HOW TO WIN ON WHEEL OF FORTUNE
Teacher Edition
List of Activities for this Unit:
ACTIVITY / STRAND / DESCRIPTION- On A Roll (1-4)
2.You’re In My Space (5-12) / PS /
Determine sample space
3.Brown Bag It (13-19) / PS / Probability with and without replacement4.Dumbledore’s Message (20-37) / PS / Statistical study of letters of the alphabet
5.SA & Multiple Choice (38-43) / PS / Probability SA & MC items
COE Connections / Disc Game
Quiz Results
MATERIALS / Dice
Number Cubes
Warm-Ups
(in Segmented Extras Folder) / Automobile Maintenance
Baseball
Vocabulary (Mathematics and ELL)
combination / probabilitycontains / producing
dependent Event / random
draw / sample space
experiment / sectors
faces / selects
indicated / similar
outcomes / successive
percent / tabulated
percentage / tally, tallies
performed / experimental probability
predict / theoretical probability
Length of the Unit: 150 minutes
Essential Questions:
- What is meant by probability?
- What is meant by sample space?
- What is meant by “with replacement” and “without replacement”?
- How does “with replacement” and “without replacement” affect the determination of probability?
- How is data gathered in a systematic way?
- How is data biased by the sources used?
- How is a position defended or refuted by using mathematical data?
- How can trends be identified in order to make inferences/predictions from a set of data?
- How is data used to support a conclusion?
- How accurate is data that is collected?
- What sources of bias will influence data?
- What factors influence a trend that may not be reflected in the collected data?
- What is meant by dependent and independent events?
- How is a prediction or inference justified?
Lesson Overview:
- Before allowing the students the opportunity to start the activity: access their prior knowledge with regards to collecting and using data. Discuss with students the games of Scrabble and Wheel of Fortune? Ask: how many students have played or seen the games on television? Discuss the rules of the games for those who are not familiar.
- Discuss whether or not this situation involves dependent or independent events.
- What is meant by a vowel or consonant?
- Discuss sources of data and bias that can be created by using certain sources.
- What is the relationship between sets of data?
- What is being asked by the questions in the problem?
- How do you decode what the problem is asking you to do?
- A good warm-up could be Automobile Maintenance or Baseball.
- How can the students make their thinking visible?
- How can you support a conclusion that you make?
- Use the passage included in this activity if you need to simplify the lesson.
Performance Expectations:
4.4.HDisplay the results of probability experiments and interpret the results.
4.5.ISummarize mathematical information, draw conclusions, and explain reasoning.
6.3.FDetermine the experimental probability of a simple event using data collected in an experiment.
6.3.GDetermine the theoretical probability of an event and its complement and represent the probability as a fraction or decimal from 0 to 1 or as a percent from 0 to 100.
7.4.ARepresent the sample space of probability experiments in multiple ways, including tree diagrams and organized lists.
7.4.BDetermine the theoretical probability of a particular event and use theoretical probability to predict experimental outcomes.
Performance Expectations and Aligned Problems
Chapter 23“How to Win on the Wheel of Fortune” Subsections: / 1-On A Roll / 2-
You’re In My Space / 3-
Brown Bag It / 4-
Dumbledore’s Message / 5-
SA & Multiple Choice
Problems Supporting:
PE 4.4.H / 1 – 3 / 9, 10 / 20 – 28, 31, 32, 34 / 43
Problems Supporting:
PE 4.5.I / 1 – 3 / 5, 6, 8 – 10 / 15 – 17 / 22, 23, 25 – 28, 32, 34, 36, 37 / 43
Problems Supporting:
PE 6.3.F / 2, 3 / 5, 6 / 22 – 34, 36, 37 / 43
Problems Supporting:
PE 6.3.G≈ 7.4.B / 5 – 9, 11 – 16, 18, 19 / 38, 41, 43
Problems Supporting:
PE 7.4.A / 2, 3 / 5, 8 / 13, 14, 16 / 22, 24 / 43
Assessment: Use the multiple choice and short answer items from Probability and Statistics that are included in the CD. They can be used as formative and/or summative assessments attached to this lesson or later when the students are being given an overall summative assessment.
HOW TO WIN ON WHEEL OF FORTUNE
ON A ROLL
Rolling Two Number Cubes Experiment: SUMS
1. In groups of three, roll your number cubes a total of 50 times. One student should roll the number cubes, one student tallies(marks)on the table the sum of the numbers on the top of each cube, and one student creates a line plot.
2. Complete the table by calculating (2 decimal places) the probability (as a percentage) ofeach sum. Check your work for accuracy.
GROUP DATA
SUM(of the two number cubes) / TALLY / NUMERICAL TOTAL / INDIVIDUAL %(TOTAL ÷ 50)
0
1example / /// / 3 / 3/50 = .06 = 6%
2 /
3
4
5
6
7
8
9
10
11
12
13
TOTAL
3. After completing the table, each group should write their total on the board. Determine the overall percent (ratio of a number to 100, means per hundred)for each sum using the information from the students and put that percent in the column “CLASS %”. That percentage(number out of 100)will be what you will use to answer the questions on the next pages.
CLASS DATA
SUM / GROUP TOTALS / CLASS TOTAL / CLASS %0
1
2
3
4
5
6
7
8
9
10
11 /
12
13
TOTAL
4. How do your group percentages compare to the class percentages for the probability of the sums?
_____The values should be close ______
______
YOU’RE IN MY SPACE
5. Create a list of all the possible outcomes (one of the possible results in a probability situation or activity). This list of outcomes is called the sample space (a sample space is a set of all possible outcomes to a specified experiment).
SAMPLE SPACE FOR THE SUM OF TWO NUMBER CUBES
+ / 1 / 2 / 3 / 4 / 5 / 61 / (1,1)
1+1=2 / (1,2)
1+2=3 / 4 / 5 / 6 / 7
2 / (2,1)
2+1=3 / 4 / 5 / 6 / 7 / 8
3 / 4 / 5 / 6 / 7 / 8 / 9
4 / 5 / 6 / 7 / 8 / 9 / 10
5 / 6 / 7 / 8 / 9 / 10 / 11
6 / 7 / 8 / 9 /
10 / 11 / 12
6.a. What is the size of the sample space? _____36______
b. What are the possible outcomes? __2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12______
7. Becky and John were playing a game called Number Cubes; the game uses one rednumber cube and one blue number cube, numbered 1 through 6. At the end of the game, Becky needed to roll a 6 and a 1 on the two number cubes to win. The table shows the outcome of tossing two cubes.
Sample Space Table for the Two Colored Number Cubes
Red cubeBlue cube / 1 / 2 / 3 / 4 / 5 / 6
1 / 1,1 / 2,1 / 3,1 / 4,1 / 5,1 / 6,1
2 / 1,2 / 2,2 / 3,2 / 4,2 / 5,2 / 6,2
3 / 1,3 / 2,3 / 3,3 / 4,3 / 5,3 / 6,3
4 / 1,4 / 2,4 / 3,4 / 4,4 / 5,4 / 6,4
5 / 1,5 / 2,5 / 3,5 / 4,5 / 5,5 / 6,5
6 / 1,6 / 2,6 / 3,6 / 4,6 / 5,6 / 6,6
Which is the probability of rolling any combination (a collection of objects in no real order) of a 6 and a 1 on the two number cubes?
A. 1 out of 6
B. 1 out of 12
C. 1 out of 18
D. 1 out of 36
8. Theoretical probability is the measure of the likelihood that an event will occur; the ratio of favorable outcomes to the number of possible outcomes. Complete the chart for theoretical probability for the sum of two number cubes.
THEORETICAL PROBABLITY FOR THE SUM OF TWO NUMBER CUBES
SUM / POSSIBLE OUTCOMES / FRACTION(POSSIBLE OUTCOMES ÷ 36) / PERCENT
0 / 0 / 0/36 / P(0)= 0%
1 / 0 / 0/36 / P(1)= 0%
2 / 1 / 1/36 / P(2)= 2.8%
3 / 2 / 2/36 / P(3)= 5.6%
4 / 3 / 3/36 / P(4)= 8.3%
5 / 4 / 4/36 / P(5)= 11.1%
6 / 5 / 5/36 / P(6)= 13.9%
7 / 6 / 6/36 / P(7)= 16.7%
8 / 5 / 5/36 / P(8)= 13.9%
9 / 4 / 4/36 / P(9)= 11.1%
10 / 3 / 3/36 / P(10)= 8.3%
11 / 2 / 2/36 / P(11)= 5.6%
12 / 1 / 1/36 / P(12)= 2.8%
13 / 0 / 0/36 / P(13)= 0%
9. For the number cubeexperiment (a test or trial), were the class experimental results close to the theoretical results? Explain.
___Answers may vary. They may or may not be close. ______
______
______
______
______
10. Based on the information from the experiment, what sum do you predict (guess) will occur the
most if you roll the number cubes 100 times? ______7______
Justify your answer.
__The sum of 7 has the most possible combinations when rolling two number cubes.______
______
______
______
______
______
11. Each face on a number cube is identified by a number from 1 through 6. Vanessa is rolling two number cubes and adding the numbers on the top faces.
Which sum is Vanessa least likely to roll?
A. 8
B. 7
C. 6
D. 5
12. When a fair coin is tossed, the experimental probability that it will land heads up is ½. In four successive (one toss after another) tosses, a fair coin lands heads up each time.
Which is likely to happen when the coin is tossed a fifth time?
A. It is more likely to land tails up than heads up.
B. It is more likely to land heads up than tails up.
C. It is equally likely to land heads up or tails up.
D. More information is needed to answer the question.
BROWN BAG IT
The Grab Bag
Dependent Event – An event whose probability is affected (changed) by the outcome of another event.
13. The brown paper bag contains similar (same) markers of three different colors, yellow, black and green. There are 5 yellow markers, 6 black markers, and 4 green markers.
If you draw one marker at random (hit and miss) and return the marker to the bag after each draw (grab),
a)What is P(Yellow)? ____5/15 = 1/3 = 331/3%
b)What is P(Black)? ____6/15 = 2/5 = 40%___
c)What is P(Purple)? ____0/15 = 0 = 0%______
d)What is P(not Yellow)? ____10/15 = 2/3 = 66 2/3%
e)What is P(Green or Yellow)? ____9/15 = 3/5 = 60%____
14. The brown paper bag contains “Classroom Passes” of three different kinds, Free Homework Passes, Bathroom Passes, and MP3 use Passes. There are 3 free homework passes, 5 bathroom passes, and 2 free MP3 use passes.
You draw one pass at random and return the pass to the bag after each draw. Complete the table to find the probability of each indicated (specific) event.
Pass Drawn / ProbabilityHomework / 3/10 = 30%
Bathroom / 5/10 = 1/2 = 50%
MP3 / 2/10 = 1/5 = 20%
Not MP3 / 8/10 = 4/5 = 80%
Bathroom or Homework / 8/10 = 4/5 = 80%
15. Now you get to keep the pass that you draw. Will this affect the probability of the next draw? Explain.
Yes. It changes the sample space which changes the probability because the number of possible outcomes is smaller by one for the next draw.
16. Below are the results of three successive draws without replacement. Complete each table.
a.) Group 1
Pass Drawn / Probability / Total # Passes Left in the Bag1st Draw / Bathroom / 5/10 = 1/2 = 50% / 9
2nd Draw / Homework / 3/9 = 1/3 = 33 1/3% / 8
3rd Draw / MP3 / 2/8 = 1/4 = 25% / 7
b.) Group 2
Pass Drawn / Probability / Total # Passes Left in the Bag1st Draw / Bathroom / 5/10 = ½ = 50% / 9
2nd Draw / Bathroom / 4/9 = 44 4/9% / 8
3rd Draw / MP3 / 2/8 = 1/4 = 25% / 7
c.) Group 3
Pass Drawn / Probability / Total # Passes Left in the Bag1st Draw / Homework / 3/10 = 30% / 9
2nd Draw / Not Homework / 7/9 = 77 7/9% / 8
3rd Draw / MP3 / 2/8 = 1/4 = 25% / 7
d.) Group 4
Pass Drawn / Probability / Total # Passes Left in the Bag1st Draw / MP3 / 2/10 = 1/5 = 20% / 9
2nd Draw / MP3 / 1/9 = 11 1/9% / 8
3rd Draw / MP3 / 0 = 0% / 7
17. Use the data in the tables above to support why a draw without replacement affects the probability of a given event.
_Students need to address the fact that not replacing a card reduces the sample space. Changing the sample space causes the probability to be altered.
______
______
18. A woman randomly selects (chooses)one marble from a bag containing 7 red marbles, 13 blue marbles, and 20 green marbles.
Which is the probability that she will select a blue marble from the bag?
A.
B.
C.
D.
19. Alison’s desk drawer contains (holds)4 blue pens and 5 black pens. Alison selects a blue pen from the drawer and does not put it back. Without looking, Alison selects a second pen from the drawer.
Which is the probability that the second pen she selects is blue?
A.
B.
C.
D.
DUMBLEDORE’S MESSAGE
Sample Passage for Alphabet Percent
(302 Letters)
This book is probably the best Harry Potter book written by J K Rowling. It is full of adventure with another Defense Against the Dark Arts teacher and Harry’s scar hurting more than ever. As you probably know, a close friend of Harry dies, but you will have to read the book to find out who it is. Dumbledore has a message for Harry – something he should have known five years ago…
A Statistical Study on the Letters of the Alphabet
Or how to win on “The Wheel of Fortune”
20.Tally the letters from the passage, one at a time, filling out table 1. Do not “jump around” the page!!!!!!! Stop when you have accounted for all 302 letters (the whole passage).
21.Calculate (2 decimal places) the probability (percentage) of finding each letter. Check your work for accuracy.
22.After completing the table for the letters that you counted, several students need to write their totals for each letter (out of 302) on the board. Determine the overall percent for each letter using the information from the students and put that percent in the column “CLASS %”. That percentage will be what you will use to answer the questions on the next pages.
TABLE 1
LETTER
/TALLY
/TOTAL
/ GROUP% / CLASS %
A / 26 / 8.6
B
/ 11 / 3.7C / / 3 / 1.0
D / 11 / 3.7
E / 31 / 10.3
F / 8 / 2.7
G / 6 / 2.0
H / 20 / 6.6
I / 17 / 5.6
J / 1 / .3
K / 7 / 2.3
L / 10 / 3.3
M / 4 / 1.3
N / 15 / 5.0
O / 28 / 9.3
P / 3 / 1.0
Q / 0 / 0
R / 27 / 9.0
S / 19 / 6.3
T / 24 / 8.0
U / 9 / 2.6
V / 5 / 1.7
W / 7 / 2.3
X / 0 / 0
Y / 10 / 3.3
Z / 0 / 0
23. Were your percentages close to the percentages tabulated (calculated)tabulated by the people who wrote on the board? ______YES_____ Why or why not?
___The data gathered is all from the same passage so we all should have the same percentages.
______
24. Ranking of the letters
TOP TEN LETTERS:BOTTOM FIVE LETTERS:
1. ______E______10.3_%22. __C and P______1.0__%
2. ______O______9.3__%23. ______J______0.3__%
3. ______R______9.0__%24. ______Q______0___%
4. ______A______8.6__%25. ______X______0___%
5. ______T______8.0__%26. ______Z______0___%
6. ______H______6.6__%
7. ______S______6.3__%
8. ______I______5.6__%
9. ______N______5.0__%
10. ____B and D______3.7__%
25. How many vowels are in the top ten? _____4___; Which ones? ___E, O, A, I_____
26. Which consonants would be the most useful in the “Wheel of Fortune”? ___R___, __T____, __H____, ___S____, ___N_____, ___B____, ___D___
27. Which vowel might be the least useful? ____ U___; What was its percent? ___2.6%_____
28. See if you can make 10 words using only the top five letters: ___rate__,_ate_, _tear_, _are_, _ear_, eat_, _tea_, _to_, _rote_, _tore_, area, error, tartar (some others: ore, tote, oat, …)
29. You should never expect to find the letter Q on “The Wheel of Fortune”. T or F
30. Almost every word requires a vowel. T or F
31. The letter K is useful when playing the game “The Wheel of Fortune”. T or F
32. Is I or O the most useful vowel? ___O____ Why? ______
_I is only 5.6% while O is 9.3%_______
33. The English language could get along fine without, if any, what three letters? ___Q, X, & Z__
Justify your answer using data from your table.
They each have 0% but there are many words in our English language that would not be possible without these letters.
34. If you were producing (creating) stickers with letters of the alphabet for use in labeling
personal items, such as books, pens, bags and bedroom doors, which 5 of these letters would
be most beneficial to have?
A BCDEFGHIJKLM
Justify your choices with information from the table. ______
These choices were made as a result of choosing the letters that appeared most often in the text. Some letters appeared more often than the choices above, but they were not an option for selection.______
35. To do a more accurate study for the “alphabet stickers”, I would need to make a survey of letters found in … (circle the best answer)
- a popular magazine
- a list of students’ names
- a dictionary
- a novel
Why did you make the selection that you did? Because if you are making stickers for kids to label their belongings then it would be helpful to know the student names.______
36. In the game of “Scrabble”, which of these letters would you expect to be worth the most points? Circle the best answer
HVS
Why did you make the selection that you did?
It had the lowest percentage of the three with 1.7%, so it wouldn’t be used as much and would be worth more points.
37. In “Scrabble”, which of these letters would you expect to be worth the least amount of points? Circle the best answer
QNK
Why did you make the selection that you did?
It had the greatest percentage of the three with 5%, so it would be used more often an dtherefore would be worth fewer points
Multiple Choice & Short Answer Practice Problems
38. To win the big prize in a lottery, you have to decide which six numbers between 1 and 52 will be randomly selected.
Which has the greatest chance of winning the prize?
A.Kenneth, who picks 1, 2, 3, 4, 5 and 6
B. Kathleen, who picks 22, 24, 26, 28, 30 and 32
C.Kyle, who picks 11, 19, 26, 34, 41 and 47
D.ALL THREE PEOPLE have exactly the same chance of winning
39. Each event described below is performed (carried out) randomly.
Which is a dependent event?
A.From a bag of 10 marbles (4 red, 6 blue), Sam pulls a blue marble, puts it back, and then pulls a red marble.
B.On a spinner with 6 congruent sectors numbered 1 through 6, Greg first spins a 4 and then a 2 on the second spin.
C.From a pack of 20 cards, Jose picks 1 card, sets it aside, and then picks a matching card on his second try.
D.Monica tosses a fair coin two consecutive times, and it lands on heads both times.
40. In a jar full of red and blue jelly beans there are 300 jelly beans altogether. There are times as many red jelly beans as blue.
Which represents the number of red jelly beans in the jar?
A. 60
B. 100
C. 180
D. 200
41. The words “mathematics” and “algebra” are written on cards with one letter on each card. One card is drawn at random,
Which is the probability that the card will have an “a” on it?
A.
B.
C.
D.
42. The breakfast buffet at the Wooden Spoon Restaurant is shown in the chart. A person is allowed to make one choice per category.
Juice / Entrée / Fruit / DrinkApple / waffles / pineapple / milk
Orange / pancakes / strawberries / coffee
grapefruit / scrambled eggs / honeydew melon / tea
Oatmeal / hot chocolate
cold cereal
Which is the number of different meal combinations that are possible?
A. 4
B. 15
C. 120
D. 180
43. Larry has 2 six-sided number cubes, one red and one blue. The faces (sides)of one of them are numbered 1 through 6, and the faces of the other are numbered 7 through 12. Larry will toss the two cubes at the same time and find the sum of the two numbers that appear on the top faces.
What is the probability that the sum will be an odd number on Larry’s first toss?
Support your answer using words, numbers and/or diagrams.
NOTE: each die has 3 odd and 3 even numbers.7 / 8 / 9 / 10 / 11 / 12
1 / 8 / 9* / 10 / 11* / 12 / 13*
2 / 9* / 10 / 11* / 12 / 13* / 14
3 / 10 / 11* / 12 / 13* / 14 / 15*
4 / 11* / 12 / 13* / 14 / 15* / 16
5 / 12 / 13* / 14 / 15* / 16 / 17*
6 / 13* / 14 / 15* / 16 / 17* / 18
Possible outcomes
Even & Even / Even & Odd
Odd & Even / Odd & Odd
There are 18 odds with a sample space of 36. Odd + Even = Odd = Even + Odd 2 of 4 = 1/2
P(sum of an odd) = 18/36 = ½ Even + Even = Even = Odd + Odd
What is the probability that the sum will be an odd number on Larry’s first toss? _1/2___
1
Teacher: Ch 23 “How to Win on Wheel of Fortune”