Margin of Error

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Objective

SWBAT calculate and explain the margin of error for a population sample.

Big Idea

Deputy Dawg is in the lead in the race for dogcatcher with 55% +/- 3%. What does +/- 3% mean and where does it come from?

Set the Stage

8 minutes

I project a brief article about a national poll that includes the plus or minus margin on my front board as an example for my students. (You can see the article in my resources.  I only use the first page, but have included the entire article if you would like to use it with the citation at the end of the article.)  I ask them to review the article for any statistics they can find, then have them pair share about what they see. (MP1, MP2)  After a few moments I ask random students to share what they talked about.  Generally they respond with comments about the percentages given, the number of voters and the margin of error.  I ask for volunteers to explain each of the values and have several willing and able to talk about the percentages of voters and the total number of people surveyed.(MP6)  However, when I ask what the margin of error percentage means my students can't really give good answers (though they'll usually try).  Not knowing the answer gives them an incentive for today's class, which I tell them will be about margin of error,  what it means, and how it works.  I give them one additional teaser before putting them to work.  I say that knowing the margin of error gives us an idea of how "confident" we can be about the results of the survey.

Put it into Action

35 minutes

You will need copies of the Margin of Error Challenge handout for this part of the lesson.  I give my students a brief explanation of what the margin of error represents (you can see this in my resources as Margin of Error video) then tell my students they will be working with a partner to complete today's challenge. (MP1, MP5) I give each student a copy of the handout and ask them to review the directions with their partner, then ask questions as needed for clarification.  I selected these challenge questions to provide a range of problems, some with small or large populations others with small or large proportions.

As the teams are working on the challenge I walk around the room giving encouragement and assistance as needed.  Most teams do fairly well with this activity, but there are always a few students who struggle with the connection between the sample size and the margin of error.  For those teams I try to ask probing questions to see where the misunderstandings lie.  For example, I might ask "How are the sample sizes for problems A and B different?" and then "What differences do you see between the margin of error for problems A and B?"  Asking directed questions helps focus my weaker students on the important parts of the activity rather than getting lost in the calculations.(MP2)

Wrap it Up

7 minutes

For this part of the lesson you will need copies of the Margin of Error Homework ChallengeI begin this wrap up by giving my students time to reflect about how margin of error, sample size, and confidence level are related.  I then ask them to write a statement/conclusion about the relationships using mathematically accurate language.  (MP6, MP7)  When I've collected all the reflection notecards, I hand out the Margin of Error Challenge as a homework assignment. (MP1, MP2) I have also included a Margin of Error video narrative that discusses the pedagogy more thoroughly.