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Browse all
M.S. Problems
Middle School
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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 6-8, 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.
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Accuracy Please
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Considering precision, accuracy, and appropriateness in finding the volume of a cone.
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Back-to-School Shopping
- Judy Ann Brown
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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?
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Back Yard Trees
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. How many different quadrilaterals can be formed by joining any four of the nine trees?
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Balancing Mobiles
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Explore two Laws of Archimedes as you puzzle through a balanced mobile.
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Baseball Attendance Figures
- Judy Ann Brown
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Pre-Algebra, 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.
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Baseball Trivia
- Judy Ann Brown
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Math Fundamentals, difficulty level 2. How many runs do the Phillies have to score before the base runners have covered a mile?
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Batter Up!
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Use statistics to help Lee convince his manager to give him a raise.
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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.
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Boxes of Stationery
- Annie Fetter, Suzanne Alejandre
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Pre-Algebra, difficulty level 3. How many sheets of paper and how many envelopes are in the box of stationery?
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Building a Snow Statue
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Determine the height of a snow statue using the given information.
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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.
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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.
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Buying Cola
- Leon Roland & class
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Pre-Algebra, difficulty level 3. Where should Chuck shop to get the most cola? Is this the best buy?
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California Dreaming
- Judy Ann Brown
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Math Fundamentals, difficulty level 3. Determine the length of time that will be needed to drive from Allentown, Pennsylvania, to Los Angeles, California.
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Canadian Soccer
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Find the distance a player runs to complete three "Double V" laps.
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Can This Be Done?
- Judy Ann Brown
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Middle School, difficulty level 1. Find the largest six-digit number that can be written following two simple rules.
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Can You Find My Numbers?
- Roya Salehi
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Pre-Algebra, difficulty level 3. I have eight numbers in my list. Use the clues to find my numbers.
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Car Rental Quandary
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Compare the car rental deals using the given information.
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Cats, Dogs, and Kids Everywhere You Look
- Judy Ann Brown
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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?
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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.
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Citius, Altius, Fortius
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Would record-holding speed skaters and runners break the speed limit in a residential zone?
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Club Competition
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Determine how many teams the Fibonacci Middle School Math Club can enter in their first competition.
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Coding Conundrums
- Mary DeYoung & class
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Pre-Algebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle.
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Coin Count
- Roya Salehi and Judy Ann Brown
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Pre-Algebra, difficulty level 3. Use the given information to determine the number of nickels and dimes in Lisa's bank.
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Commuting Conundrum
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Help Suzanne and Richard decide which train tickets will give them the most value for their dollar.
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The Complex Apartment Complex
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Find the number of apartments in a new building if each floor has twice as many apartments as the floor above.
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Counting Chicken Wings
- Annie Fetter, Suzanne Alejandre
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Pre-Algebra, difficulty level 3. Figure out how many wings are in the Biggest Bucket O' Wings.
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A Day at the Arcade
- Judy Ann Brown
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Middle School, difficulty level 2. The 25-cent 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?
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Dishwasher Discounts
- Pat Hagan
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Pre-Algebra, difficulty level 2. Purchasing a new dishwasher can involve a lot of math. Help find the best deal.
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Distance Driving
- Judy Ann Brown
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Pre-Algebra, 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.
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Dividing Daffodils
- Suzanne Alejandre
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Pre-Algebra, difficulty level 4. Help us plant our garden of daffodils.
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Downhill All the Way
- Judy Ann Brown
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Pre-Algebra, 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?
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Do you listen to WMTH or WALG?
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. Each week listeners switch radio stations. Predict the long-term distribution of listeners for each station.
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Ducky Promenade
- Leon Roland & class (poetry by Annie Fetter)
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Pre-Algebra, difficulty level 3. Find the weight of a duckling and two ducks after reading this poem.
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Duke is Missing
- Judy Ann Brown
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Pre-Algebra, 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?
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Even Number Puzzle
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. How many even four-digit whole numbers exist such that the thousands digit is odd, and all four digits are different?
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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.
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Fall Festival Frolic
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. How many different types of candy are needed to make at least 50 different treat bags?
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Falling into Sequences
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Find the 20th term in a sequence using both a recursive method and an explicit formula.
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Flipping Over Pennies
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. How many equally likely outcomes are there when flipping 10 coins?
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Football Figures
- Judy Ann Brown
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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?
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Frequent Flier Figuring
- Judy Ann Brown
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Math Fundamentals, difficulty level 2. Use Web resources to help plan the shortest route from Allentown, Pennsylvania, to New Orleans, Louisiana.
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Gearing Up
- Suzanne Alejandre
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Pre-Algebra, difficulty level 3. Think about and explain the relationship between three different-sized gears.
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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.
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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?
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The Graduating Class
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Use the information about students with different grades to determine the number of students in Mrs. Smith's class.
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Grandmother's Birthday Party
- Judy Ann Brown
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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?
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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.
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Guess My Number If You Can!
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. Use division clues to reveal the secret number.
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Happy New Year!
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. A puzzle for the new year: how is the grid designed?
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