1. Drill
1, 3, 5, 7, 9, __, __
2, 5, 8, 11, 14, __, __
-3, -6, -10, -15, __
, , , __
OBJ: SWBAT use inductive reasoning in order to identify patterns and make conjectures.

2. Unit C Inductive Reasoning
Copy: C1 CN, (RS C1 is on back of notes), C1 CW, Practice A can be used for HW
Mr. Calise
Geometry

3. Motivation
How quickly can you add the odd numbers from 1 – 20?
= 12
= 22
= 32
= 42
= 52
= 1
= 4
= 9
= 16
= 25

4. Notes
Inductive Reasoning: Allows you to reach conclusions based on a pattern of specific examples.
Ex: Each morning you see your friend eating Cheerio’s for breakfast. You see this everyday for 3 weeks.
The next day what do you
expect to see when you
see your friend?
*Does that mean it will definitely happen?

5. Conjecture: A conclusion reached using inductive reasoning.
Example: Make a conjecture about the shapes.

6. Points
Regions 2 3 4 5 6

7. 4 3 12 11 13 14 10 15 27 28 16 9 5 8 1 26 17 29 2 18 31 25 30 19 24 20 21 22 23 6 7

8. True or False? All teachers are taller than students.
Can anyone prove this?
Counterexample: is something
that disproves a conjecture.
Prove it…
A counterexample can be a drawing, a statement, or a number.
-Only one counterexample is needed to disprove a statement.

9. Counter Example Song

10. Text Messages
On average, how many text messages do you send in a month?
Based on our data, high school students send at least ______ text messages a month.
Is this a true statement?
What could be a counterexample?
Is this a true statement? Why or why not?

11. 450 450 Two complementary angles cannot be congruent.
Show that the conjecture is false by finding a counterexample.
Two complementary angles cannot be congruent.
450
450

12. Lesson Quiz
Find the next item in each pattern.
1. 0.7, 0.07, 0.007, … 2.
0.0007
Determine if each conjecture is true. If false, give a counterexample.
3. The quotient of two negative numbers is a positive number.
4. Every prime number is odd.
5. Two supplementary angles are not congruent.
6. The square of an odd integer is odd.
true
false; 2
false; 90° and 90°
true

13. 1. 0, 2, 4, 6, 8, _____, _____ 2. 1, 2, 4, 7, 11, _____, _____
Follow This Pattern
1. 0, 2, 4, 6, 8, _____, _____
2. 1, 2, 4, 7, 11, _____, _____
3. 16, 8, 4, 2, 1, _____, _____
4. 1, 1, 2, 3, 5, 8, _____, _____
5. 4, –4, 4, –4, 4, _____, _____
6. 1, ½ , ¼ , ⅛, _____, _____
7. 1, 10, 100, 1000, 10000, ____, ____
8. 1, 8, 27, 64, 125, _____, _____
9. 1, 3, 6, 10, _____, _____
10. 27, 9, 3, 1, _____, _____

14. 11. 49, 36, 25, 16, _____, _____ 12. a, c, e, g, i, _____, _____
Follow This Pattern
, 36, 25, 16, _____, _____
12. a, c, e, g, i, _____, _____
13. 3, 5, 7, 9, 11, _____, _____
, _____, 5, 2, _____, –4, –7
15. 1, 3, 9, 27, 81, _____, _____
16. J, F, M, A, _____, _____
17. 3, –6, 12, –24, 48, _____, _____
18. 8, 7, 5, 4, 2, _____, _____
19. 1/2, 2/4, 3/6, 4/8, _____, _____
20. 1, 6, 11, 16, 21, _____, _____