In this lesson you will
is used in science and mathematics
Use inductive reasoning to make
about sequences of numbers
is the process of observing data, recognizing patterns, and
making generalizations based on those patterns. You probably use inductive
reasoning all the time without realizing it. For example, suppose your history
teacher likes to give “surprise” quizzes. You notice that, for the first four chapters
of the book, she gave a quiz the day after she covered the third lesson. Based on
the pattern in your observations, you might generalize that you will have a quiz
after the third lesson of every chapter. A generalization based on inductive
reasoning is called a
Example A in your book gives an example of how inductive reasoning is used in
science. Here is another example.
In physics class, Dante’s group dropped a ball from different heights and
measured the height of the first bounce. They recorded their results in this table.
Make a conjecture based on their findings. Then predict the first-bounce height
for a drop height of 280 cm.
If you divide each first-bounce height by the corresponding drop height, you get
the following results: 0.75, 0.74, 0.7625, 0.75, 0.76, 0.7375. Based on these results,
you could make this conjecture: “For this ball, the height of the first bounce will
always be about 75% of the drop height.”
Based on this conjecture, the first-bounce height for a drop height of 280 cm
would be about 280
0.75, or 210 cm.
Example B in your book illustrates how inductive reasoning can be used to make
a conjecture about a number sequence. Here is another example.
Consider the sequence
Make a conjecture about the rule for generating the sequence. Then find the next
Drop height (cm)
First-bounce height (cm)
Discovering Geometry Condensed Lessons
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