CCSS.Math.Content.HSS-IC.A.2
The standard
Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
Common Core State Standards for Mathematics
What this standard means
Students need to compare a claimed probability model with actual results from a random process. They should use simulations, dot plots, or repeated trials to judge whether an outcome is believable under the model or unusual enough to question it.
Mastery looks like explaining, with evidence, why a result is or is not surprising. Students should refer to simulated results, not just gut feeling. Common trouble spots are thinking rare means impossible, treating small samples as proof, and forgetting that a model can be reasonable even when one trial looks strange.
Ways to teach it
- Have students flip a coin 50 times, record streaks, then compare their longest streak to a class simulation of 200 trials.
- Ask students to write whether 8 heads in 10 flips is strong evidence of an unfair coin, using simulated data to justify.
- Give a dot plot of 100 simulated outcomes and ask students to mark whether an observed result falls in an unusual region.
- Connect to quality control by testing whether a snack bag filling machine matches its claimed average using simulated sampling results.
Plan a lesson for CCSS.Math.Content.HSS-IC.A.2
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Related standards
- CCSS.Math.Content.HSS-IC.A
Understand and evaluate random processes underlying statistical experiments
- CCSS.Math.Content.HSS-IC.B.5
Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
- CCSS.Math.Content.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...
- CCSS.Math.Content.7.SP.C.7b
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.