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Middle School
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Middle School: Discrete Math
The study of discrete mathematics, with problems involving algorithms,
apportionment, combinatorics, graph theory, lattices, or trees, often
begins in the middle grades, where problems are most likely to explore
permutations and combinations or graph theory.
Many of the problems listed below were designed with grades 68 in mind;
others, from our Discrete Math Problem of the Week, are a bit more
difficult, but are appropriate for able middleschool students or can be
simplified for use in the middleschool classroom.
For relevant sites on the Web, browse and search
Discrete Math 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?
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Coding Conundrums
 Mary DeYoung & class

PreAlgebra, difficulty level 2. Explore encoding and decoding in this cipher puzzle.
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The Confession Letter
 Ethel Breuche

Discrete Math, difficulty level 1. Students are asked to decode the letter left by the murderer from last week's puzzle.
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Cooking Dinner
 Leigh Nataro

Discrete Math, difficulty level 2. Using graphs and critical paths, find the amount of time it takes to make dinner.
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Coverage
 Larry Sue

Discrete Math, difficulty level 1. This classic problem asks whether the given shape covers the given grid.
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The Doughnut Dilemma
 Leigh Nataro

Discrete Math, difficulty level 3. How many ways can you choose three doughnuts from six different types of doughnuts?
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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.
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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?
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Flipping Over Pennies
 Judy Ann Brown

PreAlgebra, difficulty level 3. How many equally likely outcomes are there when flipping 10 coins?
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The Forever Green Nursery
 Leigh Nataro

Discrete Math, difficulty level 3. Does the number of trees in a nursery increase, decrease, or stabilize?
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The Fourth of July Parade
 Ethel Breuche

Discrete Math, difficulty level 3. After the parade, the people on the float I was on shook hands with each other. The Mayor came over and shook hands with only the people he knew. How many people did he know if there were 1625 handshakes altogether?
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A Great Way to Make Money?
 Leigh Nataro

Discrete Math, difficulty level 2. Is it better to rely on a weekly pay of $10, or take a chance on the money that is in a paper bag?
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Heads or Tails
 Leigh Nataro

Discrete Math, difficulty level 2. Is it possible to have an arrangement of four coins go from HHHH to TTTT based on the rules given for flipping the coins?
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High School Reunion
 Leigh Nataro

Discrete Math, difficulty level 1. Find the minimum number of meeting times needed so that no committee member will miss a meeting.
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Homework and Candy
 Leigh Nataro

Discrete Math, difficulty level 1. Use the Hamilton method to apportion candy among three children.
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Homework Phone Pals
 Leigh Nataro

Discrete Math, difficulty level 1. Using the given clues, figure out which students are homework phone pals.
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King Euler's Blueprint
 Leigh Nataro

Discrete Math, difficulty level 1. Can you walk a path that will go through every doorway once?
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Leaping Frogs
 Leigh Nataro

Discrete Math, difficulty level 2. Find a formula to determine the number of moves needed to have the frogs switch places on their lily pads.
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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.
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The Locker Problem
 Ethel Breuche

Discrete Math, difficulty level 2. This classic number theory problem investigates properties of prime numbers, perfect squares, and counting in a problem that involves opening and closing locker doors.
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Math Club Ski Trip
 Judy Ann Brown

PreAlgebra, 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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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.
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The Musicians' Dilemma
 Daniel Weinstein

Discrete Math, difficulty level 1. The musicians need to cross a bridge but only two may go at a time, using the flashlight. They take different amounts of time to cross but they have only seventeen minutes to get to the concert. How can they do this?
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Pegging Possibilities
 Michael Urbut

PreAlgebra, difficulty level 2. Explore the number of possible arrangements of pegs in this logic game.
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Pothole Repair
 Leigh Nataro

Discrete Math, difficulty level 2. Plan a route for the road crews to take.
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Rock Star Poisoned
 Ethel Breuche

Discrete Math, difficulty level 1. Malonda is found poisoned in her dressing room. Solve this murder mystery using the clues given.
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Roses, Roses, Roses
 Larry Sue

Discrete Math, difficulty level 1. Bob must bring his girlfriend roses to say he's sorry. Explore some of the ramifications of combining modular arithmetic and interpersonal relationships.
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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?
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The Take Away Game
 Leigh Nataro

Discrete Math, difficulty level 3. Find the strategy to guarantee that you will always win in this game.
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The Termite and the Cube
 Jared Hammond

Discrete Math, difficulty level 1. Can a termite, traveling only vertically or horizontally through a 3x3x3 Rubiklike cube, go through every cube exactly once and wind up in the very center?
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The Tiny Town of Smallsville
 Leigh Nataro

Discrete Math, difficulty level 2. An exercise in recursion: Based on birth and death data, how long will it take the town of Smallsville to double its population?
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TrickorTreat Route
 Judy Ann Brown

PreAlgebra, difficulty level 4. Which of the many possible routes should the Anderson children take on their Halloween trek?
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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?
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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?
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Who Broke Mom's Favorite Vase?
 Leigh Nataro

Discrete Math, difficulty level 1. Using logic, determine who is lying and who is telling the truth about who broke Mom's favorite vase.
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Wraparound Universe
 Jeff Weeks

PreAlgebra, difficulty level 4. Explore the game of tictactoe using a cylindrical tictactoe board.
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Yearbook Deadlines
 Leigh Nataro

Discrete Math, difficulty level 2. Find the critical path to determine the earliest time that the school yearbook can be completed.
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