2.1 Inductive Reasoning.

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Presentation transcript:

2.1 Inductive Reasoning

Inductive Reasoning Process of considering several facts and then making an educated guess based on these facts. Recognizing patterns and making predictions.

Describe the pattern. Find the next number. 625, multiply the previous number by 5 1, 5, 25, 125, … 1, 2, 4, 7, 11, … 1, 4, 9, 16, 25, …. 16, add the next consecutive integer to the previous # 36, square of consecutive whole numbers

Based on the chart…make a function rule relating x and y. 1 2 3 y 4 8 12 y = 4x x 1 2 3 y 5 7 y = 2x + 1

Conjectures A conjecture is an unproven statement that is based on observations. Not necessarily a true statement.

Complete the conjecture based on the pattern. Conjecture: The product of any two even numbers is ________________. 4 x 2 = 8 6 x 8 = 48 -2 x -8 = 16 10 x 4 = 40 -4 x 6 = -24 -6 x 12 = -72 EVEN Conjecture: The sum of any two consecutive whole numbers is ________________. 4 + 5 = 9 6 + 7 = 13 11 + 12 = 23 7 + 8 = 15 12 + 13 = 25 20 + 21 = 41 ODD

Is the conjecture true or false? Any four-sided polygon is a square. FALSE! Four-Sided Polygons: rectangle, rhombus, trapezoid, parallelogram. For a conjecture to be true it must be true for ALL cases. An example that proves a conjecture false is called a counterexample.

Determine if the conjecture is true or false Determine if the conjecture is true or false. Give a counterexample if false. Jose is a child living in Argentina, where spring begins in September and ends in December. Because he sees the days getting longer in these months, he makes a conjecture that the days are getting longer all over the world. Is his conjecture true or false? FALSE! Counterexample: New Jersey – September – December the days are getting shorter!

Determine if the conjecture is true or false Determine if the conjecture is true or false. Give a counterexample if false. 1.) Given: Collinear points D, E, and F. Conjecture: DE + EF = DF False. Counterexample: EF + FD = ED E F D 2.)Conjecture: The difference of two positive numbers is positive. False. Counterexample: 20 – 25 = -5