mrs. mcconaughygeometry1 patterns and inductive reasoning during this lesson, you will use inductive...
TRANSCRIPT
Mrs. McConaughy Geometry 1
Patterns and Inductive Patterns and Inductive ReasoningReasoning
During this lesson, you willuse inductive reasoning to
make conjectures.
Mrs. McConaughy Geometry 2
Standards/Assessment Anchors:
Daily Warm Up
Mrs. McConaughy Geometry 3
Inductive reasoning ___________
Conjecture __________________________
Give an example of when you have used inductive reasoning in the real world.
Mrs. McConaughy Geometry 4
reasoning based upon patterns you observe.
VocabularyVocabulary
Inductive reasoning ______________________________________________
Conjecture _____________________________________________________
Counterexample __________________________________________________
the conclusion you reach using inductive reasoning
an example for which the conjecture is incorrect
Mrs. McConaughy Geometry 5
Examples: Number and Letter Patterns
Finding and Using a Finding and Using a PatternPattern
Mrs. McConaughy Geometry 6
Finding and Using a Pattern Use inductive reasoning to a. find a pattern
for each sequence, then b. use the pattern to find the next term in each sequence below:20, 18, 16, 14, __ A, C, F, J, O, __
1, 3, 6, 10, 15, 21, ___ a, 6, c, 12, e, 18, __
½, 9, 2/3, 10, ¾, 11, __ 1, 3/2, 9/4, 27/8, __
12
28
4/5
U
g
81/16
Mrs. McConaughy Geometry 7
Using Inductive Reasoning to Make Conjectures
EXAMPLE
3 + 5 = 8-3 + 5 = 2-1 + 1 = 013 +27 = 4051 + 85 = 136Conjecture: The sum of
two odd numbers is always ___________.
EXAMPLE
3 * 4 = 1212 * 5 = 6011 * -4 = -44-24 * -3 = 72-7 * 8 = - 56Conjecture: The
product of ________________________________________________.
an even integer
a prime number and an even integer is always an even integer.
Mrs. McConaughy Geometry 8
Examples: Picture Patterns
Finding and Using a Finding and Using a PatternPattern
Mrs. McConaughy Geometry 9
EXAMPLE: Testing a Conjecture
When points on a circle are joined by as many segments as possible, overlapping regions are formed inside the circle as shown above. Use inductive reasoning to make a conjecture about the number of regions formed when five points are connected.
Mrs. McConaughy Geometry 10
Did you guess that the number of regions doubles at each
stage?
Now find a counterexample to show this conjecture is false.
Points Regions
2 2
3 4
4 8
5 16
6 ?31
Mrs. McConaughy Geometry 11
Testing a ConjectureNot all conjectures turn out to be true. You can prove
that a conjecture is false by finding one
counterexamplecounterexample.
Mrs. McConaughy Geometry 12
Applying Conjectures to Business
Mrs. McConaughy Geometry 13
1. Find the next term in the following sequence:
2. Use inductive reasoning to make a conjecture:
3. Counterexample:4. Draw the next picture in the picture
pattern below:
Final Checks for Understanding
Mrs. McConaughy Geometry 14
Homework Assignments:
Day 1: Inductive Reasoning WS
Day 2: Number Patterns WS
Day 3: Picture Patterns WS