TOPICS
This page:
all middle school
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

Browse all Middle School Problems of the Week
Participation in the Middle School Problems of the
Week allows teachers and students to address the
NCTM
Problem Solving Standard for Grades 68, enabling students to
build new mathematical knowledge through problem solving; solve problems
that arise in mathematics and in other contexts; apply and adapt a
variety of appropriate strategies to solve problems; and monitor and
reflect on the process of mathematical problem solving.
For background information elsewhere on our site, explore the
Middle School area of
the Ask Dr. Math archives, our Middle
School Student Center, and our Middle
School Teachers' Place.
Access to these problems requires a Membership.

Accuracy Please
 Judy Ann Brown

PreAlgebra, difficulty level 3. Considering precision, accuracy, and appropriateness in finding the volume of a cone.
... more>>

BacktoSchool Shopping
 Judy Ann Brown

Math Fundamentals, difficulty level 2. Mrs. Bender noticed that the total of the items her children purchased was $155. Can you determine the cost of one pair of jeans?
... more>>

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>>

Baseball Attendance Figures
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the difference between the greatest possible number of people at the stadium and the least possible number of paid admissions to the game.
... more>>

Baseball Trivia
 Judy Ann Brown

Math Fundamentals, difficulty level 2. How many runs do the Phillies have to score before the base runners have covered a mile?
... more>>

Batter Up!
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Use statistics to help Lee convince his manager to give him a raise.
... more>>

The Big Picture!
 Judy Ann Brown

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

Boxes of Stationery
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery?
... 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>>

Buying Cola
 Leon Roland & class

PreAlgebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy?
... more>>

California Dreaming
 Judy Ann Brown

Math Fundamentals, difficulty level 3. Determine the length of time that will be needed to drive from Allentown, Pennsylvania, to Los Angeles, California.
... more>>

Canadian Soccer
 Judy Ann Brown

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

Can This Be Done?
 Judy Ann Brown

Middle School, difficulty level 1. Find the largest sixdigit number that can be written following two simple rules.
... more>>

Can You Find My Numbers?
 Roya Salehi

PreAlgebra, difficulty level 3. I have eight numbers in my list. Use the clues to find my numbers.
... more>>

Car Rental Quandary
 Judy Ann Brown

PreAlgebra, difficulty level 3. Compare the car rental deals using the given information.
... more>>

Cats, Dogs, and Kids Everywhere You Look
 Judy Ann Brown

Middle School, difficulty level 2. A Logic problem: Patty's dog and Oscar's cat are both namesakes of the owner of the cat named Oscar...Who owns the dog Patty?
... 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>>

Citius, Altius, Fortius
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Would recordholding speed skaters and runners break the speed limit in a residential zone?
... more>>

Club Competition
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition.
... more>>

Coding Conundrums
 Mary DeYoung & class

PreAlgebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle.
... more>>

Coin Count
 Roya Salehi and Judy Ann Brown

PreAlgebra, difficulty level 3. Use the given information to determine the number of nickels and dimes in Lisa's bank.
... more>>

Commuting Conundrum
 Suzanne Alejandre

PreAlgebra, difficulty level 2. Help Suzanne and Richard decide which train tickets will give them the most value for their dollar.
... more>>

The Complex Apartment Complex
 Judy Ann Brown

PreAlgebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above.
... more>>

Counting Chicken Wings
 Annie Fetter, Suzanne Alejandre

PreAlgebra, difficulty level 3. Figure out how many wings are in the Biggest Bucket O' Wings.
... more>>

A Day at the Arcade
 Judy Ann Brown

Middle School, difficulty level 2. The 25cent token dispensing machine only accepts quarters and half dollars one at a time. How many different combinations of coins, using quarters (q) and half dollars (h), are there to purchase the desired number of tokens?
... more>>

Dishwasher Discounts
 Pat Hagan

PreAlgebra, difficulty level 2. Purchasing a new dishwasher can involve a lot of math. Help find the best deal.
... more>>

Distance Driving
 Judy Ann Brown

PreAlgebra, 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.
... more>>

Dividing Daffodils
 Suzanne Alejandre

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

Downhill All the Way
 Judy Ann Brown

PreAlgebra, 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?
... more>>

Do you listen to WMTH or WALG?
 Judy Ann Brown

PreAlgebra, difficulty level 4. Each week listeners switch radio stations. Predict the longterm distribution of listeners for each station.
... more>>

Ducky Promenade
 Leon Roland & class (poetry by Annie Fetter)

PreAlgebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem.
... more>>

Duke is Missing
 Judy Ann Brown

PreAlgebra, difficulty level 3. Duke's head is 6 inches long, his tail is as long as his head plus half the length of his body, and his body is as long as the head and tail combined. How long is Duke?
... more>>

Even Number Puzzle
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many even fourdigit whole numbers exist such that the thousands digit is odd, and all four digits are different?
... 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>>

Fall Festival Frolic
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different types of candy are needed to make at least 50 different treat bags?
... more>>

Falling into Sequences
 Judy Ann Brown

PreAlgebra, difficulty level 3. Find the 20th term in a sequence using both a recursive method and an explicit formula.
... more>>

Flipping Over Pennies
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many equally likely outcomes are there when flipping 10 coins?
... more>>

Football Figures
 Judy Ann Brown

Middle School, difficulty level 2. This year we have already won as many games as we lost last year. How many games will the team play this year?
... more>>

Frequent Flier Figuring
 Judy Ann Brown

Math Fundamentals, difficulty level 2. Use Web resources to help plan the shortest route from Allentown, Pennsylvania, to New Orleans, Louisiana.
... more>>

Gearing Up
 Suzanne Alejandre

PreAlgebra, difficulty level 3. Think about and explain the relationship between three differentsized gears.
... 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>>

The Graduating Class
 Judy Ann Brown

PreAlgebra, difficulty level 3. Use the information about students with different grades to determine the number of students in Mrs. Smith's class.
... more>>

Grandmother's Birthday Party
 Judy Ann Brown

Middle School, difficulty level 1. Alice and Jessica are writing invitations for a surprise birthday party for their grandmother. Determine how many invitations they have written?
... more>>

Graphing for Area
 Judy Ann Brown

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

Guess My Number If You Can!
 Judy Ann Brown

PreAlgebra, difficulty level 4. Use division clues to reveal the secret number.
... more>>

Happy New Year!
 Judy Ann Brown

PreAlgebra, difficulty level 4. A puzzle for the new year: how is the grid designed?
... more>>
Page: 1
2
3
[next>]
