Patterns and Inductive Reasoning

1 / 15

# Patterns and Inductive Reasoning - PowerPoint PPT Presentation

Patterns and Inductive Reasoning. Inductive reasoning. Reasoning that is based on patterns you observe. Example: 2,5,8,11,… What do you see? How do you know? Justify. Conjecture. A conclusion you reach using inductive reasoning. Example: 1 = 1 = 1x1 1 + 3 = 4 = 2x2

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Patterns and Inductive Reasoning' - bud

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Patterns and Inductive Reasoning

Inductive reasoning
• Reasoning that is based on patterns you observe.
• Example: 2,5,8,11,…
• What do you see?
• How do you know?
• Justify
Conjecture
• A conclusion you reach using inductive reasoning.
• Example:
• 1 = 1 = 1x1
• 1 + 3 = 4 = 2x2
• 1 + 3 + 5 = 9 = 3x3
• 1 + 3 + 5 + 7 = 16 = 4x4
• Make a conjecture about the sum of the first 30 odd numbers.
• How do you know?
Counterexample
• An example for which the conjecture is incorrect.
• Example: Find a counterexample for this conjecture.
• The square of any number is greater than the original number.
• Can you think of a number that makes this false?
• How do you know that number makes the conjecture false?
Guided Practice
• Pages 6 – 7 (selected problems 1 – 30)
Peer and Independent WORK
• Pages 7 – 8 (selected problems 31 – 46)
Isometric drawing
• Isometric drawing – a drawing on isometric dot paper to show three sides of a figure from a corner view.
• Example – p. 10
• In Greek, isosmeans “equal” and metron means “measure.”
• In an isometric drawing, all 3-D measurements are scaled equally.
• What do you know about 3-D drawings?
• Is it important? Why or why not?
Orthographic drawing
• Orthographic drawing – another way to show a three-dimensional figure. It shows the top view, front view, and right-side view.
• Example : p. 11 #2
• Have you ever seen an orthographic drawing in real-life?
• When should they be used?
• Why?
Foundation drawing
• Foundation drawing – shows the base of a structure and the height of each part.
• Example: p. 11 #3
• When would someone use this type of drawing?
• Why would that be a better choice?
Net
• Net – a two-dimensional pattern that you can fold to form a three dimensional figure.
• Have you seen a net?
• When are they used?
• Do you think they are helpful?
• Why or why not?
• What is different about it from the other drawings?
• Which do you prefer?
• Do you think we should use all 4?
• Why or why not?
Guided practice
• Page 13 (1 – 16)
Peer and Independent Practice
• Pages 13 – 14 (18 – 32)
Homework
• Page 9 # 54 -55
• Page 15 # 33 - 34
Homework for 8-12-13
• 54.When he was in the third grade, German mathematician Karl Guass (1777-1855) took ten seconds to sum the integers from 1 to 100. Now it’s your turn. Find a fast way to sum the integers from 1 to 100; from 1 to n. ( Hint: Use Patterns)
• 55. a. Write the first six terms of the sequence that starts with 1, and for which the difference between consecutive terms is first 2, and then 3, 4, 5, and 6.
• b. Evaluate (n2 + n)/ 2 for n =1, 2, 3, 4, 5, and 6. Compare the sequence you get with your answer for part (a).
• c. Examine the diagram at the right n + 1
• and explain how it illustrates a value of # # # *
• (n2 + n)/ 2. n # # * *
• d. Draw a similar diagram to represent # * * *
• (n2 + n)/ 2 for n=5.