Starting Point 1'1

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Starting Point 1.1
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Chapter 1 Section 1 Vocabulary

• Exercise
• Problem
• Strategy
• POLYAS FOUR STEP PROCESS
• 1) Understand The Problem
• 2) Devise A Plan
• 3) Carry Out The Plan
• 4) Look Back

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Devise A Plan

• Guess and Test
• Draw a Picture / Diagram
• Use a Variable
• Look for a Pattern
• Make a List
• Solve a Simpler / Equivalent Problem
• Use Reasoning Direct / Indirect
• Use Properties of Numbers
• Work Backwards

• Use Cases
• Solve an Equation
• Look for a Formula
• Do a Simulation
• Use a Model
• Use Dimensional Analysis / Conversion Factors
• Identify Subgoals
• Use Coordinates
• Use Symmetry

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Figure 1.1
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More Vocabulary

• Cryptarithm collection of words where letters
  represent numbers p.8
• Tetromino shape made up of four squares where
  the squares must be joined along an entire side
  p.10
• Variables / Unknowns
• Equation
• Solution
• Solve an Equation

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Starting Point 1.2
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Chapter 1 Section 2 Vocabulary

• Different
• Pascals Triangle
• Sequence
• Terms
• Counting Numbers
• Ellipsis
• Fibonacci Sequence
• Inductive Reasoning
• Sierpinski Triangle / Sierpinski Gasket

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Pascals Triangle
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Why is it that the number of petals in a flower
is often one of the following numbers 3, 5, 8,
13, 21, 34 or 55? The explanation is linked to
another famous number, the golden mean, itself
intimately linked to the spiral form of certain
types of shell. Let's mention also that in the
case of the sunflower, the pineapple and of the
pinecone, the correspondence with the Fibonacci
numbers is very exact, while in the case of the
number of flower petals, it is only verified on
average (and in certain cases, the number is
doubled since the petals are arranged on two
levels).
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Fibonnaci Sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,
...
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Sierpinski Triangle / Sierpinski Gasket
Start with a solid (filled) equilateral triangle
fig 1. Divide this into four smaller
equilateral triangles using the midpoints of the
three sides of the original triangle as the new
vertices. Remove the interior of the middle
triangle (that is, do not remove the boundary)
fig 2. Now repeat this procedure on each of the
three remaining solid equilateral triangles to
obtain fig 3. Keep repeating the process on each
triangle fig 4, 5.
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Figure 1.27
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Section 1.2/Problem Set A/3a
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Section 1.2/Problem Set A/3b
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Section 1.2/Problem Set B/2a