Transcript Slide 1 - Math GR. 6-8

Probability and Statistics
Is it Fair or Unfair
Teacher Quality Grant
What does it mean to be fair?
Activity 1: Fair and Unfair Games
• Have you ever felt that a game you were
playing wasn't fair but you weren't sure
why?
– You can use probability to decide whether a
game is fair or unfair.
Activity 1: Fair and Unfair Games
1. A spinner has 8 equal sections. Four sections are
gray, three are white, and one is blue. Keri and
Josh use the spinner to play a game. The rules
are:
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Players alternate turns.
Keri gets a point if she lands on gray or blue.
Josh gets a point if he lands on white or blue.
First player to earn 10 points wins.
Activity 1: Fair and Unfair Games
2. Josh lost the first game and said the game wasn't
fair. Keri said the 8 sections were equal, so the
game was fair. What do you think of her
argument? Does it prove that the game is fair?
3. If you were playing this game, would you take the
gray and blue sections or the white and blue
sections? Why?
Activity 1: Fair and Unfair Games
Try this:
1. Shane and Amanda play a number cube game.
Shane gets a point if he rolls a number evenly
divisible by 2. Amanda gets a point if she rolls a
number evenly divisible by 3. Is the game fair?
Explain.
Activity 1: Fair and Unfair Games
Draw Conclusions:
1. Change one rule in Keri and Josh’s game to
make the game fair.
Activity 2: Fair and Unfair Games
Activity 2:
• This activity is also included on the PDF with
Activity 1 complete the activity in groups of 3.
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Your group is taking on the rolls of Kara, Derik,
and Heather in the activity.
Activity 3: Fair and Unfair Games
Activity 3:
• Materials: Cubes
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Get into groups of 3 and complete the activity 3
Activity 3: Fair and Unfair Games
1. Suppose you tossed a number cube. Which
outcome would be more likely, a 5 or an even
number? Explain your reasoning.
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an even number; there are three even numbers you
could toss (2, 4, 6) but only one 5 (5).
2. Toss a number cube 20 times. Record the
number of times you roll a 5 and the number
of times you roll an even number.
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Because there are three even numbers but only one 5,
students will probably roll an even number more often
than they roll a 5.
Activity 3: Fair and Unfair Games
3. Do the results of your experiment in Step 2
confirm your reasoning in Step 1? Explain
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Blue is most likely because there are more blue marles
than any other color. Green is the last likely because there
are fewer green marbles than any other color
Activity 3: Fair and Unfair Games
4. If you withdraw one marble from the bag at
random, which is the most likely color that you
will draw? Which is the least likely? Explain.
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blue: 11/16 ; red: 4/16 ; green: 1/16
5. For each of the three colors, find the
probability that you will draw that color.
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11/16 ; 1/16
7. Of the three probabilities, which is greatest?
Which is least?
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Event B
Activity 3: Fair and Unfair Games
Activity 3: Fair and Unfair Games
9. no; Sector 3 is bigger than the other two sections, so it is
more likely that you will spin 3 than either of the other two
numbers. Sector 2 is smaller than the other two sections,
so it is less likely that you will spin 2 than either of the other
two numbers.
10. agree; because Sector 3 is bigger than the other sectors,
Joey has a better chance of winning than either Mark or
Kenny has.
Activity 3: Fair and Unfair Games
13.
Fair
12.
Unfair
11. Fair
More Activities
• Lesson Plan
– http://www.learnnc.org/lp/pages/3786
– Racing Game
– Racing Game Field
• Pig Games
– Greedy Pig Dice Game
– Pig Dice Game