1. Represent the following situation algebraically and solve.
Warm Up:
Represent the following situation algebraically and solve.
The drama club at a high school is going to raise money by printing calendars that feature photos of scenes from its recent plays. The cost of printing the calendars is $5.50 per calendar. The photographer also charges a one-time cost of $200 for taking the photos. The club has $1500 to cover the initial costs of the calendar. How many calendars can they order?

2. Missing Forms:
Trae, Matt, Lauren, Olivia S.M.

3. Inductive Reasoning Quiz Reults and Corrections
-When finished place in your file folder (in the filing cabinet)

4. Last Class:
Introduction to Deductive Reasoning

5. Deductive Reasoning
Deductive Reasoning: Drawing a specific 
conclusion through logical reasoning by starting with general assumptions that are known to be valid. Or more simply, proving.
Proof: A mathematical argument showing that a 
statement is valid in all cases, or that no counterexample exists.

6. Inductive vs. Deductive video: https://www. khanacademy
deductive-and-inductive-reasoning/v/deductive-reasoning-1

7. ? Our Goal? To prove mathematical statements using logical arguments.
Ex.1: Jon discovered a pattern when adding integers
= 15
(-15) + (-14) + (-13) + (-12) + (-11) = -65
(-3) + (-2) + (-1) = -5
Conjecture:
He claims that whenever you add five consecutive integers, the 

sum is always 5 times the median ?

8. It would be impossible to prove Jon's conjecture using 

every single possibility as there are an infinite number 

of possibilities.
We need to use algebra to help us "prove" the 
conjecture is true for all possibilities.

9. **Give out Notes

10. Last Class:
How could we represent any even number 
algebraically?
How could we represent any odd number 
algebraically?

12. Prove that when an even number is multiplied by any other even number, the product is even.

13. When I add the squares of 2 even numbers, I get an even number
When I add the squares of 2 even numbers, I get an even 
number. Support this conjecture using inductive reasoning, and 
then prove that it is true.

14. Prove the following conjecture: When an odd number is squared, 
the result is always odd.

15. Independent Practice:
Page 31 # 1 and 5 due tomorrow!

18. 71 7 + 1 = 8 8 ÷ 3 = 2.66666... ∴ 71 can not be divided by 3 45
Conjecture:  Add the digits of a number and determine if
the sum is divisible by three. If it is, the
original number is divisible by 3. 45
4 + 5 = 9 9 ÷ 3 = 3
∴ can be divided by 3 71
7 + 1 = 8 8 ÷ 3 =
∴ can not be divided by 3

19. ab = 10a + b ab = 9a + a + b ab = 9a + (a+b)
Since 9a can be divided by 3,
if a+b is divisible by 3,
the whole number must be divisible by 3

20. Independent Practice:
Pages # 1, 5, 7, 10, 17 due Tuesday

21. Textbook: Page 31
#1, 2, 3, 5, 6, 9, 11, 12, 

13, 14, 16, 18, 19, 20