# Lesson 10

Estimating Proportions from Samples

### Lesson Narrative

The mathematical purpose of this lesson is for students to use data from a random sample and simulation to estimate a population proportion and to understand margin of error for a population proportion estimate. The work of this lesson connects to prior work because students were introduced to the concept of margin of error when estimating a population mean from sample data. The work of this lesson connects to upcoming work because students will explore the relationship between sample size and margin of error. When students interpret the meaning of the margin of error in the context of a problem they are reasoning abstractly and quantitatively (MP2).

### Learning Goals

Teacher Facing

• Calculate the margin of error for a population proportion estimate.
• Use data from a random sample to determine an estimate for a population proportion.

### Student Facing

• Let’s estimate population proportions with some data.

### Required Preparation

Create a bag for each pair of students. Each bag has 20 slips of paper cut from copies of the blackline master with 14 of them marked “Pass” and 6 marked “Fail.” Data from the class will need to be collected with a dot plot created from the data set and the mean and standard deviation of the class data set calculated.

Acquire devices that can run GeoGebra (recommended) or other statistical technology. It is ideal if each student has their own device. (A GeoGebra Statistics tool is available under Math Tools.)

### Student Facing

• I can estimate the margin of error using standard deviation.
• I know that a larger margin of error means more variability, and I should be less confident in my estimate of the population mean.
• I know that a smaller margin of error means less variability, and I can be more confident in my estimate of the population mean.
• I understand that different samples from the same population can still have different statistics.