VI. Probability and Discrete Mathematics

 
  1. Probability
  2. Discrete Mathematics

 

Additional Links to General Mathematics Sites

 

2. Discrete Mathematics

Middle School

  1. Benchmark 1. "Use manipulatives, diagrams and the fundamental theorem of counting to count permutations and combinations."
    1. Discrete Math Project - Discrete Mathematics (VI.2.MS.1,2,3,4,5&6)
      This site is an excellent resource for teacher lesson plans for discrete math.
    2. How Many Valentines - Discrete Mathematics (VI.2.MS.1)
      A story problem is given which allows the student to solve and then see the correct answer and why it is correct. There is a space given to make corrections and write what he/she did correctly or incorrectly.
    3. The Most Colorful Map of All - Discrete Mathematics (VI.2.MS.1,3,5,&6)
      This lesson allows you to connect reading and mathematics in a fun and interesting way. Map coloring is used as a way of stimulating student's to think logically and to use strategies to solve problems which are both interesting and pertinent. Excellent resources are included for the teacher to use, copy, and share.
    4. Webmath - See How Many Combinations You Can Make - Discrete Mathematics (VI.2.MS.1)
      This site allows students to input names of things or objects and see how many possible combinations can be made. A detailed explanation is provided for how to find the solution.
    5. Welcome to the Hotel Infinity - Discrete Mathematics (VI.2.MS.1,3,5&6)
      This lesson allows you to connect reading and mathematics in a fun and interesting way. The Hotel Infinity story is shared with students (copies can be made for their use) to raise questions about the logic and mathematics found in the text. Teacher resources are include vocabulary, background information, and questions to expand student thinking about the story.
  2. Benchmark 2. "Use sets and set relationships to explore and solve simple algebraic and geometric problems."
    1. Definition of Sets - Discrete Mathematics (VI.2.MS.2)
      Students are given three sets and must use the definition of sets to match each problem with its correct answer. Students are given points based on when they correctly matched a picture and expression.
    2. Discrete Math Project - Discrete Mathematics (VI.2.MS.1,2,3,4,5&6)
      This site is an excellent resource for teacher lesson plans for discrete math.
    3. Fractals - Discrete Mathematics (V1.2.MS.2)
      This site covers the definition of fractals and had an interactive activity where students can create their own Sierpinski Triangles, etc. It also includes a section for teachers.
    4. Intersection and Union - - Discrete Mathematics (VI.2.MS.2)
      Students are given six puzzles and expressions and must match them up. Students are given points based on when they correctly matched a picture and expression.
    5. Patterns in Mathematics: Logic Patterns - Discrete Mathematics (VI.2.MS.2)
      This interactive site allows students to complete logic problems involving identifying the attributes of objects. The activities are simple to do but require the student think logically and in an organized manner.
    6. Venn Diagrams - Discrete Mathematics (VI.2.MS.2)
      Blank Venn Diagrams provided for insertion of elements and descriptions; ability to view when finished by clicking "Show me". This is a teacher directed activity.
  3. Benchmark 3. "Solve problems involving networks, for example planning delivery routes or counting paths between points."
    1. Bike Route - Discrete Mathematics (VI.2.MS.3)
      This site would be great for 5th and 6th grade students.  This interactive game involves finding the shortest route to a destination.
    2. Discrete Math Project - Discrete Mathematics (VI.2.MS.1,2,3,4,5&6)
      This site is an excellent resource for teacher lesson plans for discrete math.
    3. Games on Graphs - Discrete Mathematics (VI.2.MS.3&6)
      This lesson uses games to explore graphs. Stories are used to inspire students to create a game to simulate the story. A variety of example game boards using graphs are included along with background information for the teacher. Lesson plans include big ideas and follow-up questions along with more games for continued use. Students are asked to think logically about the number of possible outcomes and a problem which can be examined over time is included.
    4. The Ice Cream Stands Problem - Discrete Mathematics (VI.2.MS.3&6)
      The Ice Cream Stands Problem: This problem involves planning for efficiently using resources. There are many solutions to the problem, although the solutions that require the least amount of resources will be the best ones for the problem as stated. Various strategies can be used to approach the problem, and no single strategy is better than all the rest. This is a teacher lesson plan.
    5. The Most Colorful Map of All - Discrete Mathematics (VI.2.MS.1,3,5,&6)
      This lesson allows you to connect reading and mathematics in a fun and interesting way. Map coloring is used as a way of stimulating student's to think logically and to use strategies to solve problems which are both interesting and pertinent. Excellent resources are included for the teacher to use, copy, and share.
    6. Welcome to the Hotel Infinity - Discrete Mathematics (VI.2.MS.1,3,5&6)
      This lesson allows you to connect reading and mathematics in a fun and interesting way. The Hotel Infinity story is shared with students (copies can be made for their use) to raise questions about the logic and mathematics found in the text. Teacher resources are include vocabulary, background information, and questions to expand student thinking about the story.
  4. Benchmark 4. "Explore recurrence relations and iterations."
    1. Discrete Math Project - Discrete Mathematics (VI.2.MS.1,2,3,4,5&6)
      This site is an excellent resource for teacher lesson plans for discrete math.
    2. The Twelve Days of Christmas and Pascal's Triangle - Discrete Mathematics (VI.2.MS.4)
      Using Pascal's triangle, find the number of items given each day in the song, "The 12 Days of Christmas". This is a teacher lesson plan.
    3. Tower of Hanoi - Discrete Mathematics (VI.2.MS.4)
      The Tower of Hanoi puzzle was invented by the French mathematician Edouard Locas in 1883. We are given a tower of eight disks, initially stacked in decreasing size on one of three pegs, moving only one disk at a time and never a larger one onto a smaller. The puzzle is well known to students of Computer Science since it appears in virtually any introductory text on data structures of algorithms. Its solution touches on two important topics discussed later on: recursive functions and stacks; & recurrence relationships. This is a student activity.
    4. Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond - Discrete Mathematics (VI.2.MS.4)
      This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. Graphs, equations, tables, and technological tools are used to investigate the effect of varying parameters on the long-term population. Students will complete a numerical analysis, a graphical analysis, and a symbolic analysis from the data.
  5. Benchmark 5. "Continue to use manipulatives and drawings to model the concepts and procedures for the standard arithmetic algorithms, and develop and analyze their own and other students' algorithms to accomplish a task or solve a mathematical problem."
    1. Discrete Math Project - Discrete Mathematics (VI.2.MS.1,2,3,4,5&6)
      This site is an excellent resource for teacher lesson plans for discrete math.
    2. Euclid's Game - Discrete Mathematics (VI.2.MS.5)
      Great interactive alogrithm game.  This also introduces students to the great mathematician Euclid.
    3. Fibonacci Numbers - Discrete Mathematics (VI.2.MS.5&6)
      From this table of contents page, you can choose which activity involving Fibonacci's work you would like students to explore.  The marked activities are student interactive activities.
    4. The Most Colorful Map of All - Discrete Mathematics (VI.2.MS.1,3,5,&6)
      This lesson allows you to connect reading and mathematics in a fun and interesting way. Map coloring is used as a way of stimulating student's to think logically and to use strategies to solve problems which are both interesting and pertinent. Excellent resources are included for the teacher to use, copy, and share.
    5. Welcome to the Hotel Infinity - Discrete Mathematics (VI.2.MS.1,3,5&6)
      This lesson allows you to connect reading and mathematics in a fun and interesting way. The Hotel Infinity story is shared with students (copies can be made for their use) to raise questions about the logic and mathematics found in the text. Teacher resources are include vocabulary, background information, and questions to expand student thinking about the story.
  6. Benchmark 6. "Use discrete mathematics concepts as described above to model situations and solve problems; and look for whether or not there is a solution (existence problems), determine how many solutions there are (counting problems) and decide upon a best solution (optimization problems)."
    1. Count On - Discrete Mathematics (VI.2.MS.6)
      This game is an ancient one and students love it.  The Tower of Hanoi allows students to practice solving problems using a model and determine the best outcome.  This is an excellent discrete mathematics activity.  This particular site offers wonderful graphics and the game pieces are easy to manipulate. To get to this particular game once one has pulled up the Count On homepage, click on games, click on Virtual MathFest, and finally click on The Tower of Hanoi.
    2. Discrete Math Project - Discrete Mathematics (VI.2.MS.1,2,3,4,5&6)
      This site is an excellent resource for teacher lesson plans for discrete math.
    3. Fibonacci Numbers - Discrete Mathematics (VI.2.MS.5&6)
      From this table of contents page, you can choose which activity involving Fibonacci's work you would like students to explore.  The marked activities are student interactive activities.
    4. Games on Graphs - Discrete Mathematics (VI.2.MS.3&6)
      This lesson uses games to explore graphs. Stories are used to inspire students to create a game to simulate the story. A variety of example game boards using graphs are included along with background information for the teacher. Lesson plans include big ideas and follow-up questions along with more games for continued use. Students are asked to think logically about the number of possible outcomes and a problem which can be examined over time is included.
    5. The Ice Cream Stands Problem - Discrete Mathematics (VI.2.MS.3&6)
      The Ice Cream Stands Problem: This problem involves planning for efficiently using resources. There are many solutions to the problem, although the solutions that require the least amount of resources will be the best ones for the problem as stated. Various strategies can be used to approach the problem, and no single strategy is better than all the rest. This is a teacher lesson plan.
    6. The Most Colorful Map of All - Discrete Mathematics (VI.2.MS.1,3,5,&6)
      This lesson allows you to connect reading and mathematics in a fun and interesting way. Map coloring is used as a way of stimulating student's to think logically and to use strategies to solve problems which are both interesting and pertinent. Excellent resources are included for the teacher to use, copy, and share.
    7. Welcome to the Hotel Infinity - Discrete Mathematics (VI.2.MS.1,3,5&6)
      This lesson allows you to connect reading and mathematics in a fun and interesting way. The Hotel Infinity story is shared with students (copies can be made for their use) to raise questions about the logic and mathematics found in the text. Teacher resources are include vocabulary, background information, and questions to expand student thinking about the story.

| Back | Next |