Math Forum - Problems Library - Middle School, Geometry

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Middle School: Geometry

In grades 6-8, students learn to use the defining properties of two- and three-dimensional objects to describe, classify, and understand the relations that exist among them. Students also explore the relations among the angles, side lengths, perimeters, areas, and volumes of similar objects, and study such geometric ideas as congruence, similarity, and the Pythagorean relationship. Middle-school students use coordinate geometry to study properties of geometric shapes (such as regular polygons), and they investigate transformations such as flips, turns, slides, and scaling, using such transformations to learn about congruence, similarity, and line or rotational symmetry of objects. Finally, students learn to recognize geometry in other areas such as art, science, and everyday life.

Middle School Problems of the Week that require students to use geometry to solve them are listed below. They address the NCTM Geometry Standard for Grades 6-8.

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 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.

Back Yard Trees - Judy Ann Brown
Pre-Algebra, difficulty level 4. How many different quadrilaterals can be formed by joining any four of the nine trees? ... more>>

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

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

Chamique the Archer - Mr. Marthinsen's Geometry Class
Pre-Algebra, difficulty level 3. Chamique wants to know the probability of hitting a bull's-eye with a randomly shot arrow. ... more>>

Exploring Area - Judy Ann Brown
Pre-Algebra, difficulty level 4. Find information about Pick's theorem and solve an area problem using this method. ... more>>

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

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
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>>

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

Picture-Perfect Geometry - Judy Ann Brown
Pre-Algebra, difficulty level 2. Graph four points and name the figure that you have drawn. ... 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>>

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

Shapes Rock - Judy Ann Brown
Pre-Algebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides. ... 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>>

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>>

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>>

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 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>>

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

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

Wraparound Universe - Jeff Weeks
Pre-Algebra, difficulty level 4. Explore the game of tic-tac-toe using a cylindrical tic-tac-toe board. ... more>>

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