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Chapter 2 Calendar (reworked from original schedule)

Learn how to make conjectures based on patterns and use counterexamples to disprove statements. Practice identifying patterns, making conjectures, and finding counterexamples with numbers and geometric figures.

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Chapter 2 Calendar (reworked from original schedule)

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  1. Chapter 2 Calendar (reworked from original schedule)

  2. Patterns and Inductive Reasoning Chapter 2-1

  3. Make conjectures based on inductive reasoning. • conjecture • counterexample • Find counterexamples. Standard 1.0Students demonstrate understanding byidentifying and giving examples ofundefined terms, axioms, theorems, and inductiveand deductive reasoning. (Key) Standard 3.0Studentsconstruct and judge the validity of a logical argument and give counterexamples to disprove a statement.(Key) Lesson 1 MI/Vocab

  4. Patterns • What is next?

  5. ×2 ×3 ×4 ×5 Patterns and Conjecture Make a conjecture about the next number based on the pattern. 2, 4, 12, 48, 240 Find a pattern: 2 4 12 48 240 The numbers are multiplied by 2, 3, 4, and 5. Conjecture: The next number will be multiplied by 6. So, it will be 6 ● 240 or 1440. Answer:1440 Lesson 1 Ex1

  6. Describe the pattern and find the next number. • 1, 4, 16, 64… • Multiply by 4 • 256 • -5, -2, 4, 13… • Add subsequent multiples of 3. {3, 6, 9, 12…) • 25 • 5, 7, 14, 16, 32, 34… • Add 2, then multiply by 2 • 68

  7. A.B. C.D. • A • B • C • D Lesson 1 CYP1

  8. Conjecture • An unproven statement based on prior facts • All Football players are dumb. • All English teachers are short. • All even numbers are divisible by 2.

  9. Counterexample A specific example that proves a conjecture is false Give a counterexample to the conjecture that: • “All months end in the letter y.” • March, April, September, etc. • “All numbers are divisible by 2.” • 3, 7, 39, etc. • “For all real numbers x, x2  x. • .5, .1, .938, etc.

  10. Geometric Conjecture For points L, M, and N, LM = 20, MN = 6,and LN = 14.Make a conjecture and draw a figure to illustrate your conjecture. Given: points L, M, and N; LM = 20, MN = 6, and LN = 14. Examine the measures of the segments. Since LN + MN = LM, the points can be collinear with point N between points L and M. Answer: Conjecture:L, M, and N are collinear. Lesson 1 Ex2

  11. Given: ACE is a right triangle with AC = CE. Which figure would illustrate the following conjecture? ΔACE is isosceles, C is a right angle, and is the hypotenuse. A.B. C.D. • A • B • C • D Lesson 1 CYP2

  12. UNEMPLOYMENTBased on the table showing unemployment rates for various counties in Texas, find a counterexample for the following statement. The unemployment rate is highest in the cities with the most people. Answer: Maverick has a population of 50,436 people in its population, and it has a higher rate of unemployment than El Paso, which has 713,126 people in its population. Lesson 1 Ex3

  13. DRIVINGBased on the table, which two states could be used as a counterexample for the following statement?The greater the population of a state, the lower the number of drivers per 1000 residents. • A • B • C • D • Texas & California • Vermont & Texas • Wisconsin & West Virginia • Alabama & West Virginia Lesson 1 CYP3

  14. Homework Chapter 2-1 • Pg 80 1, 2, 5 – 16, 25 – 30, 33, 40, 43 – 48

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