Download C1 Inductive Reasoning

DRILL
a)
b)
c)
d)
1, 3, 5, 7, 9, __, __
2, 5, 8, 11, 14, __, __
-3, -6, -10, -15, __
,
,
, __
OBJ: SWBAT use inductive reasoning in order to
identify patterns and make conjectures.
UNIT C
INDUCTIVE REASONING
Mr. Calise
Geometry
MOTIVATION
How
quickly can you add the odd
numbers from 1 – 20?
1
= 1
1+3
= 4
1+3+5
= 9
1+3+5+7
= 16
1 + 3 + 5 + 7 + 9 = 25
2
=1
2
=2
2
=3
2
=4
2
=5
NOTES
Inductive Reasoning: Allows you to reach
conclusions based on a pattern of specific
examples.
Ex: Each morning you see your friend
eating Cheerio’s for breakfast. You see
this everyday for 3 weeks.
The next day what do you
expect to see when you
see your friend?
*Does that mean it will definitely happen?
Conjecture: A
conclusion reached using
inductive reasoning.
Example: Make a conjecture
about the shapes.
Points Regions
2
3
4
5
6
2
4
3
12
11
10
13
27
9
8
14
28
1
26
15
16
17
29
2
31
25
30
18
19
24
22
23
7
21
20
6
5
TRUE OR FALSE?
 All
teachers are taller than students.
 Can
anyone prove this?
 Counterexample:
is something
that disproves a conjecture.
A counterexample can be a drawing, a
statement, or a number.
-Only one counterexample is needed to
disprove a statement.
COUNTER EXAMPLE SONG
TEXT MESSAGES
 On
average, how many
text messages do you
send in a month?
 Based
on our data, high
school students send at
least ______ text messages
a month.
 Is
this a true statement?
 What
could be a
counterexample?
Show that the conjecture is false by finding a
counterexample.
Two complementary angles cannot be
congruent.
0
45
0
45
Lesson Quiz
Find the next item in each pattern.
1. 0.7, 0.07, 0.007, … 2.
0.0007
Determine if each conjecture is true. If false,
give a counterexample.
3. The quotient of two negative numbers is a positive
number. true
4. Every prime number is odd. false; 2
false;
5. Two supplementary angles are not congruent. 90° and
90°
6. The square of an odd integer is odd. true
FOLLOW THIS PATTERN
 1.
0, 2, 4, 6, 8, _____, _____
 2. 1, 2, 4, 7, 11, _____, _____
 3. 16, 8, 4, 2, 1, _____, _____
 4. 1, 1, 2, 3, 5, 8, _____, _____
 5. 4, –4, 4, –4, 4, _____, _____
 6. 1, ½ , ¼ , ⅛, _____, _____
 7. 1, 10, 100, 1000, 10000, ____, ____
 8. 1, 8, 27, 64, 125, _____, _____
 9. 1, 3, 6, 10, _____, _____
 10. 27, 9, 3, 1, _____, _____
FOLLOW THIS PATTERN
 11.
 12.
 13.
 14.
 15.
 16.
 17.
 18.
 19.
 20.
49, 36, 25, 16, _____, _____
a, c, e, g, i, _____, _____
3, 5, 7, 9, 11, _____, _____
11, _____, 5, 2, _____, –4, –7
1, 3, 9, 27, 81, _____, _____
J, F, M, A, _____, _____
3, –6, 12, –24, 48, _____, _____
8, 7, 5, 4, 2, _____, _____
1/2, 2/4, 3/6, 4/8, _____, _____
1, 6, 11, 16, 21, _____, _____