Sample 5.3.B.2 Complete



|Domain: Sequences, Series and Probability |

|Cluster: Precalculus |

|Standards: CCSS.Math.Content.HSS-MD.A.1, CCSS.Math.Content.HSS-MD.A.3, CCSS.Math.Content.HSS-MD.A.4, CCSS.Math.Content.HSS-MD.B.5, CCSS.Math.Content.HSS-MD.B.5a, CCSS.Math.Content.HSS-MD.B.5b,|

|CCSS.Math.Content.HSS-MD.A.2 |

|Essential Questions |Enduring Understandings |Activities, Investigation, and Student Experiences |

|Where do we see arithmetic sequences in real-life? If we |Assign a numerical value to events, and graph sample | |

|generate a function what kind of function would it be? |space. CCSS.Math.Content.HSS-MD.A.1, |Investigation Tools |

|What is a Recursion Formula and how we use it? |Calculate expected value. |1. TI-SmartView Program |

|How do we find the sum of a finite arithmetic sequence? |CCSS.Math.Content.HSS-MD.A.2 |2. WolframAlpha Website |

|Is it possible to find the sum of an infinite geometric |Understand the probability of real life events such |3. Textbook Activities |

|sequence? Explain different cases. |as winning a lottery or answering 5 multiple choice |

|Is it possible to use the binomial theorem to expand complex|questions and find the probability of different |ts/sso.html |

|numbers? |cases. CCSS.Math.Content.HSS-MD.A.3, |

|What is the difference between permutation and combination? |Application of expected values to real-life cases. |rces/ap.html |

|Explain the Fundamental Counting Principle. |CCSS.Math.Content.HSS-MD.A.4, |

|Explain the relationship between combinations and the |Use expected value for making decisions such as life |graphing-approach-5th-edition/ |

|Binomial Theorem. |insurance policies and their annual costs. | |

|Find the probability of winning different lottery games. |CCSS.Math.Content.HSS-MD.B.5, | |

|How do we calculate expected value? |CCSS.Math.Content.HSS-MD.B.5a,CCSS.Math.Content.HSS-M|Example Student Experiences: |

|In your own words explain mutually exclusive events, |D.B.5b, |1. The sum of the first 20 terms of an arithmetic sequence with common |

|complement of events, and independent events. | |difference of 3 is 650. Find the first term. |

| | |2. Write a brief paragraph explaining how to use the first two terms of a |

| | |geometric sequence to find the nth term. |

| | |3. Form the rows of Pascal’s Triangle. |

| | |4. Find the number of diagonals of any polygon and generate a formula. |

| | |5. The weather forecast indicates that the probability of rain is 40%. |

| | |Explain what this means. |

| | |6. Find the probability of winning various lottery games. |

| | |7. Find the probability of becoming a professional basketball player or |

| | |singer. |

|Content Statements | | |

|Students will be able to use sequence, factorial, and | | |

|summation notation to write the terms and sums of sequences.| | |

|Students will be able to recognize, write, and use | | |

|arithmetic sequences and geometric sequences. | | |

|Students will be able to use the Binomial Theorem and | | |

|Pascal's triangle to calculate binomial coefficients and | | |

|write binomial expansions. | | |

|Students will be able to solve counting problems using the | | |

|Fundamental Counting Principle, permutations, and | | |

|combinations. | | |

|Students will be able to find the probabilities of events | | |

|and their complements. | | |

|Students will be able to use probability to make decisions. | | |

|Students will be able to calculate the expected value of a | | |

|random variable. | | |

|Assessments | |

|Do-Now problems | |

|Warm-up questions | |

|Group/Partner Activities | |

|Oral Questioning Assessments | |

|Worksheets | |

|Student Interactive Handheld Devices | |

|Exit Cards | |

|Daily Homework | |

|Quizzes on concepts | |

|Unit Tests | |

|Equipment Needed: |Teacher Resources: |

|Promethean Board |Safari Montage: Math’s Cool and Algebra’s Cool video series |

|Blackboard | |

|ActiView Camera |Math Warehouse |

|Computer | |

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| |Kutasoftware worksheets |

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| |National Library of Virtual Manipulatives |

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| |Algebra Lessons and PowerPoint Activities |

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| |Classzone Interactive Games |

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| |Virtual Math Lab |

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| |Khan Academy Math Videos |

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| |Center of Teaching and Learning |

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| |Larson Textbook Activities |

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| |ts/sso.html |

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| |rces/ap.html |

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| |graphing-approach-5th-edition/ |

Calculate expected values and use them to solve problems

• CCSS.Math.Content.HSS-MD.A.1 (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

• CCSS.Math.Content.HSS-MD.A.2 (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

• CCSS.Math.Content.HSS-MD.A.3 (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.

• CCSS.Math.Content.HSS-MD.A.4 (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?

Use probability to evaluate outcomes of decisions

• CCSS.Math.Content.HSS-MD.B.5 (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

o CCSS.Math.Content.HSS-MD.B.5a Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.

o CCSS.Math.Content.HSS-MD.B.5b Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.

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