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Geometry with McCarthy

Section 2.1 : Using Inductive reasoning to make conjectures. Geometry with McCarthy. Missy McCarthy Okemos High School Math Instructor. What do ya know?. Let’s try a little activity to get your brain warmed up!.

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Geometry with McCarthy

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  1. Section 2.1: Using Inductive reasoning to make conjectures Geometry with McCarthy Missy McCarthy Okemos High School Math Instructor

  2. What do ya know? Let’s try a little activity to get your brain warmed up! In each of the following examples, you will find a logical sequence of five boxes. Your task is to decide which of the boxes completes this sequence. To give your answer, select one of the boxes marked A to E. At the end, you will be told whether your answers are correct or not.

  3. What comes next?

  4. What comes next?

  5. What comes next?

  6. What comes next?

  7. How did you do? Question 1: E Question 2: D Question 3: D Question 4: B An inductive reasoning test measures abilities which are important in solving problems. These tests measure the ability to work flexibly with unfamiliar information and find solutions. People who perform well on these tests tend to have a greater capacity to think conceptually as well as analytically.

  8. Inductive Reasoning When several examples form a pattern and you assume the pattern will continue, you are applying inductive reasoning. You may use inductive reasoning to draw a conclusion from a pattern. Inductive reasoning is the process of reasoning that a rule or statement is true because specific cases are true.

  9. Using inductive reasoning

  10. Making Conjectures Guess Who? Conjecture : A statement you believe to be true based on inductive reasoning

  11. Using inductive reasoning…

  12. Be careful! Some patterns have more than one correct rule. For example, the pattern 1, 2, 4, … can be extended with 8 (by multiplying each term by 2) or 7 (by adding consecutive numbers to each term).

  13. Counterexamples To show that a conjecture is always true, you must prove it. To show that a conjecture is false, you have to find only one example in which the conjecture is not true. This case is called a counterexample . A counterexample can be a drawing, a statement, or a number.

  14. False conjectures

  15. Counterexamples To show that a conjecture is ALWAYS TRUE, you must prove it. To show that a conjecture is FALSE, you have to find only one example in which the conjecture is not true. This case is called a counterexample. A counterexample can be a drawing, a statement, or a number.

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