Download It`s all about discovering patterns….

Notes 2.1 & 2.3
Geometry
Inductive Reasoning
It’s all about discovering patterns….
A skateboard shop finds that for 5 consecutive months, sales of skateboards with small wheels decreased.
January: 58
February: 55
March: 51
April: 48
May: 45
Use the information to make a reasonable conclusion about the number of small-wheeled skateboards the
shop will sell in June.
Conclusion:
Find the next two items in the pattern
0.4, 0.04, 0.004, ….
When you begin to notice a pattern and assume the pattern will continue, you are using:
Conjecture:
Counterexample:
Complete each conjecture:
1. The product of an even number and an odd number is________________.
2. Raising (-1) to an odd exponent will always result in _________________.
3. Use inductive reasoning to find the last digit of
2 85 . Then try 254 .
Write or draw a counterexample for the following conjectures:
4. You can connect any three points to form a triangle.
Counterexample:
5. For all positive numbers n,
1
n
 n.
Counterexample:
6. For any real number x , x 2  x .
7. Supplementary angles are adjacent.
Counterexample:
Counterexample:
Describe the patterns you notice in the following examples. Use the pattern to write the next 3 terms.
Describe the pattern
2, 4, 7, 11, …..
1, 2, 4, 5, 10, 11, 22….
Next three terms
To prove a conjecture FALSE all we need is one ________________________________.
To prove a conjecture TRUE we begin by using______________________________________. Just
because we observe a pattern does not mean that that pattern will continue over time.
Deductive Reasoning:
What’s the difference between Inductive and Deductive reasoning?
INDUCTIVE
DEDUCTIVE
* Observe data and notice a
pattern forming.
* You use facts or definitions…things
that are already known to be true.
* Conjectures are based off of
observing specific events and
making a generalizations about
them.
* You start with the general, and move
to the specific.
Example: “I've noticed previously
that every time I kick a ball up,
it comes back down, so I guess
this next time when I kick it up,
it will come back down, too.”
Example: “That's Newton's Law.
Everything that goes up must come
down. And so, if you kick the ball up, it
must come down.”
Determine whether the following Urban Legends are confirmed or disproved by using inductive or deductive
reasoning…
A. There is a myth that toilets and sinks drain in opposite directions in the Southern and Northern
Hemispheres. However, if you were to observe sinks draining in the two hemispheres, you would see
that this myth is FALSE!.
Inductive
or
Deductive
B. There is a myth that you should not touch a baby bird that has fallen from its nest because the
mother bird will disown the baby if she detects human scent. However, biologists have shown that
birds cannot detect human scent. Therefore, the myth is FALSE!.
Inductive
or
Deductive
Determine whether the following are confirmed or disproved by using inductive or deductive reasoning…
C. There is a myth that the Great Wall of China is the only man-made object visible from the Moon.
The Great Wall is barley visible in photographs taken from180 miles above the Earth. The Moon is
about 237,000 miles from the Earth. Therefore, the myth cannot be true.
Inductive
or
Deductive
D. There is a myth that you can balance an egg on its end only on the spring equinox (March 20). A
person was able to balance an egg on July 8, September 21, and December 19. Therefore, this myth
is false.
Inductive
or
Deductive
E. The Mavericks scored over 75 points in each of ten straight games. The newspaper predicts that
they will score more than 75 points tonight.
Inductive
or
Deductive
F. In the Dripping Springs course description manual, a student must take Theater 1 before Theater 2.
Lauren is in Theater 2, so Joseph concludes that she has taken Theater 1.
Inductive
or
Deductive