Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics

Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics Enduring understanding (Big Idea): Students will be able to use probability practices to solve real-life statistics problems. Essential Questions: 1. What is the difference between a permutation and a combination? 2. What is the difference between theoretical and experimental probability? 3. How do independence and dependence of events affect the computation of probabilities in two-stage experiments? 4. How is probability used in real-world settings? BY THE END OF THIS UNIT: Students will know… Students will be able to:  The difference between combination and  Determine if theoretical or experimental permutation problems. probability is the best course of action to  The difference between independent solve a problem. and dependent probabilities.  Use dependent and independent computations to solve probabilities Vocabulary: Population, sample, convenience sample, self-selected sample, systematic sample, random sample, bias, observational study, controlled experiment, survey, Experimental probability, theoretical probability, geometric probability, simulation, sample space, equally likely outcomes, outcome, event, complement of an event, odds, conditional probability, relative frequency, probability distribution, uniform distribution, cumulative frequency, cumulative probability, two- way frequency table, Compound event, Independent and Dependent event, mutually exclusive events, overlapping events, Fundamental Counting Principal, permutation, combination, n factorial Unit Resources: Mathematical Practices in Focus: Performance Task: 1. Make sense of problems and persevere in Pearon Alg 2 probability performance tasks.pdf solving them probability activity.pdf 2. Reason abstractly and quantitatively Project: 3. Construct viable arguments and critique l21_probability_statements_beta_complete.pdf the reasoning of others 4. Model with mathematics Test Specification Weights for the Common 6. Attend to precision Exams in Common Core Math II:

CCSS-M Included: S.IC.2, S.IC.6, S.CP.1 – S.CP.9

Abbreviation Key: CC – Common Core Additional Lessons found in Suggested Order/Pacing: Geometric Probability: Section 10.8 the Pearson online materials. Theoretical and Experimental Probability: CC-21, CB- Concept Bytes found in between lessons in Algebra 1BK: Section 12.7, CB 12.7, ER 12.7 the Pearson textbook. Algebra 2 BK: Section 11.2 ER – Enrichment worksheets found in teacher Probability Distribution and Frequency Tables: CC-22 resources per chapter. Algebra 2 BK: CB 11.3 Permutations and Combinations: CC-23,

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 1 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics Algebra 1 BK: Section 12.6, ER 12.6, Algebra 2 BK: Section 11.1 Merge information from Geometry, Compound Probability and Probability of Multiple Events: CC-24, and Algebra 1 BK: Section 12.8, ER 12.8 Algebra 1, and Algebra 2 Books to Algebra 2 BK: Section 11.3 complete this unit. Contingency Tables: CC-25 Conditional Probability: CC-26, Algebra 1 BK: CB 12.8 and Algebra 2 BK: Section 11.4

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 2 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics CORE CONTENT Cluster Title: Understand and evaluate random processes underlying statistical experiments. Standard S-IC.2 Decide if a specified model is consistent with results from a given data generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? Concepts and Skills to Master  Find the experimental probability of an event  Find the theoretical probability of an event  Use of a simulation to model an event  Make decisions about probability based on simulated events SUPPORTS FOR TEACHERS Critical Background Knowledge:  Event, possibilities, successes  Sample space, trials, outcomes  Cards in a deck, faces of a die Academic Vocabulary: Experimental probability, simulation, sample space, equally likely outcomes, theoretical probability Suggested Instructional Strategies: Starting Resources:  Utilized the TI-84 Probability Simulation App Algebra 1 Textbook  Remind students that they did simple probability in middle Correlation: school CB 12.7  Use a coin toss experiment to introduce the concepts but quickly move to simulations Algebra 2 Textbook  Use your calculator to do the simulations like coin toss and Correlation: random number generator Section 11.2, ER 11.2, CB NCDPI Unpacking: 11.3 What does this standard mean that a student will know and be able to do? 1) Explain how well and why a sample represents the variable of interest from a population. 2) Demonstrate understanding of the different kinds of sampling methods. 3) Design simulations of random sampling: assign digits in appropriate proportions for events, carry out the simulation using random number generators and random number tables and explain the outcomes in context of the population and the known proportions. Use data-generating processes such as simulations to evaluate the validity of a statistical model. Additional note from DPI for Level II: Ex. Jack rolls a 6 sided die 15 times and gets the following results: 4, 6, 1, 3, 6, 6, 2, 5, 6, 5, 4, 1, 6, 3, 2 Based on these results, is Jack rolling a fair die? Justify your answer using a simulation. Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 3 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics Sample Assessment Tasks Skill-based task: Problem Task: On a multiple choice test, each item has 4 choices, On a multiple-choice test, each item has 4 but only one choice is correct. How can you choices, but only one choice is correct. How simulate guessing the answers? Based on your can you simulate guessing the answer? simulation of at least 20 trials, what is the What is the probability that you will pass the probability that you will pass the test by guessing at test by guessing at least 6 of 10 answers least 6 of 10 answers correctly? correctly?

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 4 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics CORE CONTENT Cluster Title: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Standard: S-IC.6 Evaluate reports based on data. Concepts and Skills to Master:  Evaluate reports based on data SUPPORTS FOR TEACHERS Critical Background Knowledge: Academic Vocabulary: Population, sample, convenience sample, self-selected sample, systematic sample, random sample, bias, observational study, controlled experiment, survey Suggested Instructional Strategies: Starting Resources: What does this standard mean that a Algebra 2 Textbook Correlation: student will know and be able to do? Section 11.7 Read and explain in context data from outside reports. Evaluate reports based on data on multiple aspects (e.g. experimental design, controlling for lurking variables, representativeness of samples, choice of summary statistics, etc.)

Sample Assessment Tasks Skill-based task: Problem Task: A survey asks, “Aren’t handmade gifts always What sampling method could you use to find the better than tacky purchased gifts?” Does this percent of adults in your community who survey question have any bias? Explain. support building more nuclear power plants? What is an example of a survey question that is likely to yield unbiased information?

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 5 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics CORE CONTENT Cluster Title: Understand independence and conditional probability and use them to interpret data. Standard: S.CP.1 Describe events and subsets of a sample space using characteristics of the outcomes, or as unions, intersections, and complements of other events ("or," "and," "not.") Concepts and Skills to Master:  The probability of an impossible event is 0, (0%), the probability of a certain event is 1 (100%), and all other probabilities are between 0 and 1.  The probability that an event will occur + the probability it will not occur = 1.  Define a sample space and events within the sample space. Identify subsets from sample space given defined events, including unions, intersections and complements of events. SUPPORTS FOR TEACHERS Critical Background Knowledge:  Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities Find the area of polygons and circles. Academic Vocabulary: Experimental probability, theoretical probability, geometric probability, simulation, sample space, equally likely outcomes, outcome, event, complement of an event, odds Suggested Instructional Strategies: Starting Resources:  Use Venn diagrams to remind students Geometry Textbook Correlation: how to determine the difference between 10.8, CC.21 “and” and “or”. Algebra 1 Textbook Correlation: NCDPI Unpacking: Section 12.7 What does this standard mean that a student will know and be able to do? Algebra 2 Textbook Correlation: 1) Define the sample space for a given Section 11.2, ER 11.2 situation. Additional note from DPI for Level II: http://www.shodor.org Interactive Venn Ex. What is the sample space for rolling a die? Diagram Shape Sorter Ex. What is the sample space for randomly selecting one letter from the word MATHEMATICS? 2) Describe an event in terms of categories or characteristics of the outcomes in the sample space. Additional note from DPI for Level II: Ex. Describe different subsets of outcomes for rolling a die using a single category or characteristic. 3) Describe an event as the union, intersection, or complement of other events.

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 6 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics Additional note from DPI for Level II: Ex. Describe the following subset of outcomes for choosing one card from a standard deck of cards as the intersection of two events: {queen of hearts, queen of diamonds}. Sample Assessment Tasks Skill-based task: Problem Task: If the probability an event will occur is 74%, What is the probability that a quarterback will what is the probability it will not occur? complete his next pass if he has completed 30 of his last 40 passes?

CORE CONTENT Cluster Title: Understand independence and conditional probability and use them to interpret data. Standard S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the products of their probabilities, and use that characterization to determine if they are independent. Concepts and Skills to Master  Explain properties of Independence and Conditional Probabilities in context and simple English. SUPPORTS FOR TEACHERS Critical Background Knowledge:  Understand basic properties of probability. (7.SP.5)  Approximate probabilities of chance events through experiment. (7.SP.6)  Use Venn diagrams (II.4.S.CP.1) and two-way frequency tables. (I.S.ID.5)  (A ∩ B) is the equivalent of the probability of event A and event B occurring together. (II.4.S.CP.1) Academic Vocabulary: Conditional probability, Suggested Instructional Strategies: Starting Resources: Geometry Textbook Correlation: NCDPI Unpacking: CC-26 What does this standard mean that a student will know and be able to do? Algebra 1 Textbook Correlation: 1) Understand that two events A and B are CB 12.8 independent if and only if P(A and B)= Algebra 2 Textbook Correlation: Section 11.4 𝑃(𝐴) ∙ 𝑃(𝐵).

2) Determine whether two events are independent using the Multiplication Rule (stated above).

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 7 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics 3) Explain properties of Independence and Conditional Probabilities in context and simple English.

Additional note from DPI for Level II: Ex. For the situation of drawing a card from a standard deck of cards, consider the two events of “draw a diamond” and “draw an ace.” Determine if these two events are independent.

Ex. Create and prove two events are independent from drawing a card from a standard deck.

Sample Assessment Tasks Skill-based task: Problem Task: C and D are independent events, , and . What Suppose you randomly select a is P(C and D)? shape from this circle. What is the probability that the shape is black and has five points?

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 8 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics CORE CONTENT Cluster Title: Understand independence and conditional probability and use them to interpret data. Standard S.CP.3 Understand the conditional probability of A given B as P(A and B)/ P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as P(A) and the conditional probability of B given A is the same as P(B). Concepts and Skills to Master:  The probability that an event B will occur given that another event, A, has already occurred.  Conditional probability occurs when two events are dependent.  Define and calculate conditional probabilities. Use the Multiplication Principal to decide if two events are independent and to calculate conditional probabilities. SUPPORTS FOR TEACHERS Critical Background Knowledge: Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities Academic Vocabulary: Conditional Probability Suggested Instructional Strategies: Starting Resources: Use Venn diagrams to explore and compute Geometry Textbook Correlation: conditional probabilities. CC-26

NCDPI Unpacking: Algebra 1 Textbook Correlation: What does this standard mean that a student CB 12.8 will know and be able to do? 1) Understand that the conditional probability of Algebra 2 Textbook Correlation: event A given event B has already happened is Section 11.4 given by the formula:

2) Understand that two events A and B are Cut the Knot – Conditional Probability and independent if and only if In other words, the Independent Events: fact that one of the events happened does not change the probability of the other event http://www.cut-the- happening. knot.org/Curriculum/Probability/Condition 3) Prove that two events A and B are independent alProbability.shtml by showing that Texas A&M – Conditional Probability Additional note from DPI for Level II: Applet: Ex. For the situation of drawing a card from a standard deck of cards, consider the two events of “draw a http://www.stat.tamu.edu/~west/applets/ spade” and “draw a king.” Prove that these two events Venn1.html are independent. Ex. Create and prove two events are dependent from drawing a card from a standard deck. Sample Assessment Tasks

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 9 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics Skill-based task: Problem Task:

Given the following Venn A box contains 10 blue cubes, 5 red diagram, determine whether cubes, 5 blue marbles and 10 red events A and B are marbles. You randomly pick a blue independent. shape from the box. What is the probability you picked a cube?

ANS: 67%

CORE CONTENT Cluster Title: Understand independence and conditional probability and use them to interpret data. Standard S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Concepts and Skills to Master:  Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified.  Use a two-way table as a sample space to decide if events are independent  Use a two-way table to approximate conditional probabilities. SUPPORTS FOR TEACHERS Critical Background Knowledge: Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities Academic Vocabulary: Experimental probability, theoretical probability, geometric probability, simulation, sample space, equally likely outcomes, outcome, event, complement of an event, conditional probability, relative frequency, probability distribution, uniform distribution, cumulative frequency, cumulative probability, two-way frequency table

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 10 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics Suggested Instructional Strategies: Starting Resources: NCDPI Unpacking: Geometry Textbook What does this standard mean that a student will know and Correlation: be able to do? CC.21,CC.22, CC.25 1.Construct and interpret a two-way frequency table from a set of data on two categorical variables. Algebra 1 Textbook Additional note from DPI for Level II: Correlation: Ex.Make a two-way frequency table for the following set of data. Use Section 12.7 (see next the following age groups: 3-5,6-8,9-11,12-14,15-17. page for more resources.)

Algebra 2 Textbook Correlation: CB 11.3, Section 11. 4

Source for problem task: 2.Determine if two categorical variables are independent by analyzing a two- http://wiki.warren.kyschool way table of data collected on the two variables. s.us/groups/wcpscommonc 3.Calculate conditional probabilities based on two categorical variables from a orestandards/wiki/45424/i table and interpret in context. mages/75b78.png#697x2 Additional note from DPI for Level II: 51 Ex. Use the frequency table to answer the following questions. a. Given that a league member is female, how likely is she to be 9-11 years old? b. What is the probability that a league member is aged 9-11? c. Given that a league member is aged 9-11, what is the probability that a member of this league is a female? d. What is the probability that a league member is female? e. Are the events “9-11 years old” and “female” independent? Justify your answer.

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 11 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics Sample Assessment Tasks Skill-based task: Problem Task:

Use the table below to determine if being a girl and never having a part-time job are independent or dependent events. Then approximate the probability that a student is a girl, given that the student never had a part-time job.

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 12 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics CORE CONTENT Cluster Title: Understand independence and conditional probability and use them to interpret data. Standard S-CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Concepts and Skills to Master:  Recognize the concepts of conditional probability and independence in everyday language and everyday situations.  Explain the concepts of conditional probability and independence in everyday language and everyday situations. SUPPORTS FOR TEACHERS Critical Background Knowledge: Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities Academic Vocabulary: relative frequency, probability distribution, uniform distribution, cumulative frequency, cumulative probability, two-way frequency table, conditional probability Suggested Instructional Strategies: Resources:  Give an example of a situation where conditional Geometry Textbook Correlation: probability would be used. Explain why conditional CC.22, CC.26 probability applies to a situation.  Give an example of two independent events. What Algebra 1 Textbook Correlation: constitutes the independence of two events? CB 12.8

Instructional Expectations Algebra 2 Textbook Correlation: In both pathways, the expectation in Geometry and CCSS Section 11.3, 11.4 Mathematics II is to build on work with two-way tables from Algebra I Unit 3 (S.ID.5) to develop understanding of conditional Read more: Examples of Real Life probability and independence. Probability | eHow.com What does this standard mean that a student will http://www.ehow.com/list_7719506_r know and be able to do? eal-life-probability- Given an everyday situation describing two events, use the examples.html#ixzz1wvNUV1st context to construct an argument as to whether the events are independent or dependent. HONORS: http://myweb.cableone.net/surgett/n Additional note from DPI for Level II: mmi/webquests/probability/ Ex. Felix is a good chess player and a good math student. research project for real life Do you think that the events “being good at playing chess” applications of probability. and “being a good math student” are independent or dependent? Justify your answer. Ex. Juanita flipped a coin 10 times and got the following results: T, H, T, T, H, H, H, H, H, H. Her math partner Harold thinks that the next flip is going to result in tails because there have been so many heads in a row. Do you Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 13 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics agree? Explain why or why not. Sample Assessment Tasks Skill-based task: Problem Task: If you are using a game spinner with four sections -- red, blue, Have students find and green and yellow -- you have a 25 percent chance of landing on interpret probability red, since one of the four sections is red. What is the probability statements in media. that you're going to roll one die and get an even number? You have a 50 percent chance, since three of the six numbers on a die are even.

CORE CONTENT Cluster Title: Use the rules of probability to compute the probabilities of compound events in a uniform probability model. Standard S.CP.6 Find the conditional probability of A given B as the fractions of B's outcomes that also belong to A, and interpret the answer in terms of the model. Concepts and Skills to Master:  Find and interpret conditional probabilities using a two-way table, Venn diagram, or tree diagram. SUPPORTS FOR TEACHERS Critical Background Knowledge:  Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities  Find probabilities of compound events. (7.SP.8)  Summarize categorical data in two-way frequency tables. (I.4.S.ID.5) Academic Vocabulary: Conditional Probability

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 14 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics Suggested Instructional Strategies: Starting • Make a “human Venn diagram” where the sample space is all the Resources: students in the class. Use lengths of rope to create three overlapping circles. Geometry Textbook Assign an event to each of the three circles, such as: ate breakfast, brought Correlation: a cell phone to school, and got at least 7 hours of sleep. Have students CC.26 place themselves in the appropriate locations. Using correct probability notation, identify each of the spaces in the Venn diagram (don’t forget to Algebra 2 Textbook include the space outside the circles). Analyze, explore and record the Correlation: results in terms of conditional probabilities. Section 11.4 • Connect to probability models from other standards. NCDPI Unpacking: What does this standard mean that a student will know and be able to do? 1) Understand that when finding the conditional probability of A given B, the sample space is reduced to the possible outcomes for event B. Therefore, the probability of event A happening is the fraction of event B’s outcomes that also belong to A.

2) Understand that drawing without replacement produces situations involving conditional probability. 3) Calculate conditional probabilities using the definition. Interpret the probability in context. Additional note from DPI for Level II: Ex. Peter has a bag of marbles. In the bag are 4 white marbles, 2 blue marbles, and 6 green marbles. Peter randomly draws one marble, sets it aside, and then randomly draws another marble. What is the probability of Peter drawing out two green marbles? Sample Assessment Tasks Skill-based task: Problem Task: From the table, determine the probability of getting the Life is like a box of chocolates. Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 15 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics flu, and compare that to the probability of getting the flu Suppose your box of 36 chocolates given that an individual takes high doses of vitamin C. have some dark and some milk Cold No cold total chocolate, divided into cream or nutty Placebo 31 109 140 centers. Out of the dark chocolates, 8 Vitamin C 17 122 139 have nutty centers. Out of the milk Total 48 231 279 chocolates, 6 have nutty centers. One- third of the chocolates are dark chocolate. What is the probability that you randomly select a chocolate with a nutty center? Given that it has a nutty center, what is the probability you chose a dark chocolate? Show how you determined your answers.

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 16 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics CORE CONTENT Cluster Title: Use the rules of probability to compute the probabilities of compound events in a uniform probability model. Standard S-CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. Concepts and Skills to Master:  Mutually exclusive events P(A and B) = P(A) + P(B)  Dependent events P(A or B) = P(A) + P(B) - P(A and B) OR  Identify two events as disjoint (mutually exclusive). Calculate probabilities using the Addition Rule.  Interpret the probability in context. SUPPORTS FOR TEACHERS Critical Background Knowledge:  Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities  Computing independent events Academic Vocabulary: Compound event, Independent and Dependent event, mutually exclusive events, overlapping events Suggested Instructional Strategies: Starting Resources: 11.3 Algebra 2 Pearson Game: The Probability Path Geometry Textbook Correlation: NCDPI Unpacking: CC.24 What does this standard mean that a student will know and be able to do? Algebra 1 Textbook Correlation: 1) Understand that two events A and B are mutually Section 12.8 exclusive if and only if P(A and B) = 0. In other words, mutually exclusive events cannot occur at the same Algebra 2 Textbook Correlation: time. Section 11.3 2) Determine whether two events are disjoint (mutually exclusive). Additional note from DPI for Level II: Ex. Given the situation of rolling a six-sided die, determine whether the following pairs of events are disjoint: a. rolling an odd number; rolling a five b. rolling a six; rolling a prime number c. rolling an even number; rolling a three d. rolling a number less than 4; rolling a two

3) Given events A and B, calculate (𝐴 𝑜𝑟 𝐵) using the

Addition Rule. Interpret the probability in context. Additional note from DPI for Level II: Ex. Given the situation of drawing a card from a standard deck Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 17 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics of cards, calculate the probability of the following: a. drawing a red card or a king b. drawing a ten or a spade c. drawing a four or a queen d. drawing a black jack or a club e. drawing a red queen or a spade Sample Assessment Tasks Skill-based task: Problem Task: Classify each pair of events as dependent or independent. Suppose a number from 1 to  A month is selected at random; a number from 1 to 30 is 100 is chosen. What is the selected at random. probability that a multiple of 4  A letter of the alphabet is selected at random; another or 5 is chosen? letter is selected at random.

CORE CONTENT Cluster Title: Use the rules of probability to compute the probabilities of compound events in a uniform probability model. Standard S-CP.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. What does this standard mean that a student will know and be able to do? Calculate probabilities using the General Multiplication Rule. Interpret in context. SUPPORTS FOR TEACHERS Critical Background Knowledge:

Academic Vocabulary: Compound events, Independent and Dependent events, mutually exclusive events, overlapping events Suggested Instructional Strategies: Starting Resources: Geometry Textbook Correlation: CC-24

Algebra 1 Textbook Correlation: Section 12.8

Algebra 2 Textbook Correlation: Section 11.4 Sample Assessment Tasks Skill-based task: Problem Task: The probability that a car has two doors, given Sixty percent of a company’s sales that it is red is 0.6. The probability that a car representatives have completed training has two doors and is red is 0.2. What is the seminars. Of these, 80% have had increased probability that a car is red? sales. Overall, 56% of the representatives (whether trained or not) have had increased sales. Use a tree diagram to find the probability

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 18 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics of increased sales, given that a representative has not been trained.

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 19 Course Name: Geometry/Math II Unit 9 Unit Title: Probability and Statistics CORE CONTENT Cluster Title: Use the rules of probability to compute the probabilities of compound events in a uniform probability model. Standard S.CP.9 Use permutations and combinations to compute probabilities of compound events. Concepts and Skills to Master:  Use multiplication to quickly count the number of ways certain things can happen. SUPPORTS FOR TEACHERS Critical Background Knowledge: Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilities Academic Vocabulary: Fundamental Counting Principal, permutation, combination, n factorial, Compound events, Independent and Dependent events, mutually exclusive events, overlapping events Suggested Instructional Strategies: Starting Resources:  Get a lunch menu from the cafeteria for the day Geometry Textbook Correlation: and find the number of different lunches that can CC.23, CC.24 be served  Explain a deck of cards. Many students don’t know Algebra 1 Textbook Correlation: how many suits, colors; face cards are in a deck of Section 12.6 cards. NCDPI Unpacking: Algebra 2 Textbook Correlation: What does this standard mean that a student will Section 11.1 , ER 11.1 know and be able to do? Identify situations as appropriate for use of a permutation or combination to calculate probabilities. Use permutations and combinations in conjunction with other probability methods to calculate probabilities of compound events and solve problems.

Sample Assessment Tasks Skill-based task: Problem Task:  Find 6! A restaurant offers chicken, tuna or roast beef  Find 8! / 3! sandwiches, sides of chips, fruit, fries or slaw,  Find the permutation of 5 pick 2. and desserts of banana pudding or apple pie. If  Find the combination of 6 choose 3 you can choose one sandwich, side and dessert, how many different meals can you make?

Standards are listed in alphabetical /numerical order not suggested teaching order. PLC’s must order the standards to form a reasonable unit for instructional purposes. PAGE 20