Download Geometry - Garnet Valley School District

Geometry A Unit 1 Day 1 Notes
1.1 Patterns and Inductive Reasoning
Patterns can be expressed visually, numerically, verbally and using formulas.
I. INDUCTIVE THINKING - _____________________________________________
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A. CONJECTURE - _______________________________________________
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1) COUNTEREXAMPLE - ___________________________________
___________________________________________________________.
2) Give a counter-example to the statement:
"Even numbers are divisible by 3."
_______________
3) Give a counterexample to the statement:
"If you've been to Florida, then you've been to Disneyworld".
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2. Visual Patterns/ Expressing Patterns Verbally
A)
1) Sketch the next figure in the series.
2) Describe the pattern you saw that led you to your conjecture.
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3. Numeric Patterns/ Expressing Patterns Verbally - In each example, give the next two
numbers in the series, then describe the pattern you observed.
1, 4, 16, 64, _________, _________ . Describe the pattern you continued in words.
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-5, -2, 4, 13, _________, _________ . Describe the pattern you continued in words.
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II. More examples of multiple representations of patterns.
A. Verbal/Visual/Numeric
In each pattern, a specific number of toothpicks are used to create a pattern. Find the
number of toothpicks in each figure and make a conjecture about the number of
toothpicks needed to make the next figure.
m
Figure 1:
Number of toothpicks: __________
Figure 2:
Number of toothpicks: ___________
Figure 3:
Number of toothpicks: ____________
Figure 4:
Number of toothpicks: ____________
B. Numeric/Formula
1. Find the sum of the first 50 odd numbers.
a. The problem above can be found by brute force, but a pattern in smaller
questions might lead to an observation that cuts our work considerably.
Find the sum of the first 1 odd numbers.
1
Find the sum of the first 2 odd numbers. ________
Find the sum of the first 3 odd numbers. _______
Find the sum of the first 4 odd numbers.
________
- These smaller examples suggest a formula. Sum of first n odd integers = ___________
Find the sum of the first 50 odd numbers. _______________
C. Formula/Visual/Numeric
1. Complete the chart to find and plot three points on the graph of the line y = 2x - 3.
Then find two more points by continuing the visual or numeric patterns.
x
y
1
0
1
HW: Geometry A
Unit 1 Day 1 HW