Intro Stats>Intro Random Variables>Binomial Random Variables
Learning TargetsExperience FirstFormalize Later
Unit 1: Analyzing One-Variable Data
Day 1: Statistics: The Science and Art of Data
Day 2: Displaying Categorical Data
Day 3: Displaying Quantitative Data: Dotplots
Day 4: Displaying Quantitative Data: Stemplots
Day 5: Quiz 1.1 to 1.4
Day 6: Displaying Quantitative Data: Histograms
Day 7: Measuring Center
Day 8: Measuring Variability
Day 9: Summarizing Quantitative Data: Boxplots and Outliers
Day 10: Quiz 1.5 to 1.8
Day 11: Unit 1 Review
Day 12: Unit 1 Practice Test
Day 13: Unit 1 Test
Unit 2: Modeling One-Variable Data
Day 1: Describing Location in a Distribution
Day 2: Transforming Data
Day 3: Density Curves and the Normal Distribution
Day 4: Quiz 2.1 to 2.3
Day 5: The Empirical Rule and Assessing Normality
Day 6: Normal Distributions: Finding Areas from Values
Day 7: Normal Distributions: Finding Values from Areas
Day 8: Normal Distributions Calculations Practice
Day 9: Quiz 2.4 to 2.6
Day 10: Unit 2 Review
Day 11: Unit 2 Practice Test
Day 12: Unit 2 Test
Unit 3: Analyzing Two-Variable Data
Day 1: Relationships Between Two Categorical Variables
Day 2: Relationships Between Two Quantitative Variables
Day 3: Correlation
Day 4: More About Correlation
Day 5: Quiz 3.1 to 3.4
Day 6: Regression Lines
Day 7: The Least-Squares Regression Line
Day 8: Assessing a Regression Model
Day 9: Quiz 3.5 to 3.7
Day 10: Barbie Bungee Finale
Day 11: Unit 3 Review
Day 12: Unit 3 Review
Day 13: Unit 3 Test
Unit 4: Intro Collecting Data
Day 1: Anchored Putting Intro
Day 2: Introduction to Data Collection
Day 3: Sampling: Good and Bad
Day 4: Sampling and Surveys
Day 5: Inference for Sampling
Day 6: Quiz 4.1 to 4.4
Day 7: Observational Studies and Experiments
Day 8: How to Experiment Well
Day 9: Inference for Experiments
Day 10: Using Studies Wisely
Day 11: Quiz 4.5 to 4.8
Day 12: Anchored Putting Finale
Day 13: Unit 4 Review
Day 14: Unit 4 Practice Test
Day 15: Unit 4 Test
Unit 5: Intro Probability
Day 1: Randomness, Probability, and Simulation
Day 2: Basic Probability Rules
Day 3: Two-Way Tables and Venn Diagrams
Day 4: Conditional Probability and Independence
Day 5: Quiz 5.1 to 5.4
Day 6: General Multiplication Rule
Day 7: The Multiplication Rule for Independent Events
Day 8: The Multiplication Counting Principle and Permutations
Day 9: Combinations and Probability
Day 10: Quiz 5.5 to 5.8
Day 11: Unit 5 Review
Day 12: Unit 5 Practice Test
Day 13: Unit 5 Test
Unit 6: Intro Random Variables
Day 1: Two Types of Random Variables
Day 2: Analyzing Discrete Random Variables
Day 3: Quiz 6.1 to 6.2
Day 4: Binomial Random Variables
Day 5: Binomial Random Variables
Day 6: Analyzing Binomial Random Variables
Day 7: Normal Approximations to Binomial Distributions
Day 8: Quiz 6.3 to 6.5
Day 9: Unit 6 Review
Day 10: Unit 6 Practice Test
Day 11: Unit 6 Test
Unit 7: Intro Sampling Distributions
Day 1: What is a Sampling Distribution?
Day 2: Sampling Distributions: Center and Variability
Day 3: The Sampling Distribution of a Sample Proportion
Day 4: Quiz 7.1 to 7.3
Day 5: The Sampling Distribution of a Sample Mean
Day 6: The Central Limit Theorem
Day 7: Quiz 7.4 to 7.5
Day 8: Reese's Pieces Review
Day 9: Unit 7 Review
Day 10: Unit 7 Practice Test
Day 11: Unit 7 Test
Unit 8: Estimating a Parameter
Day 1: The Idea of a Confidence Interval
Day 2: What Affects Margin of Error?
Day 3: Quiz 8.1 to 8.2
Day 4: Estimating a Proportion
Day 5: Confidence Intervals for a Proportion
Day 6: Quiz 8.2 to 8.4
Day 7: Estimating a Mean
Day 8: Confidence Intervals for a Mean
Day 9: Quiz 8.5 to 8.6
Day 10: Four-Step Practice for Confidence Intervals
Day 11: Unit 8 Review
Day 12: Unit 8 Practice Test
Day 13: Unit 8 Test
Unit 9: Testing a Claim
Day 1: The Idea of a Significance Test
Day 2: Significance Tests and Decision Making
Day 3: Testing a Claim About a Proportion
Day 4: Significance Tests for a Proportion
Day 5: Quiz 9.1 to 9.4
Day 6: Testing a Claim About a Mean
Day 7: Significance Tests for a Mean
Day 8: Quiz 9.5 to 9.6
Day 9: Four-Step Practice for Significance Tests
Day 10: Unit 9 Review
Day 11: Unit 9 Practice Test
Day 12: Unit 9 Test
Unit 10: Comparing Two Populations or Treatments
Day 1: Estimating a Difference Between Two Proportions
Day 2: Testing a Claim about a Difference Between Two Proportions
Day 3: Quiz 10.1 to 10.2
Day 4: Estimating a Difference Between Two Means
Day 5: Testing a Claim about a Difference Between Two Means
Day 6: Quiz 10.3 to 10.4
Day 7: Paired Data: Estimating a Mean Difference
Day 8: Paired Data: Testing a Claim about a Mean Difference
Day 9: Quiz 10.5 to 10.6
Day 10: Unit 10 Review Activity - Data Collection
Day 11: Unit 10 Review Activity - Data Analysis
Day 12: Unit 10 Review
Day 13: Unit 10 Practice Test
Day 14: Unit 10 Test
Unit 11: Inference for Distributions and Relationships
Day 1: Testing the Distribution of a Categorical Variable
Day 2: Chi-Square Tests for Goodness of Fit
Day 3: Quiz 11.1 to 11.2
Day 4: Testing the Relationship Between Two Categorical Variables
Day 5: Chi-Square Tests for Association
Day 6: Quiz 11.3 to 11.4
Day 7: Estimating the Slope of a Least-Squares Regression Line
Day 8: Testing a Claim about the Slope of a Least-Squares Regression Line
Day 9: Quiz 11.5 to 11.6
Day 10: Unit 11 Review
Day 11: Unit 11 Practice Test
Day 12: Unit 11 Test
Learning Targets
Determine whether the conditions for a binomial setting are met.
Calculate probabilities involving a single value of a binomial random variable.
Make a histogram to display a binomial distribution and describe its shape.
| Tasks/Activity | Time |
|---|---|
| Activity | 20 minutes |
| Debrief Activity with Margin Notes | 5 minutes |
| QuickNotes | 5 minutes |
| Check Your Understanding | 15 minutes |
Activity: How Will Your Do on the Pop Quiz?
Our Teaching Philosophy:
Experience First,
Formalize Later (EFFL)
Learn More
Experience First
Start this lesson by announcing there will be a pop quiz! And the hardest part about this quiz is that students don’t even get to see the questions. They have to guess on all 5 multiple choice questions. Read off the correct answers to the class and let them grade their own quizzes. Be sure to celebrate any students that might pass the quiz. This activity is a chance for students to practice the two learning targets from the previous lesson: The new learning for this lesson is the third learning target: making a histogram for a binomial distribution.
Formalize Later
By doing the Three Shots activity in the previous lesson, students should have a good conceptual understanding of the binomial theorem. Consider using the same language as you did during Three Shots: Success = Make and Failure = Miss. When working through a binomial problem, we will often ask, “How many makes? What’s the probability? How many misses? What’s the probability?” Students get really used to this pattern and find binomial probability fairly easy, which no one would expect when you look at the formula the first time! We also suggest helping students to think about the binomial formula with words rather than symbols. nCr = “the number of ways to get r successes in n trials” p = “probability of success” r = “number of successes” (1 – p) = “probability of failure” n – r = “number of failures” So instead of memorizing the binomial formula with variables, we say it is “the number of ways to get r successes in n trials, multiplied by the probability of success raised to the number of successes, multiplied by the number of failures raised to the number of failures”
