Download 2-1 Patterns and Inductive Reasoning

2-1 Patterns and Inductive Reasoning
Inductive Reasoning

_______________ _______________ is reasoning based on _______________ you _______________.
Finding and Using a Pattern
Problem 1
Look for a pattern. What are the next two terms in the sequence?
a) 3, 9, 27, 81, …
b) 45, 40, 35, 30, …
c)
d)
Conjecture
 A _______________ is a _______________ you reach using _______________ reasoning.
Using Inductive Reasoning
Problem 2
a) Make a conjecture about the number
regions 20 diameters form.
b) Make a conjecture about the 21st term
in Red, White, Blue, Red, White, Blue, … .
Collecting Information to Make a Conjecture
Problem 3
a) What conjecture can you make about the sum
of the first 30 even numbers?
b) What conjecture can you make about the sum
of the first 30 odd numbers?
Number of Terms
1
2
3
4
5
6
Sum
Each sum is the _______________ of the number
of terms and the number of terms ___________ one.
Number of Terms
1
2
3
4
5
6
Sum
The sum is the number of terms _______________.
Making a Prediction
Problem 4
a) Sales of backpacks at a nationwide company decreased over a period of 6
consecutive months. What conjecture can you make about the number of
backpacks the company will sell in May?

Sales decrease by about ________ _______________ a _______________.

______ sales will be about _______________ _______________.
b) What conjecture can you make of sales in June?
c) is it reasonable to use this graph to make a
conjecture about sales in August?

About ________ fewer sold
_______. The graph does not ________ _________
_______________.
Also, _______________ _______________ in
August so sales might _______________.
Counterexample

A ____________________ is an example that shows that a conjecture is _______________.
Finding a Counterexample
Problem 5
Find a counterexample.
a) If the name of a month starts with J,
then it is a summer month.
b) You can connect ANY three points to form a
triangle.
c) When you multiply by a number by 2,
the product is greater than the original
number.
d) If an animal is green, then it is a frog.