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Geometry Quiz Conjectures and Patterns | Homework Help

Practice inductive reasoning and conjectures with number and picture patterns. Identify missing numbers, predict sequences, and find counterexamples to solidify your understanding. Complete the given sequence challenges for effective learning.

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Geometry Quiz Conjectures and Patterns | Homework Help

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  1. Welcome to Geometry

  2. Objective: Use inductive reasoning to make conjectures, use inductive reasoning in number/picture patterns

  3. Problem Mrs. Magers has given her Geometry class a pop quiz every Tuesday for the past 3 weeks. On Monday afternoon, Natalie told Imari to go home and study her Geometry notes. Why?

  4. Inductive Reasoning and Patterns • Inductive Reasoning is reasoning based on observed patterns. (We assume the observed pattern will continue. This may or may not be true.) • A conjecture is a conclusion reached through inductive reasoning. (Remember, the conjecture seems likely, but it is unproven)

  5. A single counter-example is enough to disprove a conjecture. • Example Conjecture: The difference of two integers is less than either integer. • 6-4 = 2 • 10-7 =3 • Can you find a counterexample? 8-(-15) = 23

  6. Given the pattern _____, -6, 12, _____, 48, … • a. Fill in the missing numbers. • b. Determine the next two numbers in this sequence. • c. Describe how you determined what numbers completed the sequence. Be sure to explain your reasoning. • d. Are there any other numbers that would complete this sequence? Explain your reasoning.

  7. Ex: Find the next two terms and indicate the process for generating the next term. 1) 1, 4, 9, 16, 25, 36, ___, ___ 2) 1, 3, 7, 15, 31, 63, ___, ___ 49 64 127 255

  8. 3) What figure comes next?

  9. Closure • Inductive reasoning • Conjecture • Counterexample

  10. homework • p.6-8 #12-30, 34-37, 43

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