2-1: Patterns and
Inductive Reasoning
White Board Work
Solve each equation for the variable
𝒙𝟐 − 𝟏𝟔 = 𝟎 𝟐𝒚𝟐 + 𝟐 = 𝟕𝟒 𝒈𝟐 − 𝟐𝒈 − 𝟏𝟓 = 𝟎
Objectives for this Lesson
• Use inductive reasoning to make conjectures.
• Use counterexamples to prove conjectures false.
Inductive Reasoning
Humans are wired to notice patterns.
When we recognize patterns, we can often use
them to make predictions (
). This is
part of what scientists do.
This is called
.
Recognizing Patterns
What’s the next one?
Recognizing Patterns
Recognizing Patterns
What’s the next one?
Recognizing Patterns
Conjectures are not always right!
Try it
Look for a pattern. What are the next two
terms in each sequence?
3, 9, 27, 81,
1, -2, 4, -8, 16,
Try it
Look for a pattern. What are the next two
terms in each sequence?
3, 9, 27, 81,
1, -2, 4, -8, 16,
Counterexamples
A
is an example that shows a
conjecture is incorrect (false).
I notice a pattern. Whenever I make 3 dots, I can
connect them to make a triangle. So I make the
conjecture that any 3 points form a triangle.
Is this a true conjecture? Can you think of a
counterexample?
True of False?
Only 1 counterexample is needed to state
that a conjecture is false.
We only say a conjecture is true if it is
always true.
Provide a Counterexample
1. If the name of a month starts with a J,
then it is a summer month.
2. If 𝑥 2 = 9, then 𝑥 = 3.
3. If 𝐴𝐵 ≅ 𝐵𝐶, then 𝐵 is the midpoint of
𝐴𝐶.
Do the 2-1 assignment in MathXL