more>>

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.
... more>>

Dividing Daffodils
 Suzanne Alejandre

PreAlgebra, difficulty level 4. Help us plant our garden of daffodils.
... more>>

Exploring Area
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method.
... more>>

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.
... more>>

Funny Ducks
 Ethel Breuche

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>>

Golfing Luck?
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Work with probability on the practice hole of the golf course.
... more>>

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?
... more>>

Graphing for Area
 Judy Ann Brown

PreAlgebra, difficulty level 2. Graph six points and find the area of the resulting hexagon.
... more>>

Green Pastures
 Carol Dormuth

Trig/Calc, difficulty level 1. Find the area of the cow's grazing pasture.
... more>>

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.
... more>>

How Large is the Patio?
 Judy Ann Brown

Middle School, difficulty level 2. The Smiths are putting new flagstone on their patio. How many square feet will the patio cover?
... more>>

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.
... more>>

LawnMowing Chore
 Judy Ann Brown

Math Fundamentals, difficulty level 4. Find the area of the yard that Josh, Sam, and Mark must mow.
... more>>

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.
... more>>

The New Rug
 Lisa Lavelle

Elementary, difficulty level 3. Find the number of squares needed to cover the Reading area.
... more>>

Office Tile Choice
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the total cost of purchasing tiles for my office.
... more>>

One Area  Many Solutions
 Leigh Nataro

Trig/Calc, difficulty level 2. Find the area of a triangle given the coordinates of its vertices.
... more>>

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.
... more>>

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.
... more>>

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.
... more>>

Quilting Squares
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design.
... more>>

Rabbit's Run
 Lisa Lavelle

Math Fundamentals, difficulty level 1. Help Regina develop options for building her rabbit's run.
... more>>

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.
... more>>

Spring Garden Planning
 Judy Ann Brown

PreAlgebra, difficulty level 4. Find the area as well as the length and width of my fractional garden.
... more>>

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.
... more>>

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?
... more>>
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