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Middle School
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Middle School: Combinations and Permutations
In grades 68, discrete math problems are likely to explore permutations and
combinations: see for example
Back Yard Trees
(how many different quadrilaterals can be formed by joining any four of nine
trees?), or Mr. Carmel's
Party Plan (help Mr. Carmel's class earn an ice cream party by counting
the number of possible sundaes).
Combinatorics problems appropriate for middleschool students are
listed below.
For information elsewhere on our site, see
Permutations and Combinations,
from the Dr. Math FAQ. Answers at the highschool level in the Dr. Math
archives may also be useful to middleschool students; see
Permutations and Combinations.
For relevant sites on the Web, browse and search
Combinatorics: Permutations and
Combinations 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>>

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>>

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>>

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>>

Flipping Over Pennies
 Judy Ann Brown

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

Locker Combinations
 Judy Ann Brown

PreAlgebra, difficulty level 4. In this counting problem you will need to determine the total number of possible locker combinations.
... more>>

Mr. Carmel's Party Plan
 Judy Ann Brown

PreAlgebra, difficulty level 2. Help Mr. Carmel's class earn an ice cream party by counting the number of possible sundaes.
... more>>

Pegging Possibilities
 Michael Urbut

PreAlgebra, difficulty level 2. Explore the number of possible arrangements of pegs in this logic game.
... more>>

Rampaging Reindeer
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many different ways can Santa's reindeer be arranged?
... more>>

Seating Arrangements
 Judy Ann Brown

PreAlgebra, 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?
... more>>

Student Council Elections
 Judy Ann Brown

PreAlgebra, 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.
... more>>

TrickorTreat Route
 Judy Ann Brown

PreAlgebra, difficulty level 4. Which of the many possible routes should the Anderson children take on their Halloween trek?
... more>>

Ursala is Undecided
 Melissa Kennedy, Ethel Breuche

Discrete Math, difficulty level 1. Poor Undecided Ursala has many paths to choose to get from point A to point S. Exactly how many paths does she have a choice of taking?
... more>>

Where Should I Sit?
 Judy Ann Brown

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?
... more>>

Wraparound Universe
 Jeff Weeks

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