Download 2.1 - Patterns and Inductive Reasoning.notebook

2.1 ­ Patterns and Inductive Reasoning.notebook
September 29, 2015
2.1: Patterns & Inductive Reasoning
Date: 9/28
Inductive Reasoning is reasoning based on patterns you observe.
Ex 1). Look for a pattern. What are the next two terms in each sequence?
a)
4, 8, 16, 32, …
b)
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2.1 ­ Patterns and Inductive Reasoning.notebook
September 29, 2015
A conjecture is used to find the tenth or one­hundredth term in a
sequence, it’s a conclusion you reach using inductive reasoning.
Ex 2).
a) What conjecture can you make about the 25th term in 1, 2, 3, 1, 2, 3, … ?
b) What conjecture can you make about the 21st term in R, W, B, R, W, B, … ?
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2.1 ­ Patterns and Inductive Reasoning.notebook
September 29, 2015
*It is important to gather enough information before making a conjecture.
Ex 3).
a) What conjecture can you make about the sum of the first 40 even
numbers?
b) What conjecture can you make about the sum of the first 30 odd
numbers?
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2.1 ­ Patterns and Inductive Reasoning.notebook
September 29, 2015
Ex 4). Sales of lift tickets at a ski resort increased over a period of four
consecutive months. What conjecture can you make about the
number of lift tickets the resort will sell in February?
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2.1 ­ Patterns and Inductive Reasoning.notebook
September 29, 2015
Not all conjectures are true, you should check it multiple times to be
sure. You can prove that a conjecture is false by finding one
counterexample. A counterexample is an example that shows that a
conjecture is false.
Ex 5). What is a counterexample for each conjecture?
a) If an animal is green, it is a frog.
b) Any three segments form a triangle.
c) When you multiply a number by 2, the product is divisible by 4.
d) If a flower is red, it is rose.
e) One and only one plane exists through any three points.
f) When you multiply a number by 3, the product is divisible by 6.
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2.1 ­ Patterns and Inductive Reasoning.notebook
September 29, 2015
Homework:
pg. 93 #1 ­ 3, 6 ­ 14(e), 18 ­ 27,
29, 30, 32, 33 ­ 40
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2.1 ­ Patterns and Inductive Reasoning.notebook
September 29, 2015
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