1. pencil, highlighter, GP notebook, calculator, textbook
U10D1
Have Out:
Bellwork:
Use the Rational Root Theorem to find all zeros of
by listing all the possible rational zeros.
Sketch a graph of y = P(x).
total:

2. Possible rational zerosq
Possible rational zeros
factors of 9
±1,
±3,
±9,
factors of 2
±1, ±2 +1 +1 1
Start with x = ____ 2 5 –7 –9 9 +1 +2 +7 +0 –9 +1 1 2 7 –9  +1

3. Possible rational zerosq p
Possible rational zeros
factors of 9
±1,
±3,
±9,
factors of 2
±1, ±2 –3
Start with x = ____ -6 1 2 7 –9 +1 –2 3 +1 –6 –3 +9 x
– 1 –3 2 1 –3  +1 2x
2x2
–2x
+ 3
+ 3x –3 +1

4. zeros: x = ______________
+1 set = 0 y
+1 ZPP
x – 1 = 0
x + 3 = 0
2x + 3 = 0
x = 1
x = –3
(0, 9)
–3, 1, 1
zeros: x = ______________ +3 x
(–3, 0)
(1, 0)
+1 labeled x–intercepts
+1 labeled y–intercepts
total:
+1 end behavior
+1 bounce

5. You are going to like this chapter...
because…
We are going to play games!
Let’s start with a game of…
ROCK
PAPER
SCISSORS
Rochambeaux – “_______ _______ ___________”

6. Let's play!!! ROCK PAPER SCISSORS
Rochambeaux – “_______ _______ ___________”
Part 1: Two Players
You and your table partner are going to pair up to play Rochambeaux.
Decide between your partner and you who will be Player A or Player B. Fill in your names on the worksheet.
Directions: You will play 18 rounds of Rochambeaux. The twist is that Player A wins if both players match, while player B wins if they do not match. Record who wins, A or B, on your worksheet.
Also record the number of times A wins and the number B wins below your data.
Let's play!!!

7. What you are observations?
Player B won the most. There were more mis–matches than matches.
What happened? These are called _________ Probabilities because they are what was experienced.
Empirical
On the other hand…
Theoretical
expect
___________ Probabilities – what we _________ to happen.

8. AREA MODEL
An area model shows all the __________ possibilities in an organized form.
theoretical
Label the sides of the model using the symbols:
R = rock
P = paper
S = scissor
PLAYER A 9
# of possible outcomes: ___ R P S 3
# of matches (A wins): ___ R RR RP RS
# of no matches (B wins): ___ 6
PLAYER B P RP PP PS S RS PS SS
Recall the formula for probabilities:
# of outcomes in the event
P (_____) = ________________________
event
total # of possible outcomes
P (A wins) = ___
P (B wins) = ___

9. P (A wins) = ___
P (B wins) = ___
_________ ______ - the amount we would ________ to win or lose on ________ if we played the game ______ times.
Expected
value
expect
average
many
Based on the __________ probabilities, for 18 trials, the _________ ______ for:
theoretical
expected
value
# A wins = 18
= 6
# B wins = 18
= 12

10. TREE DIAGRAM -
used to determine the probability of ________ outcomes from all the ________ outcomes.
individual
possible
PLAYER A  R P S
PLAYER B  R P S R P S R P S A B B B A B B B A
There are __ pathways to the end, so there are __ outcomes. 9 9
Write “A” at the end of each path where A wins. Put “B” at the end of each path where B wins.
likely
Since all paths (for this scenario) are equally ______, then
P (A wins) = ___
P (B wins) = ___

11. Part 1: Three Players
This time, get in teams of 3 persons.
Decide in your group who will be Player A, B or C. Fill in your names on the worksheet.
Directions: You will play 27 rounds of Rochambeaux. Here’s the twist:
Player A wins if _____ match, player B wins if _______ match, and player C wins if ______ match. Record who wins, A, B or C, on your worksheet.
all 3
2 of 3
none
empirical
Based on these 27 trials, the _________ probabilities are:
P (A wins) = ___
P (B wins) = ___
P (C wins) = ___ 27 27 27
Fill in the information above that your group EXPERIENCED.

12. What you are observations?
Player B won the most. There were more 2 of 3 matches than either all matches or no matches.
So, you just recorded the empirical probabilities, that is, what you experienced.
Theoretically, what would the probabilities have been?

13. (There are many more branches!!!!)
On a separate sheet of paper, make a tree diagram or an organized list to find the __________ probabilities for each player winning.
theoretical
Player A 
Player B 
Fill in all the branches and details similar to the one we made earlier.
(There are many more branches!!!!)
Player C 
P(all matches) =
P(2 of 3 matches) =
P(no matches) =

14. Player A R P S Player B R P S R P S R P S R P S R P S R P S R P S R P
Player C
P(all matches) =
P(2 of 3 matches) =
P(no matches) =

15. Finish the tree diagram, then work on PM 4 – 8, 10

16. Do not move until everyone’s name is called.
It’s time to
Change Seats!
Do not move until everyone’s name is called.