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Lesson Summary:
In this activity the teacher will first explore with students the connection between mathematics and card games, and learn about its history. Then students will work in groups, using a deck of cards to determine the probabilities of drawing various combinations of cards. Finally groups will determine an optimal combination, and play a tournament. Subject:
Math: Data Analysis and Probability, Problem Solving
Grade Level:
Target Grade: 6
Upper Bound: 8
Lower Bound: 6
Time Required: 30-50 minutes Authors:
Graduate Fellow Name: Candace DiBiano Teacher Mentor Name: Stacey Webb Date Submitted: 6/9/05 Date Last Edited: 6/9/05 Lesson Introduction / Motivation:
The lesson will be introduced by initiating a discussion with the students through the HYPERLINK "MathandCardGames.ppt"Math and Card Games PowerPoint. In the notes of the PowerPoint are questions that can be brought up for discussion as you are going through the slides.Lesson Plan:
After youve gone through the PowerPoint, divide the students up into groups of 3, and give each group one of the six HYPERLINK "MathPokerWorksheet.doc"Math Poker Worksheets (preferably each group should have a different one), and give each group a deck of cards.
The worksheets first give each group 4 different choices of card combinations that their group can get points for drawing. Tell the students that without doing any math or calculations, to make a hypothesis within their group on which combination would be best.
After the groups have come up with their hypotheses, tell them to use their deck of cards and what they know about probability to mathematically decide which of the combinations is best. Tell students they must fill out the information for each of the 4 options.
Explicit instructions were intentionally not given on the worksheet; allow the students time to explore the problem in their groups before giving them more detailed help with the problem.
After you think all the groups have finished the first calculation for Option 1, tell the class to stop working and listen for a moment. Tell the students there are 4 of the first card listed (aces for group 1), 4 of the second card listed (2s for group 1), and 13 cards of the suit listed. Ask the students why the probability of picking any of these cards didnt come out as (4+4+13)/52 = 21/52, but instead it came out as 19/52.
It is 19/52 because when you count the suit in the third step, theres only 11 cards left of that suit since you counted one from that suit in the first 4 cards, and one from that suit in the second 4 cards. This is perhaps the most important concept for students to take away from this lesson. I taught college freshman Business Calculus and that exact kind of question was a huge point of confusion during their probability unit.
When a group has done the math for all four options, and has decided Option 4 is the best, check their numbers with the following Answer Key (the answers are the same for each of the 6 worksheets):
Option 1: 19/52, 36.54%
Option 2: 12/52, 23.1%
Option 3: 26/52, 50%
Option 4: 28/52, 53.85%
If the groups answers are correct, given them one of the six HYPERLINK "MathPokerWorksheet2.doc"Math Poker Part 2 Worksheets. Make sure you give them the correct worksheet whose Group # matches up with the first worksheet they received.
The second worksheet is considerably harder to reason out, give them some time to explore it in their group, and then give them guiding hints. The answer is that the second option is best, if you look at the total number of points the entire deck would be worth with Option 1 and then with Option 2, you can see this:
Option 1:
5 points * 4 queens = 20 points
2 points * 24 black cards = 48 points
Total = 68 points
(We use only 24 black cards, because the two black queens were counted for 5 points, leaving us with only 24 black cards to count for 2 points)
Option 2:
2 points * 2 queens = 4 points
3 points * 26 black cards = 78 points
Total = 82 points
(We use only 2 queens, because the two black queens will be counted for 4 points with the black cards group, leaving us with only the 2 red queens.)
You can get students going along this path by encouraging them to take each card in the deck individually, and divide them up into three piles, one pile they get no points for, one pile they get the first point value for, and one pile they get the second point value for.
After a group has figured out the second worksheet, they are finished. I had the students play a tournament with another finished group, using their rules for what cards they get points for, and how many points. Each team would draw out 5 cards, and like in poker, and then choose how many they wanted to discard and redraw for. Students would only receive points for the cards they chose to get points for on their groups worksheet. The team with the highest point total after the cards were redrawn once would win the hand.
Activities used in this Lesson:
HYPERLINK "MathPokerWorksheet.doc" \t "_blank" Math Poker Worksheets These 6 worksheets are identical except for the card names and suits on each. A different one should be given out to each group, if possible.
HYPERLINK "MathPokerWorksheet2.doc" \t "_blank" Math Poker Part 2 Worksheets These 6 worksheets are identical except for the card names and suits on each. A worksheet corresponding to the groups first worksheet should be given out once they have completed the first worksheet.
Assessment:
You can give out a basic probability worksheet that involves probability with things like cards and dice to measure if the students got it.
Materials
One deck of cards per 3 students in the class
Multimedia Support and Attachments:
HYPERLINK "MathandCardGames.ppt" Math and Card Games PowerPoint
Lesson Scaling:
For lower classes, the Math Poker Part 2 Worksheet can be omitted.
References:
HYPERLINK "http://mathforum.org/library/drmath/view/53328.html" http://mathforum.org/library/drmath/view/53328.html
HYPERLINK "http://mathworld.wolfram.com/Poker.html" http://mathworld.wolfram.com/Poker.html
HYPERLINK "http://www.homepokergames.com/cardcounting.php" http://www.homepokergames.com/cardcounting.php
HYPERLINK "http://www.mitcardcounting.com/" http://www.mitcardcounting.com/
Please email us your comments on this lesson: E-mail to HYPERLINK "mailto:ljohnson@cvm.tamu.edu" ljohnson@cvm.tamu.eduPlease include the title of the lesson, whether you are a teacher, resident scientist or college faculty and what grade you used it for.
Teacher's Comments:
Keywords:
math
probability
fraction
percent
card
poker
Texas State Standards
6.3 (B) Represent ratios and percents with models, fractions, decimals
6.3 (C) Use ratios to make predictions
6.9 (B) Find the probabilities of a simple event and its complement
6.11 (A) Identify and apply mathematics to everyday experiences
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