Curriculum / Math / 7th Grade / Unit 8: Probability / Lesson 2
Math
Unit 8
7th Grade
Lesson 2 of 9
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Define probability and sample space. Estimate probabilities from experimental data.
The core standards covered in this lesson
7.SP.C.6 — 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. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
7.SP.C.7 — 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.
The foundational standards covered in this lesson
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
7.SP.A.1 — Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson requires some prior preparation and materials (brown paper bags and different colored cubes) for Anchor Problem #1. See the notes in Anchor Problem #1 for further information.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Your teacher will give you a brown bag of cubes to use in the trials described below.
Trial 1: Draw a cube from the bag and record the color. Replace the cube and shake the bag. Repeat the first step 3 more times for a total of 4 results.
Trial 2: Draw a cube from the bag and record the color. Replace the cube and shake the bag. Repeat the first step 9 more times for a total of 10 results.
Trial 3: Draw a cube from the bag and record the color. Replace the cube and shake the bag. Repeat the first step 14 more times for a total of 15 results.
Check the bag: Look inside the bag and notice the actual sample space.
A spinner with different colors on it was spun 20 times. The data recording the color of each spin is shown below.
a. What is the sample space of the spinner?
b. Does it seem that each color outcome is equally likely? Explain your reasoning.
c. Estimate the probability of spinning each color on the spinner.
d. Four spinners are shown below. Which spinner is most likely the spinner used for the data above?
A set of suggested resources or problem types that teachers can turn into a problem set
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Each of the 20 students in Mr. Anderson’s class flipped a coin ten times and recorded how many times it came out heads.
a. How many heads do you think you will see out of ten tosses?
b. Would it surprise you to see 4 heads out of ten tosses? Explain why or why not.
c. Here are the results for the twenty students in Mr. Anderson’s class. Use this data to estimate the probability of observing 4, 5, or 6 heads in ten tosses of the coin. (It might help to organize the data in a table or in a dot plot first.)
Heads or Tails, accessed on July 20, 2016, 6:42 a.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.
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.
Lesson 1
Lesson 3
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.
7.SP.C.5
7.SP.C.6 7.SP.C.7
Determine the probability of events.
7.SP.C.7.A 7.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.8 7.SP.C.8.C
List the sample space for compound events using organized lists, tables, or tree diagrams.
7.SP.C.8.B
Determine the probability of compound events.
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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