Mrs. McConaughy Geometry 1

Patterns and Inductive Patterns and Inductive ReasoningReasoning

During this lesson, you willuse inductive reasoning to

make conjectures.

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Standards/Assessment Anchors:

Daily Warm Up

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Inductive reasoning ___________

Conjecture __________________________

Give an example of when you have used inductive reasoning in the real world.

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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

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Examples: Number and Letter Patterns

Finding and Using a Finding and Using a PatternPattern

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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

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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.

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Examples: Picture Patterns

Finding and Using a Finding and Using a PatternPattern

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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.

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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

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Testing a ConjectureNot all conjectures turn out to be true. You can prove

that a conjecture is false by finding one

counterexamplecounterexample.

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Applying Conjectures to Business

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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

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Homework Assignments:

Day 1: Inductive Reasoning WS

Day 2: Number Patterns WS

Day 3: Picture Patterns WS