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geom­sept9­2.notebook
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September 09, 2015
What is the greatest number of pieces a pizza can be divided into by making only 6 straight cuts? (The pieces do not have to be the same shape.)
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What are the next three terms in this sequence?
Vocabulary
1, 1, 2, 3, 5, 8, 13, ...
inductive reasoning ­ collecting evidence,
observing patterns, and drawing conclusions
from these observed patterns
conjecture ­ a conclusion you reach by
inductive reasoning
Describe the pattern.
counterexample ­ an example for which a
conjecture is false
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Adding a Fibonacci Sequence
Leonardo Fibonacci
de Pisa
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Leonardo Fibonacci
de Pisa
4
7
11
18
29
47
76
123
199
322
• Step 1: Pick two numbers between 1 and 9 and write
one on top of the other.
• Step 2: Keep adding the bottom two numbers, until
you have a total of ten numbers.
• Step 3: To add the numbers in the column, look at the
7th number from the top, which is the 4th
from the bottom.
• Step 4: Add the tens digit to the number. 76 + 7 = 83
• Step 5: Simply tack on the ones digit of the original
number to get the sum. 836 in our example
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geom­sept9­2.notebook
September 09, 2015
True or False?
The reciprocal of a number is always less than the number itself.
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geom­sept9­2.notebook
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Using Inductive Reasoning to Make Conjectures
Using the Segment Addition Postulate
Find the next item in each pattern.
1.
2, 4, 6, 8, . . . 2.
Z, Y, X, . . .
3.
fall, winter, spring, . . .
_______________
_______________
_______________
4.
When several examples form a pattern and you assume the pattern will continue, you are applying _______________. 5.
A statement you believe to be _______________ based on inductive reasoning is called a conjecture. For Exercises 6–8, complete each conjecture by looking for a pattern in the examples.
6.
The sum of two odd numbers is _______________.
3 + 5 = 8
13 + 3 = 16
1 + 1 = 2
7.
The number of sides of a polygon that has n vertices is _______________. Book example problem:
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clear title of topic
writing (by hand) on white background
mounted onto darker colored poster backing
neat & complete
good balance, composition, and design
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