Teacher Resources
Situation Simulated
On this page you will find lesson objectives, standards, instructional notes and UDL opportunities.
Estimated Time: 180 minutes
Lesson Objectives:
- The students will design, conduct and interpret the results of a simulation.
- The students will also use simulation models for random sampling to develop margin of error and decide if difference in parameters are significant.
Key Common Core State Standards:
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? Make inferences and justify conclusions from sample surveys, experiments, and observational studies
S.IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant
Supporting Common Core State Standards:
N/A
Standards for Mathematical Practice Emphasized:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Instructional Notes:
This lesson begins with the students performing simulations. A mathematical simulation is the process of using a probability tool to model a probability situation to estimate its characteristics or solve problems. Given a scenario, the students will choose the appropriate simulation tool, design the simulation, and conduct the simulation. The student will use data collected from the simulation as evidence to help them make inferences about the given scenario. Simulations can prove to be challenging for students. They find it difficult to choose a tool to match the probability in the scenario. They also find it difficult to analyze the data table once it is developed. The more practice the students have with conducting simulations, the better they become at forming inferences and drawing conclusions. The most convenient tool for the students to use is a random number generator, which is the focal tool of this lesson.
In addition to performing the simulation, the students will analyze the margin of error and parameters involved in the simulations. Margin of error should be taught with conceptual understanding, and not with the expectation that students generate hundreds of data points to determine margin of error. Further, it is not expected that students use the z-score for margin of error. For Common Core Algebra 2, it is sufficient for students to apply margin of error using mean and two standard deviations from the mean. For further explanation of margin of error, consult the Progressions for the Common Core State Standards in Mathematics
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Sample Responses
For sample responses to the Algebra II Journal questions, visit the Algebra II Journal in the Teacher Resources.
Situation Simulated - Page 7
Note that each student or group of students will need a coin, a large sheet of paper and a marker to simulate the lighting strike experiment.
Consult pages 9 through 11 of the Progressions for the Common Core State Standards in Mathematics for an additional example and further explanations that can be used with students.
UDL Opportunities:
Principle 1: Provide Multiple Means of Representation
Checkpoint 1.1 Offer ways of customizing the display of information
Checkpoint 2.1 Clarify vocabulary and symbols
Checkpoint 2.3 Support decoding text, mathematical notation, and symbols
Checkpoint 2.5 Illustrate through multiple media
Checkpoint 3.1 Activate or supply background knowledge
Checkpoint 3.2 Highlight patterns, critical features, big ideas, and relationships
Checkpoint 3.3 Guide information processing, visualization, and manipulation
Checkpoint 3.4 Maximize transfer and generalization
Principle 2: Provide Multiple Means of Action and Expression
Checkpoint 4.1 Vary the methods for response and navigation
Checkpoint 4.2 Optimize access to tools and assistive technologies
Checkpoint 5.1 Use multiple media for communication
Checkpoint 5.2 Use multiple tools for construction and composition
Checkpoint 6.2 Support planning and strategy development
Checkpoint 6.3 Facilitate managing information and resources
Principle 3: Provide Multiple Means of Engagement
Checkpoint 7.1 Optimize individual choice and autonomy
Checkpoint 7.2 Optimize relevance, value, and authenticity
Checkpoint 8.1 Heighten salience of goals and objectives
Checkpoint 8.2 Vary demands and resources to optimize challenge
Checkpoint 8.4 Increase mastery-oriented feedback
Checkpoint 9.1 Promote expectations and beliefs that optimize motivation
Checkpoint 9.3 Develop self-assessment and reflection
