Lesson plan(s) idea(s) (THIS WILL CHANGE!)

Pattern Investigations - Discrete Math Concepts

---PRE-METACOGNITION (awareness of process):

Show a few examples that students have seen.

What do you think it is?  Write a narrative about something you have seen like this.

What is still confusing beofre we start new material?

---SPIRAL LEARNING:

These exercises/investigations can be spiraled since various aspects of the same problem can be presented age appropriate.

Many exercises in drawing, coloring (B/W & color), ... explaining pictures and patterns

Picture is worth a thousand words.

Can this pattern be formalized (GANV-Graphically/Analytically/Numeric/Verbal)?

How?

Basis of pattern:

• Rules?
• Iterative?
• Recursive?
• Closed form? mathematical, pattern, ...
• Can you program this? - Excel, graping package, IDE or programming environment, language
• Visualization?
• Specializations-->Generalizations?
• Convergence/Divergence? (rate of convergence/divergence, like scaling)
• Model
•  

 Extra thoughts - extensions:

• virtual manipulatives
•  

---POST-METACOGNITION:

Explain what you learned.  How did you learn? Can you explain this to someone and have them know about

How did your ideas change?

Can you extend this thinking to other problems?  Generalization(s).

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APPLICATION TOPICS:

Fratal (easy) - dimensionality

Measuring 1D dimension - use maps with a series of grid overlays to count the length of the UK main island

Pascal's triangle - modulo math, each small group gets to color on transparency with a different mathematical pattern, what is the pattern in the the group?  Is it better as a chart of number or as a picture, overlay transparencies

Serpinski Triangle/Gasket (what dimension between 1 and 2) - ___ - extension: 3D Serpenski tetrahedron a shape you can wrap your arms around (fixed dimension), but has infinite surface area (dimension between 2 and 3 or 3 and 4?) - is there a pattern to it's growth (geometric) - make a big the Serpinksi Tetrahedon with small envelopes.

_____ - extension: 3D Menger Sponge (what dimension)

four-color map problem

2D triangular fractals (Sierpinski traingle/gasket)

Conway's Game of Life (2D Cellular Automata) --> 1D CA

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 Some of the math textbook vendors have added a chapter on discrete math in their textbooks, but they tent to be cursory.