Montana Math MT.PLUS.DATA.DES.2

MT.PLUS.DATA.DES.2 is a cluster heading. These are the individual standards under it.

• MT.PLUS.DATA.DES.2.a

  Explaining the consequences, due to uncontrolled variables, of non-randomized assignment of subjects to groups in experiments, and

• MT.PLUS.DATA.DES.2.b

  Evaluating where bias, including sampling, response, or nonresponse bias, may occur in surveys, and whether results are representative of the population of inte...

01

What Students Need to Do

Students decide when results can describe a larger group and when they can support a cause-and-effect claim. They check how people were picked, how treatment groups were formed, and what might skew the results.

02

What Mastery Looks Like

Given a poll of students picked at random, a student can explain why its results may apply to the school but cannot show cause and effect. Given volunteers assigned to treatments by coin toss, they can explain why a difference might come from the treatment but may not apply to every student.

03

Common Misconceptions

Students often think picking people at random and assigning treatments at random serve the same purpose. They may think a large opt-in poll represents the whole school. They may miss how skipped replies, leading questions, or differences between self-chosen groups can distort results.

04

How to Assess It

Exit ticket: A school picks 50 students at random for a lunch poll, but only 15 reply. In a separate study, volunteers choose music or silence during a timed quiz. Can the poll represent the school, and can the quiz show that music caused a score difference? Explain both answers.

1. 01

   Flip coins to assign volunteers to solve the same puzzles with music or silence, then compare completion times.

2. 02

   Ask students to write why a score gap between students who chose music and those who chose silence might have another cause.

3. 03

   Sort four cards, a random school poll, an opt-in poll, coin-toss treatment groups, and self-chosen groups, into population, cause, or neither.

4. 04

   Show a school lunch survey emailed to every student; ask how skipped replies and a question like 'Aren't lunches great?' could skew results.

• MT.PLUS.DATA.DES.1

  Describe the purposes of and differences among sample surveys, experiments, and observational studies and explain how randomization relates to each.

• MT.PLUS.DATA.INF.3

  Use data from a randomized experiment to test the hypothesis that two groups are equal by: Interpreting the difference or ratio between the group means as the o...