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 discrete math
 combinations
graph theory
permutations
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Pre-Algebra
operations with numbers
number sense
number theory
fractions, decimals,
percentages
integers
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Pre-Algebra
Problems
Pre-Algebra
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Discrete Math & Counting Principles
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The basics of combinations, permutations, graph theory. These topics are often combined with probability, in which case the problems would then be listed in both categories.
Some of these problems are also in the following subcategories:
- Related Resources
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Interactive resources from our Math Tools project:
Math 7: Counting Principles
The closest match in our Ask Dr. Math archives:
Middle School Archive
NCTM Standards:
Data Analysis & Probability Standard for Grades 6-8
Access to these problems requires a Membership.
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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?
... more>>
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Basic Breakfast Buffet
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. How many days could Linnea, Joel, Karl, and Jakob stay at the hotel
before one of them would
have to repeat one of the breakfasts?
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Change Woes
- suggested by a Western Oregon University mentor
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Pre-Algebra, difficulty level 3. What coins did Lacey have before her money was mixed up with her
brother's?
... more>>
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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.
... more>>
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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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Colors of the Olympic Rings
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. If we categorize all the flags of the world by the combination of the
Olympic ring colors
that appear in them, how many categories would we have?
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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?
... more>>
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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?
... more>>
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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?
... more>>
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Kwae
- Suzanne Alejandre
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Pre-Algebra, difficulty level 3. Determine the number of kwae that can be made.
... more>>
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Locker Combinations
- Judy Ann Brown
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Pre-Algebra, difficulty level 4. In this counting problem you will need to determine the total number of possible locker combinations.
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Math Club Ski Trip
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Mrs. Germain and her friend, Mrs. Granville, need your help to plan the shortest route to visit five local ski areas.
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Money Maker?
- Leigh Nataro, Suzanne Alejandre
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Pre-Algebra, difficulty level 4. Would you rather earn $10 a week, or take a chance every week on the
money in this paper bag?
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Mr. Carmel's Party Plan
- Judy Ann Brown
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Pre-Algebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes.
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Pegging Possibilities
- Michael Urbut
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Pre-Algebra, difficulty level 2. Explore the number of possible arrangements of pegs in this logic game.
... more>>
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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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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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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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Totolospi
- Suzanne Alejandre
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Pre-Algebra, difficulty level 2. Calculate the probability of advancing on a toss when playing the game
Totolospi.
... more>>
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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?
... more>>
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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.
... more>>
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