Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
Chapter Review
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Exercise 5 Page 68

What types of reasoning do you recall?

inductive reasoning

Practice makes perfect

We are asked to complete the following sentence.

When you make conclusions based on patterns you observe, you use ?.

Let's take a look at the following figure to recognize any patterns.

After observing how the new cubes appear, we can conclude that the number of cubes increases by one at the top, one on the front, and one on the right. Therefore, there is the total increase of 3 cubes for each next figure.

Figure Number of Cubes
I 1
II 4
III 7
IV 10

We can also find the number of cubes for the fifth figure only by understanding the pattern. The number would be 10+ 3 = 13. Note that we did not use logical reasoning to make conclusions,so this is not deductive reasoning.

Deductive Reasoning

Using logical reasoning to make conclusions based on given facts.

The second type of reasoning is called inductive reasoning, which is the process of finding patterns in specific observations. We can use this reasoning to make conclusions and predict values like we did in the example.

Inductive Reasoning

Making conclusions based on observed patterns.

Finally, we can complete the given sentence.

When you make conclusions based on patterns you observe, you use inductive reasoning.