1. Lesson 1-1 Patterns and Inductive Reasoning

2. Ohio Content Standards:

3. Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. -Demonstrate fluency in computations using real numbers. -Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions.

4. Ohio Content Standards: Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. -Demonstrate fluency in computations using real numbers. -Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. Generalize and explain patterns and sequences in order to find the next term and the nth term.

5. Vocabulary:

6. Inductive Reasoning –

7. Vocabulary: Inductive Reasoning – When you make a conclusion based on a pattern of examples or past events.

8. Find the next three terms of each sequence.

9. 11.2, 9.2, 7.2, …

10. Find the next three terms of each sequence. 11.2, 9.2, 7.2, … 6, 12, 24, …

11. Find the next three terms of the sequence:

12. 101, 102, 105, 110, 117, …

13. Draw the next figure in the pattern:

17. Vocabulary:

18. Conjecture –

19. Vocabulary: Conjecture – A conclusion that you reach based on inductive reasoning.

20. Vocabulary: Conjecture – A conclusion that you reach based on inductive reasoning. Counterexample –

21. Vocabulary: Conjecture – A conclusion that you reach based on inductive reasoning. Counterexample – an example that does not follow the conjecture, proving the conjecture false.

22. Jordan studied the data below and made the following conjecture:

23. Multiplying a number by -1 produces a product that is less than -1.

24. Jordan studied the data below and made the following conjecture: Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1

25. Jordan studied the data below and made the following conjecture: Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1 15(-1) = -15 and -15 < -1

26. Jordan studied the data below and made the following conjecture: Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1 15(-1) = -15 and -15 < -1 100(-1) = -100 and -100 < -1

27. Jordan studied the data below and made the following conjecture: Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1 15(-1) = -15 and -15 < -1 100(-1) = -100 and -100 < -1 300(-1) = -300 and -300 < -1

28. Jordan studied the data below and made the following conjecture: Multiplying a number by -1 produces a product that is less than -1. 5(-1) = -5 and -5 < -1 15(-1) = -15 and -15 < -1 100(-1) = -100 and -100 < -1 300(-1) = -300 and -300 < -1 Find a counter example for his conjecture.

29. Assignment: Pgs. 7 – 9 2 – 34 evens