Chapter 1.1 patterns and inductive reasoning
Upcoming SlideShare
Loading in...5
×
 

Like this? Share it with your network

Share

Chapter 1.1 patterns and inductive reasoning

on

  • 1,329 views

 

Statistics

Views

Total Views
1,329
Views on SlideShare
1,329
Embed Views
0

Actions

Likes
0
Downloads
9
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Chapter 1.1 patterns and inductive reasoning Presentation Transcript

  • 1. Find a pattern for each sequence. Use the pattern to show the next 2 terms.
    5, 10, 20, 40, …
    1, 2, 6, 24, 120, …
    1, 3, 7, 13, 21, …
    M, V, E, M, …
    80, 160
    720, 5040
    31, 43
    J, S
  • 2. What did you just do?
  • 3. 1-1 Patterns and Inductive Reasoning
    LEQ: How do you use inductive reasoning to make conjectures?
  • 4. What is inductive reasoning?
    Reasoning that is based on patterns you observe.
    U
  • 5. Example: Finding and using a pattern. Use the pattern to show the next 2 terms in the sequence.
    3, 6, 12, 24, …
    48
    96
  • 6. 1, 2, 4, 7, 11, 16, 22, …
    29
    37
  • 7. Monday, Tuesday, Wednesday,…
    Thursday
    Friday
  • 8. What is a conjecture?
    A conclusion you reach using inductive reasoning.
  • 9. Example: Using Inductive Reasoning. Make a conjecture about the sum of the first 30 odd numbers.
    Find the first few sums. Notice that each sum is a perfect square.
    1 = 1 =
    1 + 3 = 4 =
    1 +3 + 5 = 9 =
    Using inductive reasoning you can conclude that the sum of the first 30 odd numbers is 30 squared, or 900.
  • 10. What is a counterexample?
    An example for which the conjecture is false.
    You can prove that a conjecture is false by finding one counterexample.
  • 11. Example: Testing a conjecture and finding a counterexample.
    If it is cloudy, then it is raining.
    It is cloudy and it is not raining.
  • 12.
    • If the day of the week is Monday, I will be in a bad mood.
    This Monday is Labor Day, which means that there is no school, which means that I will most definitely be in a good mood.
  • 13. Writing Prompt:
    Explain how you would use inductive reasoning to create a conjecture.
  • 14. Homework:
    Pgs. 6 – 7 #s 2 – 46 even.