Unit 6 Honors What Do You Expect

Course Name: 7 th Grade Honors Unit # 6 Unit Title: What Do You Expect?

Enduring understanding (Big Idea): Students will determine possible outcomes and use expected value to make reasonable decisions. Students will be able to determine the probability of the outcome of one event followed by a second event.

Essential Questions: What are the possible outcomes for the event(s) in this situation? Are these outcomes equally likely? Can I compute the theoretical probabilities or do I conduct an experiment? How can I determine the probability of the outcome of one event followed by a second event?

BY THE END OF THIS UNIT:

Students will know…

 How to interpret experimental and theoretical probabilities and the relationship between them

 How to use area models to analyze situations that involve two stages

 How to use probability and expected value to make decisions

 How to analyze situations that involve binomial outcomes

Vocabulary:

Odds

Outcomes

Theoretical Probability

Complementary

Events

Tree Diagram

Binomial Probability

Events

Probability

Experimental Probability

Events Certain

Area Models

Expected Value

Equally Likely

Fundamental Counting Principle Independent Events

Sample Space

Unit Resources

Learning Task: Mathematical Reflections

Performance Task: Check-up(s) and Quizzes

Project: The Carnival Game

Unit Review Game: Study Guide (problems around the room)

Students will be able to…

 Interpret experimental and theoretical probabilities and the relationship between them

 Review strategies for identifying possible outcomes and analyzing probabilities, such as using lists or tree diagrams

 Determine the expected value of a probability situation

 Distinguish between equally likely and nonequally likely events

 Determine if a game is fair or unfair

 Use probability strategies such as tree diagrams and lists

Mathematical Practices in Focus:

1Make sense of problems and persevere in solving them

2Reason abstractly and quantitatively

3Construct viable arguments and critique the reasoning of others

4Model with mathematics

5Use appropriate tools strategically

6Attend to precision

7Look for and make use of structure

8Look for and express regularity in repeated reasoning

CCSS-M Included:

7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8, 7.NS.2, 7.NS.3, 7.RP.2

Suggested Pacing: 13 Days

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.

CCSS-M Included:


Unit Plans

Standards: 7.SP.5; 7.SP.6; 7.SP.7;

7.SP.8, (a-c):

Evaluating Games of Chance

Standards: 7.SP.6; 7.SP.7 (a-b);

7.sp.8 (a-c):

Analyzing Situations Using an Area

Model

Investigation

1.1

Matching Color

1.2

Red and Blue is a Winner

1.3

Playing the Multiplication Game

Mathematical Reflections 1

Evaluations Games of Chance

2.1 Making Purple

2.2 Choosing Paths

2.3 Finding the Best Arrangement


Analyzing Situations Using an Area Model

Suggested ACE Questions

ACE: 1,2, 14-19

ACE: 3-10, 20-22, 29

ACE: 11-13, 23-28, 30-33

ACE: 1-3, 13-14, 25

ACE: 4-7, 15-22, 26

ACE: 8-12, 23-24, 27-28

Standards: 7.SP.6; 7.SP.7(a-b);

7.SP.8 (a-c):

Expected Value

Standards: 7.SP.6; 7.SP.7(a-b);

7.SP.8 (a-c):

Binomial Outcomes

3.1 One-and –One Free Throws

3.2 Finding Expected Values

3.3 Choosing Pay Plans


Expected Values

4.1 Guessing Answers

4.2 Ortonville

4.3 A Baseball Series


Binomial Outcomes

Looking Back and Looking Ahead

Probability Reasoning

ACE: 1-3, 10-15

ACE: 4-7, 16-19, 23-26, 28

ACE: 8-9, 20-22, 27

ACE: 1-2, 11

ACE: 3-9, 12-13, 18-22

ACE: 10, 14-17

CORE CONTENT

Cluster Title: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.

Standard: 7.SP. 5: Investigate chance processes and develop, use, and evaluate probability models.

Concepts and Skills to Master:

 Ability to Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring

 Ability to review basic probability concepts, such as fair games, experimental probability, theoretical probability, and fraction notation for expressing probability.

 Ability to use probability and payoff to calculate the long term average result of a game of chance

SUPPORTS FOR TEACHERS

Critical Background Knowledge

 Gathering, analyzing, and displaying data to show trends

 Understanding chance

Academic Vocabulary

Area Model, Tree Diagram, Expected Value, Binomial Probability, Fraction Notation, Fair Games, Theoretical

Probability, Experimental Probability




Suggested Instructional Strategies:

 Introduce by asking questions about experiments

 Discuss experiments and the different type of experiments

 Introduce by using dice asking what the probability

 of get a one (1/6)

Introduce by using coins asking what the probability of getting tails or head?

Sample Assessment Tasks

Skill-based task

There are three choices of jellybeans – grape, cherry and orange. If the probability of getting a grape is 3/10 and the probability of getting cherry is 1/5, what is the probability of getting orange?

Resources:

 Textbook Correlation: Investigation 1

 MARS Task: A01 http://map.mathshell.org/materials/tasks.php

 Graphing Calculator Task: Flipping Out

Problem Task

The container contains 2 gray, 1 white, and 4 black marbles.

Without looking, if Eric chooses a marble from the container, will the probability be closer to 0 or to 1 that Eric will select a white marble? A gray marble? A black marble? Justify each of your predictions.

CORE CONTENT

Cluster Title: Investigate chance processes and develop, use, and evaluate probability models

Standard: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.


 Ability to gather organize data to determine possible outcomes

 Ability to use an area model to analyze the theoretical probabilities for two stage outcomes

 Ability to stimulate and analyze probability situations involving two stage outcomes

 Ability to distinguish between equally likely and non equally likely outcomes by collecting data and analyzing experimental probabilities



 Understanding how to create ratios to represent situations

 Understanding when and how to operate fractions to determine probability

 Understanding how to gather and organize data

 Knowing the difference between theoretical and experimental probabilities

 Knowing how to multiply probabilities

 Using probabilities to make inferences and predictions about populations based on analysis of populations samples


Area Model, Tree Diagram, Expected Value, Binomial Probability, Fractional Diagram, Outcomes, Organized Lists,

Replacement





 Introduce by explaining different type of probabilities

 Introduce what an area model is and how to analyze

Resources:

 Textbook Correlation: Investigation 2

 MARS Task:

A10 Card Game

Will it Happen? Inside Mathematics

 Graphing Calculator Task: Will You Have a Seat!



Suppose we toss a coin 50 times and have 27 heads and

23 tails. We define a head as success. The relative frequency of heads is: 27/50= 54%. The probability of a head is 50%. The difference between the relative frequency is 54% and the probability of 50% is due to small sample size.

Problem Task

Each group receives a bag that contains 4 green marbles, 6 red marbles, and 10 blue marbles. Each group performs

50 pulls, recording the color of marble drawn and replacing the marble into the bag before the next draw. Students compile their data as a group and then as a class. They summarize their data as experimental probabilities and make conjectures about theoretical probabilities (How many green draws would are expected if 1000 pulls are conducted? How many green drawn if 10,000 pulls?).

CORE CONTENT

Cluster Title: Investigate chance processes and develop, use, and evaluate probability models.

Standard: 7.SP.7 (a-b): Develop a probability model and use it to find probabilities of events.

Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.


 Ability to develop a uniform probability model by assigning equal probability to all outcomes

 Ability to use the model to determine probabilities of events

 Ability to develop a probability model by observing frequencies in data generated from a chance process.

 Ability to understand the difference between the probability of an outcome and the long term averages



Ability to use probability to make decisions



 Using data collected from samples of populations to determine experimental probabilities

 Develop techniques for simulating situations in order to collect and organize data



Develop strategies for analyzing complex games or situations to determine theoretical probabilities


Area Model, Tree Diagram, Expected Value, Binomial Probability, Sample Population, Experimental Probability,

Theoretical Probability





 Introduce by asking questions about experiments

 Discuss experiments and the different type of experiments

 Find probability by during different examples students can relate to before getting into investigation

Resources:

Win

 Textbook Correlation: Investigation 3

 MARS Task:

E02 Counting Trees

E12 Candy Bars

Graphing Calculator Task: One and One Easy



If Mary chooses a point in the square, what is the probability that it is not in the circle?

Problem Task

Jason is tossing a fair coin. He tosses the coin ten times and it lands on heads eight times. If Jason tosses the coin for the eleventh time, what is the probability that it will land on heads?

CORE CONTENT

Cluster Title: Investigate chance processes and develop, use, and evaluate probability models.

Standard:

7.SP.8 (a-c): Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.


 Ability to understand that the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs

 Ability to represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams

 Ability to design and use a simulation to generate frequencies for compound events

 Ability to analyze a binomial situation

 Ability to analyze a binomial situation with multiple stage outcomes



 Using expected values of favorable and unfavorable outcomes to make inferences and predictions

 Using expected values to make recommendations

 Using expected vales to develop solutions to real world problems


Area Model, Tree Diagram, Expected Value, Binomial Probability, Favorable Outcomes, Unfavorable Outcomes,

Compound Events, Binomial Situations, Multiple Stage Outcomes, Sample Spaces, Simulation





 Gathering Data using tables

 Understand binomial and how it related to probability

 Understand what it means to be equally likely

 Know and understand tree diagrams and frequency tables



How many ways could the 3 students, Amy, Brenda, and

Carla, come in 1st, 2nd and 3rd place?

Resources:

 Textbook Correlation: Investigation 4



MARS Task: E06: Lottery

C12 Memory Game

E09 Spinner Bingo

 Calculator Graphing Task: Plinko (additional tasks) http://secondarymath.cmswiki.wikispaces.net/7th+Gra de+Probability

Problem Task

Students conduct a bag pull experiment. A bag contains 5 marbles. There is one red marble, two blue marbles and two purple marbles. Students will draw one marble without replacement and then draw another. What is the sample space for this situation? Explain how the sample space was determined and how it is used to find the probability of drawing one blue marble followed by another blue marble.



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