2-1 inductive reasoning & conjecture inductive reasoning is reasoning that uses a number of...
TRANSCRIPT
1
2-1 Inductive Reasoning & Conjecture
INDUCTIVE REASONING is reasoning thatuses a number of specific examples to arrive at a conclusion
When you assume an observed pattern will continue, you are using
INDUCTIVE REASONING.
2
2-1 Inductive Reasoning & Conjecture
A CONCLUSION reached usingINDUCTIVE REASONING is called aCONJECTURE.
3
2-1 Inductive Reasoning & Conjecture
Example 1Write a conjecture that describes the pattern in each sequence.
Use your conjecture to find the next term in the sequence.
4
2-1 Inductive Reasoning & Conjecture
Example 1aWhat is the next term?3, 6, 12, 24,
Conjecture: Multiply each term by 2 to get the next term.
The next term is 24 •2 = 48.
5
2-1 Inductive Reasoning & Conjecture
Example 1bWhat is the next term?
2, 4, 12, 48, 240Conjecture:
To get a new term, multiply the previous number by the position of the new number.The next term is 240•6 =1440.
6
2-1 Inductive Reasoning & ConjectureExample 1c
Conjecture: The number of small trianglesis the perfect squares.
9,4,13,2,1 222
?1 4 9
What is the next
shape?
7
2-1 Inductive Reasoning & Conjecture
The next big triangle should have _____ little triangles.
=16
94
1
8
2-1 Inductive Reasoning & Conjecture
EX 2Make a conjecture about each value or geometric relationship. List or draw some examples that support your conjecture.
9
2-1 Inductive Reasoning & Conjecture
EX 2aThe sum of an odd number and an even number is __________.
Conjecture: The sum of an odd number and an even number is ______________.
an odd numberExample: 1 +4 = 5Example: 26 +47 = 73
10
2-1 Inductive Reasoning & Conjecture
EX 2bFor points L, M, & N, LM = 20, MN = 6, AND LN = 14.
L MN
14 6
20
11
2-1 Inductive Reasoning & Conjecture
Conjecture: N is between L and M. OR
L, M, and N are collinear.
L MN
12
2-1 Inductive Reasoning & Conjecture
Assignment:p.93 – 96 (#14 – 30 evens, 40 – 44, 64 – 66 all)
13
2-3 Conditional Statements
CONDITIONAL STATEMENTA statement that can be written in if-then form
An example of a conditional statement: IF Portage wins the game tonight, THEN we’ll be sectional champs.
14
2-3 Conditional Statements
HYPOTHESISthe part of a conditional statement immediately following the word IF
CONCLUSIONthe part of a conditional statement immediately following the word THEN
15
2-3 Conditional StatementsExample 1
Identify the hypothesis and conclusion of the conditional statement.
a.) If a polygon has 6 sides, then it is a hexagon.
Hypothesis: a polygon has 6 sidesConclusion: it is a hexagon
16
2-3 Conditional StatementsExample 1 (continued)
b.) Joe will advance to the next round if he completes the maze in his
computer game.Hypothesis: Joe completes the maze in his
computer gameConclusion: he will advance to the next
round
17
2-3 Conditional StatementsExample 2Write the statement in if-then form, Then identify the hypothesis and conclusion of each conditional statement.
18
2-3 Conditional Statementsa.) A dog is Mrs. Lochmondy’s favorite animal.If-then form:
If it is a dog, then it is Mrs. Lochmondy’s favorite animal.Hypothesis:
it is a dogConclusion:
it is Mrs. Lochmondy’s favorite animal
19
2-3 Conditional Statementsb.) A 5-sided polygon is a pentagon.If-then form:
If it is a 5-sided polygon then it is a pentagon.Hypothesis:
it is a 5-sided polygonConclusion:
it is a polygon
20
2-3 Conditional Statements
CONVERSE:The statement formed by exchanging thehypothesis and conclusion
21
2-3 Conditional StatementsExample 3Write the conditional and converse of the statement.
Bats are mammals that can fly.Conditional:
If it is bat, then it is a mammal that can fly.Converse:
If it is a mammal that can fly, then it is a bat.
22
2-3 Conditional Statements
Assignment:p.109-111(#18 – 30, evens50, 52)
23
2-4 Deductive Reasoning
24
2-4 Deductive Reasoning
25
2-4 Deductive Reasoning
26
2-4 Deductive Reasoning
27
2-4 Deductive Reasoning
28
2-4 Deductive Reasoning
29
2-4 Deductive Reasoning
30
2-4 Deductive Reasoning