Curriculum / Math / 7th Grade / Unit 8: Probability / Lesson 7
Math
Unit 8
7th Grade
Lesson 7 of 9
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List the sample space for compound events using organized lists, tables, or tree diagrams.
The core standards covered in this lesson
7.SP.C.8.B — Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Following the introduction to compound events in Lesson 6, in this lesson students learn how to organize the sample space for compound events. Within each organizational tool, there is a structure embedded that ensures each possible outcome is accounted for (MP.7). Ensure students see and can utilize this structure as they create their own organized spaces.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
An experiment involves a spinner and a fair coin, shown below. The spinner will be spun one time, and the coin will be flipped one time.
What are all of the possible outcomes for this experiment? Organize your information in a list, table, or tree diagram.
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Imagine a game in which two fair four-sided dice are rolled at the same time. These dice are in the shape of a pyramid, and when a die is rolled, the outcome is determined by the side that lands face down. The possible values (corresponding to the four sides of the die) for each die are as follows:
Die #1: 1, 2, 3, or 4 Die #2: 2, 4, 6, or 8
a. A certain game determines the movement of players' game pieces based on the SUM of the numbers on the face down sides when two dice are rolled.
What is the probability of obtaining a sum of 5?
What is the probability of obtaining a sum that is more than 5?
What is the probability of obtaining a sum that is at most 5?
What is the probability of obtaining a sum that is at least 5?
b. Another game determines movement of the game pieces based on the DIFFERENCE in the numbers on the face down sides. The difference for purposes of this game will always be computed as the larger number value rolled minus the smaller number value rolled. In this way, the difference will always be positive or 0.
What is the probability of obtaining a difference of 5?
What is the probability of obtaining a difference that is more than 5?
What is the probability of obtaining a difference that is less than or equal to 5?
Tetrahedral Dice, accessed on June 14, 2017, 2:44 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
At an ice cream store, a customer can make a sundae that includes ice cream, one candy topping, and one liquid topping. The options are listed below.
a. How many different sundae combinations are possible, assuming both a candy and liquid topping are selected?
b. Use a list, table, or tree diagram to show all possible outcomes.
c. How many different sundaes include mint chip ice cream and hot fudge topping?
d. Assuming each sundae combination is equally likely, what is the probability that the store’s next customer orders a sundae with vanilla ice cream and gummy bears?
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
An experiment involves flipping a fair coin and rolling a fair six-sided die.
a. List all possible outcomes of the experiment. Use an organized list, table, or tree diagram.
b. What is the probability of getting a head and an even number?
c. What is the probability of getting a tail and the number 4?
d. What is the probability of getting a 5?
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Next
Determine the probability of compound events.
Topic A: Probability Models of Simple Events
Understand the probability of an event happening is a number between 0 and 1, ranging from impossible to certain.
Standards
7.SP.C.5
Define probability and sample space. Estimate probabilities from experimental data.
7.SP.C.67.SP.C.7
Determine the probability of events.
7.SP.C.7.A7.SP.C.7.B
Use probability to predict long-run frequencies.
7.SP.C.6
Design and conduct simulations to model real-world situations.
7.SP.C.7
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Topic B: Probability Models of Compound Events
Conduct simulations with multiple events to determine probabilities.
7.SP.C.87.SP.C.8.C
7.SP.C.8.B
7.SP.C.8
Design and conduct simulations to model real-world situations for compound events.
7.SP.C.8.C
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