Learning Activity

Is This Normal? Extending the Normal Distribution

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 and standard deviation of a data set. 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

After/Explain/Elaborate
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. Direct each student to the Desmos learning activity, Is It Normal? Extend.
  2. Instruct the students to follow and answer the prompts provided in the activity. (There are teaching prompts and sample responses at the bottom of the activity.)
  3. Circulate while students are working and assist with any questions or problems they might encounter.
  4. The teacher can monitor students' progress on Desmos to identify problems or gaps in learning.
  5. If the majority of students struggle with a common topic, pause the activity, and address the misconception.
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. If using with a whole group, the teacher should have students write their answers on whiteboards or on paper and check for mistakes. 

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.)

Prior to the lesson, the teacher will need to assign Is It Normal? Extend through Google Classroom or another online learning platform. 

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. 

The teacher should work through the problems and be familiar with possible student responses. (Teaching prompts and sample responses at the bottom fo the activity.)

Optional:  Prepare a copy of the normal curve with percentages for each student to use. (This copy has 3 curves per page)

Digital Tools / Resources

Is This Normal? Extend - Desmos Activity
http://teacher.desmos.com/activitybuilder/custom/5f009d78277abd3653443c34

Approved Date

Owner (Author)

mrswhite
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