Geometry
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Unit 2: Reasoning & Proof
Lesson 2.1:
What is Inductive Reasoning and How Can We Use It?
Also: Can you find patterns? Can you describe patterns and continue them?
"Inductive Reasoning is reasoning based on patterns you observe." -Pearson
A conjecture is a conclusion that you draw after using inductive reasoning.
Consider the following pattern:
Consider the following pattern:
Make a conjecture: What will be the 4th figure? What will be the 5th figure?
Describe the pattern using language and mathematics.
What will the 100th figure look like? Will the shaded portion be a square or a recangle?
Can you pose a question in regards to the pattern?
Let's look at another pattern:
Design your own pattern.
When you are done, share it with your partner.
Can they follow your inductive reasoning and make their own conclusion
based on the pattern that you have created?
...
A counterexample is an example that disproves a certain conjecture. For example, if someone were to foolishly say, "Nobody likes vegetables," you could provide them with a counterexample of Julie Welske, who particularly enjoys Brussels sprouts several times a week. |
Inductive reasoning sometimes leads to faulty conclusions. Since it is based on observations, human bias can interfere with results. Terrible conclusions have been reached as a result of humans assuming things to be true, just because everyone has always thought they were true. The scientific method should be employed at all times to ensure you can accurately discover what is true and what is not true (false). Please consider the following: |
Inductive reasoning has its flaws.
We need another tool of thinking besides just looking for patterns.
We need to learn to think deductively. More on this in Lesson 2.4.
But first, we need to learn about the conditional.
The conditional is the workhorse of logical thinking.