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2.1 – Use Inductive Reasoning

2.1 – Use Inductive Reasoning. Inductive Reasoning:. Make predictions based on patterns. Conjecture:. An unproven statement that is based on observations. Counterexample:. A statement that contradicts a conjecture. 1. Sketch the next figure in the pattern.

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2.1 – Use Inductive Reasoning

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  1. 2.1 – Use Inductive Reasoning

  2. Inductive Reasoning: Make predictions based on patterns Conjecture: An unproven statement that is based on observations Counterexample: A statement that contradicts a conjecture

  3. 1. Sketch the next figure in the pattern.

  4. 1. Sketch the next figure in the pattern.

  5. 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 30, 35 5, 10, 15, 20 25, +5 +5 +5 +5

  6. 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 486, 1,458 2, 6, 18, 54 162, x3 x3 x3 x3

  7. 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. -729, 2,187 3, -9, 27, -81 243, x-3 x-3 x-3 x-3

  8. 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 23, 30 2, 3, 5, 8, 12 17, +1 +2 +3 +4 +5

  9. 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 95, 191 2, 5, 11, 23 47, x2+1 x2+1 x2+1 x2+1

  10. 3. Describe a pattern in the numbers. Write the next three numbers in the pattern. 21, 34 1, 1, 2, 3, 5, 8 13, 1+1 1+2 2+3 3+5 5+8

  11. Make a table displaying the relationship between the number of sides of a shape and the number of diagonals from one vertex. Then make a conjecture for all n-gons. # of sides (n) 3 4 5 6 7 … 25 … n # of diagonals from 1 vertex 0 1 2 3 4 22 n – 3

  12. 5. Show the conjecture is false by finding a counterexample. Any four-sided polygon is a square. Rectangle

  13. 5. Show the conjecture is false by finding a counterexample. The square root of all even numbers is even. 1.414213

  14. HW Problem # 17 Ans: Example: 25 = 10

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