# Lesson 8

Not Always Ideal

### Lesson Narrative

The mathematical purpose of this lesson is to generate data and use it to support or oppose mathematical claims based on a model. The work of this lesson connects to prior work because students used the normal distribution to model data in a histogram. The work of this lesson connects to upcoming work because students will use random samples to estimate population parameters and will be introduced to the concept of margin of error. When students use the results of simulation to support or oppose a mathematical claim, they are constructing viable arguments and critiquing the reasoning of others (MP3).

### Learning Goals

Teacher Facing

• Comprehend that probabilities from simulations may differ from expected probabilities.
• Use data to critique (orally and in writing) mathematical claims based on a model in different cases.

### Student Facing

• Let’s see how closely data matches expectations.

### Required Preparation

For the activity What Is Reasonable? each student needs a coin or access to a device for the digital version of the activity. For the activity Is That Fair? students will each need to cut blank pieces of paper into 25 approximately equal sized pieces. It will be helpful if each student has a pair of scissors. In each activity 5 observations from each student will need to be collected to create a box plot. Statistical technology can help do that quickly.

### Student Facing

• I can justify a mathematical claim using evidence.
• I know how to use mathematical evidence to find the difference between when outcomes are unfair or due to random chance.
• I understand why it's important to be skeptical of data that seems unfair.