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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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Power Outage
- Jackson Geometry Class
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Pre-Algebra, difficulty level 3. The power went out. Use the current reading on the clocks to determine when the power went out, and for how long.
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Price Fluidity
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Compare the per-gallon cost of eleven different liquids, and put them in order from least to most expensive.
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Quilting Squares
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Help with some quick calculations of the amount of fabric needed for this quilt design.
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Rampaging Reindeer
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. How many different ways can Santa's reindeer be arranged?
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Rounding Mountains
- Judy Ann Brown
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Math Fundamentals, difficulty level 2. Use estimated figures to determine the maximum and minimum differences between the heights of two mountains.
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Runsums, Part 1
- Ron Knott
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Pre-Algebra, difficulty level 3. By spotting the pattern, tell me the smallest number that is a sum of a run of one hundred consecutive numbers.
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Runsums, Part 2
- Ron Knott
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Pre-Algebra, difficulty level 3. Explore number patterns and report on what you have learned.
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Sailing Around the World
- Leon Roland & class
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Pre-Algebra, difficulty level 2. Determine the amounts of the supplies that Giuseppi Linguini will need to sail around the world.
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Santa's Little Helpers
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Help Santa to solve the puzzle created by the clever elves.
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Saturday Bike Ride
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Now that spring has arrived, Ali and Maya decide to dust off their bikes and go for a Saturday ride. Help find what time they will meet.
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Scientific Sums
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Find the sum of a set of numbers written in scientific notation.
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Seating Arrangements
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Four new students arrive in Mrs. Brown's homeroom. After a few minutes she turns to them and says, "There are 1680 ways
that you can sit in the empty seats." How many empty seats are there in the room?
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Seating Dilemma
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Count the number of ways to seat people, if some are math teachers who cannot be next to each other.
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Seesaw
- Suzanne Alejandre
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Pre-Algebra, difficulty level 3. How did the four friends balance on the seesaw?
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Sequence of Exercise
- Judy Ann Brown
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Middle School, difficulty level 2. Each day Chris and Jody jog three blocks farther than they did the day before. How many days have Chris and Jody been jogging?
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Shapes Rock
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Find the number of diagonals in a polygon of 40 sides.
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Shine On Harvest Moon
- Judy Ann Brown
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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.
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Shopping Spree
- Judy Ann Brown
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Middle School, difficulty level 1. Jamie is shopping for holiday presents. How many $9.49 shirts can she buy? How much change will she have left?
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The Silver Mile
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Determine the total value of the coins in a silver mile.
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Simple Arithmetic
- Judy Ann Brown
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Middle School, difficulty level 2. Titles can be deceiving - this is a simple arithmetic problem but you need to find the numbers.
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A Simple Reversal
- Judy Ann Brown
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Math Fundamentals, difficulty level 1. The product of 3 and 24 is 72. The sum of 3 and 24 is 27, which is the reverse of 72. Can you find other pairs of numbers such that their product is the reverse of their sum?
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Snow Day Phone Chain
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. Use the given information to find out how many phone calls were made.
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Spring Garden Planning
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. Find the area as well as the length and width of my fractional garden.
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Square Dancing
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. The sum of each couple's numbers is a perfect square. Use other information in the problem to find the number of Ashley's partner.
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A Stellar Garden
- Bill Marthinsen
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Pre-Algebra, difficulty level 3. Martha Stewart wants to rebuild her ugly garden. She needs help calculating the areas in the new garden.
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Student Council Elections
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. Find the number of ways names can be arranged on the student council ballot, and figure the odds that a brother and sister will both be listed first in their respective races.
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Study Hall Games
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. I polled the students to find out which of the three games in my closet they might like to play. Then I created a math problem using the results of the poll.
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Super Bowl XXXIII
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Based on the winners and points scored during the past 15 Super Bowl games, which team should win Super Bowl XXXIII?
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Super Bowl XXXII
- Judy Ann Brown
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Middle School, difficulty level 2. The Super Bowl committee has decided to create a plaque to hang in the NFL Hall of Fame. Your job is to determine how many of each letter or symbol must be made in gold.
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A Surfer's Tessellation
- Mr. Marthinsen's First Period Class
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Pre-Algebra, difficulty level 2. Shane is re-tiling his surf shack. How many of each kind of tile will he need, and what does a big tile cost?
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Temperature Change
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Use the given information to find the temperature.
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Three-dimensional Television
- Mr. Marthinsen's Geometry Class
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Pre-Algebra, difficulty level 3. Help my friend find which TV will fit snugly into her TV nook.
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Tiling Triangles
- Suzanne Alejandre
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Pre-Algebra, difficulty level 3. Given the dimensions of a large triangle, find the dimensions of the 25 small triangles that tile it.
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The Tower of Hanoi Puzzle
- Roya Salehi
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Pre-Algebra, difficulty level 4. Tower of Hanoi: What is the minimum number of moves it will take to transfer 25 disks from one post to another?
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Treasure Hunt Math
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Use clues to find the mystery palindrome.
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Trick-or-Treat Route
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. Which of the many possible routes should the Anderson children take on their Halloween trek?
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Valley Springs Snow Cream
- Kelly Crisp
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Pre-Algebra, difficulty level 3. Compare the volume of a sphere, cone, and cylinder using ice cream.
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Volume Experiment
- Judy Ann Brown
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Math Fundamentals, difficulty level 2. Make a prediction, conduct an experiment, and report your findings.
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What Day Is It Today?
- Roya Salehi
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Math Fundamentals, difficulty level 2. Sophie tells the truth only on Monday, Tuesday, Wednesday, and Thursday. Her sister tells the truth only on Monday, Friday, Saturday, and Sunday. If they both confess to their mom that "Yesterday I lied," what day is it today?
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Where Does Mrs. Darien Live?
- Judy Ann Brown
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Middle School, difficulty level 2. Use clues to help Mrs. Darien's students find her house number.
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Where Should I Sit?
- Judy Ann Brown
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Middle School, difficulty level 3. On Monday three new students arrived in Mrs. King's homeroom... How many empty seats were there in Mrs. King's room?
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Who Brought the Candy Corn?
- Judy Ann Brown
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Middle School, difficulty level 3. Five children dressed in different costumes arrived for a Halloween party riding bicycles. Who drinks Root Beer? Who brought the candy corn? How did you figure this out?
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Wilda's Swamp Water
- Judy Ann Brown
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Pre-Algebra, difficulty level 3. Measure 8 quibits of swamp water using only 6-quibit and 10-quibit containers.
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Wraparound Universe
- Jeff Weeks
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Pre-Algebra, difficulty level 4. Explore the game of tic-tac-toe using a cylindrical tic-tac-toe board.
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