Learning Activity

Is This Normal? The Normal Distribution Explained

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Students will work through a Desmos activity on Normal Distribution. They will be reminded of how to find the mean of a data set. The process of finding the standard deviation of a set of data values will be introduced. Students will practice doing both calculations. Next, using the mean and standard deviation they will define the intervals in a normal curve and will approximate the percentage of items in each interval using the Empirical Rule.

This activity results from the ALEX Resource Development Summit.

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.25

From a normal distribution, use technology to find the mean and standard deviation and estimate population percentages by applying the empirical rule.

Unpacked Content

UP:MA19.A2.25

Vocabulary

  • Normal distribution
  • Population Percentages
  • Empirical Rule
  • Normal curve
  • Mean
  • Standard deviation

Knowledge

Students know:
From a normal distribution,
  • Techniques to find the mean and standard deviation of data sets using technology.
  • Techniques to use calculators, spreadsheets, and standard normal distribution tables to estimate areas under the normal curve.

Skills

Students are able to:
  • From a normal distribution, accurately find the mean and standard deviation of data sets using technology.
  • Make reasonable estimates of population percentages from a normal distribution.
  • Read and use normal distribution tables and use calculators and spreadsheets to accurately estimate the areas under a normal curve.

Understanding

Students understand that:
Under appropriate conditions,
  • The mean and standard deviation of a data set can be used to fit the data set to a normal distribution.
  • Population percentages can be estimated by areas under the normal curve using calculators, spreadsheets, and standard normal distribution tables.

Phase

During/Explore/Explain
Learning Objectives

Learning Objectives

Students will be able to:

- find the mean of a data set.

- find the standard deviation of a data set.

- use the mean and standard deviation to define the intervals in a normal distribution.

- use the empirical rule to approximate the area under the normal distribution.

Activity Details

  1. The teacher will assign Is It Normal? through Google Classroom or another online learning platform.
  2. The teacher will direct each student to the Desmos learning activity, Is It Normal? in Google Classroom or preferred online learning platform.
  3. This lesson will be taught as a whole group activity.
  4. The teacher will guide the students through each slide while explaining and teaching the skills using the slides.
  5. The teacher will instruct the students to answer the prompts provided in the activity.  
  6. The teacher should provide insight and guidance on each slide.
  7. As the students complete the prompts, the teacher should monitor students' progress on Desmos to identify problems or gaps in learning.
  8. Once the students answer their prompts, they can share their answers and they can see three other students' answers for a comparison of the correctness of their work.
  9. The teacher should answer the students' questions immediately to prevent misunderstandings.
Assessment Strategies

Assessment Strategies

The teacher can assess the students' answers in Desmos for assessment purposes. The teacher should correct the students' mistakes or misunderstandings.

Variation Tips

Students could work in pairs to complete this activity. If students do not have access to a device, the activity could be done as a whole group activity without assigning Is It Normal? through Google Classroom. If using with a whole group, the teacher should have students write their answers on whiteboards or on paper and check for mistakes. The teacher could print a Teacher Guide as use for note-taking if students need it for re-enforced instruction.

 

Background and Preparation

Background / Preparation

The teacher will need to ensure the classroom has the following:

  1. Internet connection (WiFi).
  2. Classroom set of computers, iPads, or smart devices. (If allowed students can use their own personal devices.)
  3. Prior to the lesson, the teacher will need to assign Is It Normal? in Google Classroom.
  4. Prior to the lesson, the teacher should be familiar with Desmos and should create a free class code for the activity. If the teacher does not have a Desmos account, he/she will need to create a free Desmos account.
  5. Prior to the lesson, the teacher should work through the activity and be prepared to address questions. (The teacher can print a Teacher Guide to assist in this preparation.) 

Digital Tools / Resources

Is This Normal? Desmos Activity
https://teacher.desmos.com/activitybuilder/custom/5effda3d11f90c3d4b1fd7c6

Approved Date

Owner (Author)

mrswhite
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