Transcript Chapter 1.1 Geometry

Warm up
• In your numbered group, please discuss and answer
the following questions
• 1) What is “pattern”? What do you think it has to do
with Geometry?
• 2) Give some examples of “patterns” you can think of
• 3) What do you guys think of these statements:
– Lebron James is the best basketball player
– Kanye West is a music genius
Chapter 1.1 Patterns and
Inductive Reasoning
Vocabulary
• Inductive reasoning = reasoning that is based
on patterns you observe
• Conjecture = conclusion you reach using
inductive reasoning
Example #1
• Find a pattern for each sequence, use the
pattern to show the next two terms in the
sequence
• A) 3, 6, 12, 24….
• B) 1, 2, 4, 7, 11, 16, 22…
Example #3 Do it with a partner
• Find the pattern, then state what number comes
next
– A) 1, 4, 16, 64, 256…?
– B) 4, 9, 16, 25, 36, 49…?
– C) 30, 10, 3.33, 1.11, 0.370…? (Think carefully)
• Clue: First check for addition, then subtraction,
then multiplication, then division. Also think of
perfect squares or cubed numbers, or exponents
Vocabulary
• Counterexample = an example that for which the
conjecture (conclusion) is incorrect
• Example:
• Statement: “The difference of two integers is less
than either integer”
• Conclusion: False because -5-(-6) = 1 and 1>-5
and 1>-6
Example #2
• Find the next shape
?
Example
• Can you find a counterexample?
• 1) The square of any number is greater than
the original number
• 2) You can connect any three points to form a
triangle
Homework
• P6 #1, 3, 5, 9, 11, 17, 19, 23, 25, 27, 29