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Course Name: Geometry/Math II Unit 9Unit 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…

The difference between combination and permutation problems.

The difference between independent and dependent probabilities.

Students will be able to: Determine if theoretical or experimental probability

is the best course of action to solve a problem. 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 factorialUnit Resources:Performance Task: Pearon Alg 2 probability performance tasks.pdfprobability activity.pdfProject: l21_probability_statements_beta_complete.pdf

Test Specification Weights for the Common Exams in Common Core Math II:

Suggested Order/Pacing:Geometric Probability: Section 10.8 Theoretical and Experimental Probability: CC-21, Algebra 1BK: Section 12.7, CB 12.7, ER 12.7Algebra 2 BK: Section 11.2Probability Distribution and Frequency Tables: CC-22Algebra 2 BK: CB 11.3Permutations and Combinations: CC-23, Algebra 1 BK: Section 12.6, ER 12.6, Algebra 2 BK: Section 11.1Compound Probability and Probability of Multiple Events: CC-24, and Algebra 1 BK: Section 12.8, ER 12.8 Algebra 2 BK: Section 11.3Contingency Tables: CC-25Conditional Probability: CC-26, Algebra 1 BK: CB 12.8 and Algebra 2 BK: Section 11.4

Mathematical Practices in Focus:1. Make sense of problems and persevere in solving

them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the

reasoning of others4. Model with mathematics

6. Attend to precision

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

Abbreviation Key:CC – Common Core Additional Lessons found in the Pearson online materials.CB- Concept Bytes found in between lessons in the Pearson textbook.ER – Enrichment worksheets found in teacher resources per chapter.

Merge information from Geometry, Algebra 1, and Algebra 2 Books to complete this unit.

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

Standard % Constructed Response

% Multiple-Choice

Category Percentage(Statistics)

S-IC 0% 7% - 10% 7% - 10%S-CP 0%

http://secondarymath.cmswiki.wikispaces.net/file/view/l21_probability_statements_beta_complete.pdf

http://secondarymath.cmswiki.wikispaces.net/file/view/probability%20activity.pdf

http://secondarymath.cmswiki.wikispaces.net/file/view/Pearon%20Alg%202%20probability%20performance%20tasks.pdf


CORE CONTENTCluster 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 TEACHERSCritical 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:

Utilized the TI-84 Probability Simulation App Remind students that they did simple probability in middle school Use a coin toss experiment to introduce the concepts but quickly move to

simulations Use your calculator to do the simulations like coin toss and random number

generatorNCDPI Unpacking: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, 2Based on these results, is Jack rolling a fair die? Justify your answer using a simulation.

Starting Resources:Algebra 1 Textbook Correlation:CB 12.7

Algebra 2 Textbook Correlation:Section 11.2, ER 11.2, CB 11.3

Sample Assessment TasksSkill-based task:On a multiple choice test, each item has 4 choices, but only one choice is correct. How can you simulate guessing the answers? Based on your simulation of at least 20 trials, what is the probability that you will pass the test by guessing at least 6 of 10 answers correctly?

Problem Task:On a multiple-choice test, each item has 4 choices, but only one choice is correct. How can you simulate guessing the answer? What is the probability that you will pass the test by guessing at least 6 of 10 answers correctly?


Teacher Created Argumentation Tasks (W1-MP3&6): Assume that an event is neither certain nor impossible. Then the odds in favor of the event is the ratio of the number of favorable outcomes to the number of unfavorable outcomes. Would you rather play a game in which your odds of winning are ½, or a game in which your probability of winning is ½? Sate your answer, support your answer with relevant data and be prepared to defend your position.


CORE CONTENTCluster 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 dataSUPPORTS FOR TEACHERSCritical Background Knowledge:Academic Vocabulary:Population, sample, convenience sample, self-selected sample, systematic sample, random sample, bias, observational study, controlled experiment, surveySuggested Instructional Strategies:What does this standard mean that a student will know and be able to do?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.)

Starting Resources:Algebra 2 Textbook Correlation:Section 11.7

Sample Assessment TasksSkill-based task:A survey asks, “Aren’t handmade gifts always better than tacky purchased gifts?” Does this survey question have any bias? Explain.

Problem Task:What sampling method could you use to find the percent of adults in your community who support building more nuclear power plants? What is an example of a survey question that is likely to yield unbiased information?



CORE CONTENTCluster 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 TEACHERSCritical 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, oddsSuggested Instructional Strategies:

Use Venn diagrams to remind students how to determine the difference between “and” and “or”.

NCDPI Unpacking:What does this standard mean that a student will know and be able to do?

1) Define the sample space for a given situation.Additional note from DPI for Level II:Ex. What is the sample space for rolling a die?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.

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}.

Starting Resources:Geometry Textbook Correlation:10.8, CC.21

Algebra 1 Textbook Correlation:Section 12.7

Algebra 2 Textbook Correlation:Section 11.2, ER 11.2

http://www.shodor.org Interactive Venn Diagram Shape Sorter

Sample Assessment TasksSkill-based task:If the probability an event will occur is 74%, what is the probability it will not occur?

Problem Task:What is the probability that a quarterback will complete his next pass if he has completed 30 of his last 40 passes?

CORE CONTENTCluster 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.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


Concepts and Skills to Master Explain properties of Independence and Conditional Probabilities in context and simple English.


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:


1) Understand that two events A and B are independent if and only if P(A and B)= 𝑃(𝐴) ∙ 𝑃(𝐵).

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

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.

Starting Resources:Geometry Textbook Correlation: CC-26

Algebra 1 Textbook Correlation:CB 12.8


Sample Assessment TasksSkill-based task:

C and D are independent events, , and

. What is P(C and D)?

Problem Task:Suppose you randomly select a shape from this circle. What is the probabilitythat the shape is black and has five points?



CORE CONTENTCluster 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 TEACHERSCritical Background Knowledge:Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilitiesAcademic Vocabulary:Conditional ProbabilitySuggested Instructional Strategies:Use Venn diagrams to explore and compute conditional probabilities.


1) Understand that the conditional probability of event A given event B has already happened is given by the formula:

P (A|B )= P(A∧B)P (B)

2) Understand that two events A and B are independent if and only if P (A|B )=P (A )∧P (B|A )=P (B ) . In other words, the fact that one of the events happened does not change the probability of the other event happening.

3) Prove that two events A and B are independent by showing that P (A|B )=P (A )∧P (B|A )=P (B ) .

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 spade” and “draw a king.” Prove that these two events are independent.Ex. Create and prove two events are dependent from drawing a card from a standard deck.

Starting Resources:Geometry Textbook Correlation:CC-26



Cut the Knot – Conditional Probability and Independent Events:

http://www.cut-the-knot.org/Curriculum/Probability/ConditionalProbability.shtml

Texas A&M – Conditional Probability Applet:

http://www.stat.tamu.edu/~west/applets/Venn1.html


Given the following Venn diagram, determine whether events A and B are independent.

Problem Task:

A box contains 10 blue cubes, 5 red cubes, 5 blue marbles and 10 red marbles. You randomly pick a blue shape from the box. What is the probability you picked a cube? ANS: 67%

CORE CONTENTStandards 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

http://www.stat.tamu.edu/~west/applets/Venn1.html




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 TEACHERSCritical Background Knowledge: Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilitiesAcademic 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 tableSuggested Instructional Strategies:NCDPI Unpacking:What does this standard mean that a student will know and be able to do?1.Construct and interpret a two-way frequency table from a set of data on two categorical variables.Additional note from DPI for Level II:Ex.Make a two-way frequency table for the following set of data. Use the following age groups: 3-5,6-8,9-11,12-14,15-17.

2.Determine if two categorical variables are independent by analyzing a two-way table of data collected on the two variables.3.Calculate conditional probabilities based on two categorical variables from a table and interpret in context.Additional note from DPI for Level II: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.

Starting Resources:Geometry Textbook Correlation:CC.21,CC.22, CC.25

Algebra 1 Textbook Correlation:Section 12.7 (see next page for more resources.)

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

Source for problem task:http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/wiki/45424/images/75b78.png#697x251

Sample Assessment TasksSkill-based task: Problem Task:


http://wiki.warren.kyschools.us/groups/wcpscommoncorestandards/wiki/45424/images/75b78.png%23697x251




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.



CORE CONTENTCluster 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 TEACHERSCritical Background Knowledge:Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilitiesAcademic Vocabulary:relative frequency, probability distribution, uniform distribution, cumulative frequency, cumulative probability, two-way frequency table, conditional probabilitySuggested Instructional Strategies:

Give an example of a situation where conditional probability would be used. Explain why conditional probability applies to a situation.

Give an example of two independent events. What constitutes the independence of two events?

Instructional Expectations In both pathways, the expectation in Geometry and CCSS Mathematics II is to build on work with two-way tables from Algebra I Unit 3 (S.ID.5) to develop understanding of conditional probability and independence. What does this standard mean that a student will know and be able to do?Given an everyday situation describing two events, use the context to construct an argument as to whether the events are independent or dependent.

Additional note from DPI for Level II:Ex. Felix is a good chess player and a good math student. Do you think that the events “being good at playing chess” 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 partnerHarold thinks that the next flip is going to result in tails because there have been so many heads in a row. Do you agree? Explain why or why not.

Resources:Geometry Textbook Correlation:CC.22, CC.26


Algebra 2 Textbook Correlation:Section 11.3, 11.4

Read more: Examples of Real Life Probability | eHow.com http://www.ehow.com/list_7719506_real-life-probability-examples.html#ixzz1wvNUV1st

HONORS:http://myweb.cableone.net/surgett/nmmi/webquests/probability/ research project for real life applications of probability.

Sample Assessment TasksSkill-based task:If you are using a game spinner with four sections -- red, blue, green and yellow -- you have a 25 percent chance of landing on red, since one of the four sections is red. What is the probability 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.

Problem Task:Have students find and interpret probability statements in media.

CORE CONTENTCluster 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


http://myweb.cableone.net/surgett/nmmi/webquests/probability/

http://myweb.cableone.net/surgett/nmmi/webquests/probability/

http://www.ehow.com/list_7719506_real-life-probability-examples.html#ixzz1wvNUV1st





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 TEACHERSCritical 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 ProbabilitySuggested Instructional Strategies:• Make a “human Venn diagram” where the sample space is all the students in the class. Use lengths of rope to create three overlapping circles. Assign an event to each of the three circles, such as: ate breakfast, brought a cell phone to school, and got at least 7 hours of sleep. Have students place themselves in the appropriate locations. Using correct probability notation, identify each of the spaces in the Venn diagram (don’t forget to include the space outside the circles). Analyze, explore and record the results in terms of conditional probabilities.• 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?

Starting Resources:Geometry Textbook Correlation:CC.26


Sample Assessment TasksSkill-based task:From the table, determine the probability of getting the flu, and compare that to the probability of getting the flu given that an individual takes high doses of vitamin C.

Problem Task:Life is like a box of chocolates. Suppose your box of 36 chocolates have some dark and some milk chocolate, divided into cream or nutty centers. Out of the dark chocolates, 8 have nutty centers. Out of the



Cold No cold totalPlacebo 31 109 140

Vitamin C 17 122 139Total 48 231 279

milk 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.



CORE CONTENTCluster 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.


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 eventsSuggested Instructional Strategies:11.3 Algebra 2 Pearson Game: The Probability PathNCDPI Unpacking:What does this standard mean that a student will know and be able to do?

1) Understand that two events A and B are mutually exclusive if and only if P(A and B) = 0. In other words, mutually exclusive events cannot occur at the same time.

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 fiveb. rolling a six; rolling a prime numberc. rolling an even number; rolling a threed. 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 of cards, calculate the probability of the following:a. drawing a red card or a kingb. drawing a ten or a spadec. drawing a four or a queend. drawing a black jack or a clube. drawing a red queen or a spade

Starting Resources:Geometry Textbook Correlation:CC.24


Algebra 2 Textbook Correlation: Section 11.3

Sample Assessment TasksSkill-based task:Classify each pair of events as dependent or independent.

A month is selected at random; a number from 1 to 30 is selected at random.

A letter of the alphabet is selected at random; another letter is selected at random.

Problem Task:Suppose a number from 1 to 100 is chosen. What is the probability that a multiple of 4 or 5 is chosen?

CORE CONTENTCluster 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|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


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 TEACHERSCritical Background Knowledge:

Academic Vocabulary:Compound events, Independent and Dependent events, mutually exclusive events, overlapping eventsSuggested Instructional Strategies: Starting Resources:

Geometry Textbook Correlation:CC-24



Sample Assessment TasksSkill-based task:The probability that a car has two doors, given that it is red is 0.6. The probability that a car has two doors and is red is 0.2. What is the probability that a car is red?

Problem Task:Sixty percent of a company’s sales representatives have completed training seminars. Of these, 80% have had increased sales. Overall, 56% of the representatives (whether trained or not) have had increased sales. Use a tree diagram to find the probability of increased sales, given that a representative has not been trained.



CORE CONTENTCluster 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 TEACHERSCritical Background Knowledge:Adding and multiplying fractions, Converting fractions to decimals, Calculating simple probabilitiesAcademic Vocabulary:Fundamental Counting Principal, permutation, combination, n factorial, Compound events, Independent and Dependent events, mutually exclusive events, overlapping eventsSuggested Instructional Strategies:

Get a lunch menu from the cafeteria for the day and find the number of different lunches that can be served

Explain a deck of cards. Many students don’t know how many suits, colors; face cards are in a deck of cards.

NCDPI Unpacking:What does this standard mean that a student will 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.

Starting Resources:Geometry Textbook Correlation:CC.23, CC.24


Algebra 2 Textbook Correlation:Section 11.1 , ER 11.1


Find 6! Find 8! / 3! Find the permutation of 5 pick 2. Find the combination of 6 choose 3

Problem Task:A restaurant offers chicken, tuna or roast beef sandwiches, sides of chips, fruit, fries or slaw, and desserts of banana pudding or apple pie. If you can choose one sandwich, side and dessert, how many different meals can you make?


Teacher Created Argumentation Tasks (W1-MP3&6)Can a permutation and a combination with the same total and choices have the same solution? Justify your answer.

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