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Contributor: Marlene Vogel. Lesson ID: 10903
Can you make an educated guess if you'll like this lesson? Learn definitions and techniques from zoo animals, bikes, and practical charts and graphs. It's reasonable to believe you will learn a lot!
Elephango Zoo Animals Water Ingestion
The bar graph above represents the amount of water the animals at the Elephango Zoo ingest each month. Use the graph above to answer the questions below (You can click on the questions to reveal their answers):
Inductive reasoning is used often in geometry.
It allows you to make conclusions and conjectures based on patterns of examples or past events. Inductive reasoning is an extremely important part of the world of mathematics, since many mathematicians have made mathematical discoveries through the use of inductive reasoning.
Below is a simple example of the use of inductive reasoning and making a conjecture:
Assume that you are given the sequence 2, 4, 6, 8, ….
Even though this is a simple example, it is helpful in illustrating the steps you need to go through when using inductive reasoning and making your conjecture.
Read the steps below:
You add to the previous term to get the next term.
You would have to add 2 to the last term in the sequence to get the next one. 8 + 2 = 10, so the next term in the sequence would be 10.
You could continue to add 2 to each term until you reach the 10^{th} term, or you could multiply 10 and 2 to get the 10^{th} term.
Notice that in the placement of each term in the sequence above, when the term is multiplied by 2, the answer is in the place of the term. Term 1 is 2 (1 x 2 = 2). Term 2 is 4 (2 x 2 = 4).
If you multiply Term 10 by 2 you will get the term (10 x 2 = 20). Therefore, the 10^{th} term is 20.
Below is another sample problem. See if you can make the conjecture:
A local bike shop noticed that the sales of its children's bicycles was decreasing. Using the graph below and inductive reasoning, can you predict how many bikes the shop will sell in June?
Monthly sales:
January - 57 bikes
February - 54 bikes
March - 51 bikes
April - 48 bikes
May - 45 bikes
Here is a note of caution when using inductive reasoning:
Good for you!
You will use inductive reasoning and making conjectures quite a bit in geometry, with many more challenging problems ahead.
In the Got It? section, you will have opportunities to practice your new skills to assure your understanding of these new concepts.