1. Patterns and Inductive Reasoning
SpringBoard Lesson 1-2
Patterns and Inductive Reasoning
Objectives:
1) To use inductive reasonings to make conjectures.

2. Ex. 1: Find the next term in the sequence:
Inductive Reasoning – Is reasoning that is based on patterns you observe.
If you observe a pattern in a sequence you can use inductive reasoning to find the next term.
Ex. 1: Find the next term in the sequence:
A) 3, 6, 12, 24, ___, ___
B) 1, 2, 4, 7, 11, 16, 22, ___, ___ C) 48 96
Rule: x2 29 37
Rule: +1, +2, +3, +4, …

3. Conjecture – A conclusion you reach using inductive reasoning.
Inductive Reasoning assumes that an observed pattern will continue. This may or may not be true.
Ex: x = x • x
This is true only for x = 0 and x = 1
Conjecture – A conclusion you reach using inductive reasoning.

4. Ex. 2: Make a conjecture about the sum of the first 30 odd numbers.
= 12
= 22
= 32
= 42
= 52
= 302
1 = 1
= 4
= 9
= 16
= 25 =
900

5. To show that a conjecture is always true, you must prove it.
To show that a conjecture is false, you have to find only one example in which the conjecture is not true. This case is called a counterexample.
A counterexample can be a drawing, a statement, or a number.

6. Counter Example – To a conjecture is an example for which the conjecture is incorrect.
Ex.1-3: The first 3 odd prime numbers are 3, 5, 7. Make a conjecture about the 4th.
3, 5, 7, ___
One would think that the rule is add 2, but that gives us 9 for the fourth prime number.
Is that true?
What is the next odd prime number? 11

7. Each year the price increased by $1.50.
GEOMETRY LESSON 1-1
The price of overnight shipping was $8.00 in 2000, $9.50 in 2001, and $11.00 in Make a conjecture about
the price in 2003.
Write the data in a table. Find a pattern.
2000
$8.00
2001
2002
$9.50
$11.00
Each year the price increased by $1.50.
A possible conjecture is that the price in 2003 will increase by $1.50.
If so, the price in 2003 would be $ $1.50 = $12.50.
1-1

8. Inductive Reasoning
1. Look for a pattern.
2. Make a conjecture.
3. Prove the conjecture or find a counterexample.