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# Margin of Error

Lesson 10 of 17

## 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?

*50 minutes*

#### Set the Stage

*8 min*

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.

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#### Put it into Action

*35 min*

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)*

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#### Wrap it Up

*7 min*

*For this part of the lesson you will need copies of the Margin of Error Homework Challenge. *I 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.

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- UNIT 1: First Week!
- UNIT 2: Algebraic Arithmetic
- UNIT 3: Algebraic Structure
- UNIT 4: Complex Numbers
- UNIT 5: Creating Algebraically
- UNIT 6: Algebraic Reasoning
- UNIT 7: Building Functions
- UNIT 8: Interpreting Functions
- UNIT 9: Intro to Trig
- UNIT 10: Trigonometric Functions
- UNIT 11: Statistics
- UNIT 12: Probability
- UNIT 13: Semester 2 Review
- UNIT 14: Games
- UNIT 15: Semester 1 Review

- LESSON 1: Intro to Stats
- LESSON 2: Categorically Quantified
- LESSON 3: Sampling Simplified
- LESSON 4: Drawn and Quartered
- LESSON 5: Crazy Correlations
- LESSON 6: In the Middle
- LESSON 7: How's Your Spread
- LESSON 8: What's Normal
- LESSON 9: Not Normal
- LESSON 10: Margin of Error
- LESSON 11: Is It Significant
- LESSON 12: Simulations
- LESSON 13: Z is a good score!
- LESSON 14: Testing 1,2,3
- LESSON 15: Testing 4,5,6
- LESSON 16: Stats Review
- LESSON 17: Stats Assessment