Warm Up: *How would you represent these same numbers algebraically??? Give 3 numbers that are: -odd -even -consecutive odd -consecutive even -perfect squares -consecutive perfect squares *How would you represent these same numbers algebraically???

Homework Check -Reminder: **Inductive and Deductive Reasoning Unit Test TOMORROW!**

Outcomes Review: LR1. Analyze and prove conjectures using logical reasoning, to 
solve problems. LR2. Analyze puzzles and games that involve numerical 
reasoning, using problem-solving strategies.

1. I give you a conjecture. You support it using 
inductive reasoning (examples) 2. I give you a conjecture. You find a 
counterexample. 3. I give you an operation(s) to do with some 
numbers. You come up with a conjecture. (What happens when you add three odd 
numbers). 4. Some english logic problems. Ex: All dogs are hairy. Jim is hairy. Therefore, 
Jim is a dog. 5. Prove conjectures deductively (odd/even and 
number tricks) 6. Number Puzzle (easy): Sudoku.... 7. Find the error in the proof and/or create an invalid proof

Vocabulary: -Conjecture -Inductive Reasoning -Deductive Reasoning -Proof

Invalid Proof: A proof that contains an error in reasoning or that contains invalid assumptions. Assumption: A statement assumed to be true. Circular Reasoning: An argument that is incorrect because it makes use of the conclusion 
to be proved.

1. Write the number that corresponds to the month of your birth. 2. Multiply that number by 4. 3. Add 12 to the answer. 4. Multiply by 25. 5. Add your age to the answer. 6. Add 13. 7. Subtract 365. 8. Add 52. 9. Tell me your answer. 10. Prove that this will always work!!

Jean says she can prove that 1 ₵ = $1 Jean's Proof $1 = $1 100₵  (1 dollar is the same as 100 cents) (10₵)2 (100 can be written as 102) ($0.1)2 (10 cents = $0.10) $0.01 (0.12 = 0.01) 1₵  ($0.01 = 1₵) 1₵ = $1 Does Jean's proof make sense? 
Why or Why not?

How many handshakes for the 3rd person? 14 Strangers are put into a room for the first time. Each 
person shook the hand of every other person. How many 
hand shakes were exchanged? How many handshakes for the 3rd person?

Inductive reasoning - find a pattern to determine the solution What type of reasoning are you using to solve this problem? Inductive reasoning - find a pattern to determine the solution What pattern do you notice? 1st  - 13 handshakes 2nd  - 12 handshakes 3rd - 4th  - ..... 12th - 13th - 14th - 13+12+11+10+9+8+7+6+5+4+3+2+1 = 91 handshakes

8 people, Dave, Angie, Josh, Tanya, Joy, Stu, Sue and Linus, sat 
around a table playing a partner game. Dave and his partner were 
to the left of Stu. Across from Dave was Sue, who was to the right 
of Josh. Dave's brother's partner, Tanya, was across from Stu. Joy 
was not on Stu's right.

Suduko

Review Questions: p. 58 - Self-Test Do # 4, 5 Journal 1. What is the difference 
between inductive and deductive 
reasoning? 2. What is a counterexample, 
and what is its purpose?

Review Questions: Page 58 # 4, 5 Pages 61-62 # 4, 5, 7, 9, 10, 12, 13, 15