Maryland Math S.IC.A.1.a

MathGrades 9–12Making Inferences and Justifying Conclusions

The Standard

S.IC.A.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Introduce sampling distributions as a means to explore variability in sample statistics and ultimately evaluate a claim about a population.

Maryland College and Career Ready Standards for Mathematics (2025) · UNDERSTAND AND EVALUATE RANDOM PROCESSES UNDERLYING

Teacher's field guide

What Students Need to Do: Students simulate many random samples of the same size under a claim about a population. They calculate a percentage for each sample and use the spread of those percentages to judge an observed result.
What Mastery Looks Like: Given a claim that half of students ride the bus, a student can plot the bus-rider percentage from each of many 20-student samples. They can explain why a result far from the usual range casts doubt on the claim but does not prove it false.
Common Misconceptions: Students may plot each person's answer instead of one percentage per sample. They may treat one sample percentage as the exact population percentage or think any difference from the claim disproves it.
How to Assess It: Exit ticket: A school claims half its students ride the bus, but 18 of 20 randomly chosen students ride it. Describe what you would plot after repeating 20 fair coin flips 50 times, and explain how the plot could help you judge the claim.

Lesson moves

Give pairs 20 coins; have them flip all 20 ten times, record each heads percentage, and add their results to a class dot plot.
Ask, 'If half the school rides the bus, would 18 riders in a random sample of 20 surprise you? Why?'
Play 'Typical or Surprising': show counts of 9, 12, and 18 riders out of 20, then have students place them on the coin-flip plot.
Show a mock survey with 18 bus riders out of 20; students write a note to the principal comparing it with their plot.

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