Systematic Listing and Counting

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Discrete Mathematics

• Systematic Listing and Counting
• Vertex Edge Graphing

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What is Discrete Math?
Discrete mathematics is the branch of mathematics
that deals with arrangements of distinct objects.
It includes a wide variety of topics and
techniques that arise in everyday life, such as
how to find the best route from one city to
another where the objects are cities arranged on
a map. It also includes how to count the number
of different combinations for toppings for
pizzas, how to best schedule a lists of tasks to
be done, and how computers store and retrieve
arrangements of information on a screen.
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What is Discrete Math?
Discrete mathematics is the mathematics used by
decision makers in our society, from workers in
government to those in health care,
transportation, and telecommunications. Its
various applications help students see the
relevance of mathematics in the real world.
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Themes of Discrete Mathematics

• Systematic Listing and Counting
• Using Discrete Mathematical Models
• Applying Iterative Patterns and Processes
• Organizing and Processing Information
• Finding the Best Solution Using Algorithms

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Systematic Listing and Counting

• Elementary students should be able to make a list
  of all the possible outcomes of a simple
  situation such as the number of outfits that can
  be worn using two coats and three hats.

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Using Discrete Mathematical Models

• Elementary students should recognize that a
  street map can be represented by a graph and that
  routes can be represented by paths in graphs.

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Applying Iterative Patterns and Processes

• Elementary students should be able to recognize
  and investigate sequences on pinecones and
  patterns on floor tiling.

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Organizing and Processing Information

• Elementary students should be able to investigate
  ways to represent and classify data according to
  attributes like color or shape, using
  relationships like family trees, and into
  structures like tables

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Finding the Best Solution Using Algorithms

• Elementary students should be able to discuss
  different ways of dividing up a pile of snacks,
  and should determine the shortest path from one
  site to another on a map laid out on a classroom
  floor

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Discrete Math Technology Standards

• Standard 3 Students use technology tools to
  enhance learning, to increase productivity and
  creativity and to construct technology-enhanced
  models, prepare publications and to produce other
  creative works.
• Standard 6 Students use technology to make and
  support decisions in the process of solving
  real-world problems.

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Systematic Listing andCounting

• What are some ideas you have
• about items that can be combined?

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Cookie Combinations
Today we will be making different cookies to
eat. We have sugar cookies. On our cookies we
will spread one kind of frosting, vanilla or
chocolate. We will also put one kind of
sprinkle, chocolate or red/white/blue. How
many different cookie combinations can we make?
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Other Combination Ideas

• Ice Cream Sundae Scoops, Mix-In,
  Double/Triple Dip
• Fish Bowl
• Flower Bouquet
• Outfits
• Line Order

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Systematic Listing andCounting

• Do you have additional ideas about items that can
  be combined?
• Each group will take one of the ideas from the
  list and write a problem that would be
  appropriate for kinder or 1st grade.
• PO 1. Make arrangements that represent the
  number of
• combinations that can be formed by pairing items
  taken from
• 2 sets, using manipulatives (e.g., How many
  outfits can one
• make with 2 different color shirts and 2
  different pairs of
• pants?).

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Math for Us

• Probability Grand Prix

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Vertex Edge Graphing

• What is it???
• Reasoning and thought processes that you use
  when
• constructing a seating chart
• make a schedule for a field trip or conferences
• determine the order and route for your errands

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Vertex Edge Graphing

• What are the fewest number of colors needed so
  that no touching edges share the same color on
  each design? Do you notice any patterns?
• Construct designs of your own that would need to
  be colored with 2, 3, 4, and 5 colors.

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Vertex Edge Graphing with Children

• What question/prompt might you pose to children
  to help them complete a vertex edge design?
• How could the performance objective be written in
  kid friendly language?
• PO 1. Color pictures with the least number of
  colors so that no common edges share the same
  color (increased complexity throughout grade
  levels).

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Vertex Edge Graphing with Children

• Elmer the Patchwork Elephant
• Flags
• Tesselations
• Quilts

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Vertex Edge Graphs

• Vertex Coloring

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Different or Shortest Routes

• Dora the Explorer
• Tarp Map
• The Princess and the Tiger

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AIMS Sample S2C3 (Gr. 3)
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AIMS Sample S2C3 (Gr. 3)
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AIMS Sample S2C3 (Gr. 4)
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AIMS Sample S2C3 (Gr. 5)
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AIMS Sample S2C3 (Gr. 5)
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AIMS Sample S2C4 (Gr. 3)
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AIMS Sample S2C4 (Gr. 4)
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AIMS Sample S2C4 (Gr. 4)
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AIMS Sample S2C4 (Gr. 5)
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AIMS Sample S2C4 (Gr. 5)