TOPICS
This page:
geometry
About Levels
of Difficulty
Algebraic
Reasoning
distanceratetime
Arithmetic
estimation
exponents & roots
factors, factoring, &
prime numbers
fractions, decimals &
percents
measurement
pi
ratio & proportion
Discrete Math
combinations &
permutations
graph theory
Geometry
area
circumference &
perimeter
Pythagorean...
volume
Logic
Patterns
Probability
Statistics
Browse all
M.S. Problems
Middle School
Home
About the
PoW Library

Middle School: Geometry
In grades 68, students learn to use the defining properties of
two and threedimensional 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.
Middleschool 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 68.
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 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.

Back Yard Trees
 Judy Ann Brown

PreAlgebra, difficulty level 4. How many different quadrilaterals can be formed by joining any four of the nine trees?
... more>>

Balancing Mobiles
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
... more>>

Building a Snow Statue
 Judy Ann Brown

PreAlgebra, difficulty level 3. Determine the height of a snow statue using the given information.
... 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>>

Canadian Soccer
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps.
... 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>>

Exploring Area
 Judy Ann Brown

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

Graphing for Area
 Judy Ann Brown

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

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

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

Peanut's Back Yard
 Jonathan Bauer

PreAlgebra, 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>>

PicturePerfect Geometry
 Judy Ann Brown

PreAlgebra, difficulty level 2. Graph four points and name the figure that you have drawn.
... 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>>

Pi Day Treats
 Judy Ann Brown

PreAlgebra, difficulty level 3. Help Mrs. Granville and Mrs. Germain plan a Pi Day celebration.
... 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>>

Seesaw
 Suzanne Alejandre

PreAlgebra, difficulty level 3. How did the four friends balance on the seesaw?
... more>>

Shapes Rock
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides.
... 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>>

Threedimensional Television
 Mr. Marthinsen's Geometry Class

PreAlgebra, difficulty level 3. Help my friend find which TV will fit snugly into her TV nook.
... more>>

Tiling Triangles
 Suzanne Alejandre

PreAlgebra, 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

PreAlgebra, 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

PreAlgebra, difficulty level 4. Explore the game of tictactoe using a cylindrical tictactoe board.
... more>>
Page: 1
