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Focus Plan Texarkana Independent School District GRADING PERIOD: Teacher: 3rd Six Weeks PLAN CODE: Tipton Course/subject: Mathematics Grade(s): 8 Time allotted for instruction: 1 – 1 ½ hours Title: Probability and the Alphabet Lesson TOPIC: Probability, statistics TAKS Objective: Objective 5: The student will demonstrate an understanding of probability and statistics. FoCUS TEKS and Student Expectation: (11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: (B) use theoretical probabilities and experimental results to make predictions and decisions (11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to: (C) select and use different models to simulate an event Supporting TEKS and Student Expectations: Concepts Probability Statistics Enduring Understandings/Generalizations/Principles The student will understand that Probability is the chance that some event will happen. It is the ratio of the number of ways a certain event can occur to the number of possible outcomes. Statistics is the branch of mathematics that deals with collecting, organizing, and analyzing data. Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District I. Sequence of Activities (Instructional Strategies) A. Focus/connections Prior to this lesson, you will need enough newspaper articles (that will be written on) for every other student in your class. Introduction: Tell the class that today you are going to play hangman. Play a short game of hangman with the class. B. Instructional activities (demonstrations, lectures, examples, hands-on experiences, role play, active learning experience, art, music, modeling, discussion, reading, listening, viewing, etc.) Ask the class: “Would it be good to always pick a Q when playing this game?” (Class should say no.) Have several volunteers tell why they would not pick a Q. Explain to the class that statistics and probability play an important part in our lives and are particularly useful in helping make wise decisions. Ask students how many letters are in the alphabet. Next ask whether there are some letters in the alphabet that are used more than others. Now explain that the probability of an outcome for a particular event is a number telling us how likely a particular outcome is to occur. This number is the ratio of the number of ways the outcome may occur to the number of total possible outcomes for the event. Probability is usually expressed as a fraction or decimal. Since the number of ways a certain outcome may occur is always smaller or equal to the total number of outcomes, the probability of an event is some number from 0 through 1. Now give the class the following example: suppose there are 10 balls in a bucket numbered as follows: 1, 1, 2, 3, 4, 4, 4, 5, 6, and 6. A single ball is randomly chosen from the bucket. What is the probability of drawing a ball numbered 1? Explain to the class that there are 2 ways to draw a 1, since there are two balls numbered 1. The total possible number of outcomes is 10, since there are 10 balls. The probability of drawing a 1 is the ratio 2/10 = 1/5. Next give the class this example: suppose a card is drawn at random from a regular deck of 52 cards. What is the probability that the card is an ace? Explain to the class that there are 4 different ways that the card can be an ace, since 4 of the 52 cards are aces. There are 52 different total outcomes, one for each card in the deck. The probability of drawing an ace is the ratio 4/52 = 1/13. C. Guided activity or strategy After students have an understanding of probability, have them get into pairs. Each pair will need one article from the newspaper and an Alphabet Study Worksheet. Tell the pairs to start at the beginning of their article and tally the letters until 200 letters are counted. Students will record their answers on the worksheet provided. One student may call out and the other may tally. Let the students work for about 7 minutes and then ask them to stop. After they have stopped counting, have the students figure the percentage of probability of finding each letter. Have students compare and contrast their results. Ask: “Were there any discrepancies?” , “Were there any similarities”. Students will need to justify their answers. D. Accommodations/modifications Students requiring modifications may work with a peer during the guided activity. E. Enrichment Students requiring enrichment may peer tutor/reteach during the guided activity. II. STUDENT PERFORMANCE A. Description Students will complete the Probability Worksheet independently. Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District iii. B. Accommodations/modifications C. Enrichment Assessment of Activities A. Description Individual student grades may be taken on the Probability Worksheet. B. Rubrics/grading criteria Grades may be taken based on the Probability Worksheet Answer Key and Grading Rubric. C. Accommodations/modifications D. Enrichment E. IV. Sample discussion questions How is probability used in the real-world? Why is it important to know how to make predictions? TAKS Preparation A. Transition to TAKS context The teacher will lead the students in a discussion of how probability problems may look in test format by placing the following TAKS questions on the overhead/board. B. Sample TAKS questions 1. Fidel tosses four fair coins. What is the probability that all four coins will land heads up? A. 1/16 B. 1/8 C. 1/4 D. 1/2 2. A spinner and a fair number cube are used in a game. The spinner has an equal chance of landing on 1 of 4 colors: red, purple, blue, or green. The faces of the cube are labeled 1 through 6. What is the probability of a player spinning the color red and then rolling a 5 or 6? F. 3/10 G. 1/8 H. 1/12 J. 1/24 V. Key Vocabulary Probability, statistics VI. Resources A. Textbook Glencoe Mathematics ~ Applications and Connections Chapter 6: Exploring Number Patterns Simple Events, pp. 253-256 Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District B. Supplementary materials Alphabet Study Worksheet Probability Worksheet Probability Worksheet Answer Key and Grading Rubric C. Technology Students may be taken to the computer lab to work with the probability websites below: http://www.bbc.co.uk/education/mathsfile/shockwave/games/fish.html http://www.mathgoodies.com/lessons/vol6/challenge_vol6.html http://nces.ed.gov/NCESKids/Probability/ VII. follow up activities (reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.) Have students brainstorm how statistics and probability can help them in their daily lives. Discuss how often different individuals can come up with different statistics and how this information would impact a decision. You could also have students predict what some of the most common words in writing are and why. VIII. Teacher Notes If you have a VCR in your classroom, you might want to record a segment of Wheel of Fortune to show at the beginning of class. This would be a great introduction to this lesson. Division of Curriculum and Instruction School Improvement Department Texarkana Independent School District