# Lesson 11

Reducing Margin of Error

### Lesson Narrative

The mathematical purpose of this lesson is to use samples of different sizes to find proportions of populations, to estimate margin of error from data, and to understand the relationship between sample size and margin of error. The work of this lesson connects to previous work because students used data from random samples to estimate population proportions and to estimate the margin of error. The work of this lesson connects to upcoming work because students will use random samples to estimate population means and associated margins of error. When students use and analyze data to make connections between sample size and margin of error they are looking for and making use of structure (MP7).

### Learning Goals

Teacher Facing

• Generalize that a greater sample size usually leads to a smaller margin of error.
• Use data from samples to determine proportions of populations and estimate a margin of error.

### Student Facing

• Let’s estimate population proportions and explore margin of error.

### Required Preparation

Each student will need a paper bag. Each student will also need paper and scissors to be able to make slips of paper for every other student in the class and themselves.

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 describe why a larger sample size usually leads to a smaller margin of error.
• I understand that sample size influences the size of the margin of error for a data set.

### Glossary Entries

• margin of error

The maximum expected difference between an estimate for a population characteristic and the actual value of the population characteristic.

### Print Formatted Materials

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