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Picturing the Normal World
Resource ID#: 130177
Primary Type: Lesson Plan
This document was generated on CPALMS - www.cpalms.org
This is an introductory lesson on normally distributed data. Students will collect their own height
data and view the data distribution for their class. They analyze this data and decide if they are
normal or not.
Subject(s): Mathematics
Grade Level(s): 9
Intended Audience: Educators
Suggested Technology: Graphing Calculators, Computer for Presenter, LCD Projector
Instructional Time: 40 Minute(s)
Keywords: Empirical Rule, Normal Distribution, Sample Mean, standard deviation, variance,
histogram
Instructional Component Type(s): Lesson Plan, Worksheet, Assessment
, Presentation/Slideshow, Formative Assessment
Resource Collection: FCR-STEMLearn Algebra
ATTACHMENTS
WorkSheet extra practice.docx
WorkSheet extra practice key.docx
World Worksheet Homework.docx
World Worksheet Homework Key.docx
World Lesson Powerpoint.pptx
World Worksheet activity teacher guide.docx
World Worksheet activity for students.docx
LESSON CONTENT

Lesson Plan Template:
General Lesson Plan

Learning Objectives: What should students know and be able to do as a result of this
lesson?
Students will be able to:
o
o

Interpret data percentages using the Empirical Rule (68-95-99.7 rule).
Use the Empirical Rule to estimate number of data values in a normal population that fall within a
certain range.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should already be able to:
o
o
o
o

Guiding Questions: What are the guiding questions for this lesson?
o
o

Interpret the meaning and calculate standard deviation.
Calculate percentages.
Calculate mean, median, mode and range.
Construct frequency table and histogram.
How can you use standard deviations to interpret data?
What real data sets have distributions that are approximately symmetric and bell shaped?
Teaching Phase: How will the teacher present the concept or skill to students?
Continuing with the attached PowerPoint after the warm-up, the teacher will:
1. Introduce normal curve concept by stating that many real-life data sets have distributions that are
approximately symmetric and bell shaped.
2. Present some examples that represent a normal distribution data. (tree heights or most natural heights,
life spans of a fish or any life span of a group, hours that 60 watt light bulbs last, etc.)
3. Use the frequency table to show students that data will approximate a bell shape graph.
4. Introduce the Empirical Rule and explain how valuable the standard deviation is as a measure of
variation.
5. Show how to interpret standard deviation and how to find percentages of data using Empirical Rule.
6. After this explanation, the teacher should present attached activity to students. This activity involves
collecting heights of students in the class.
7. After data collection the teacher should have students record that information on a histogram. (The
teacher could give the students the standard deviation if they don't have time to find it or allow them
technology to calculate it.) With this graph, students should be able to make conclusions about their heights
and if the data appears normal. If it doesn't appear normal the teachers should tell the students to assume
normality to practice using the Empirical Rule. The teacher will ask students what they know about their
personal height and where do they fall on the bell curve. Discussion should occur to the accuracy of these
calculations since it is not normal and that we can only use these as approximations.
8. Continue to the Independent Practice worksheet, attached. See the write-up below.
9. Distribute the homework worksheet, attached. See the write-up in the summative assessment section.

Guided Practice: What activities or exercises will the students complete with teacher
guidance?
Students will be asked to complete an attached worksheet activity where they collect height of students in
the classroom and analyze their heights using a normal curve.
Answers to questions posed on the PowerPoint slides are in the note section of the PowerPoint.

Independent Practice: What activities or exercises will students complete to reinforce
the concepts and skills developed in the lesson?
The students will complete the attached extra practice worksheet. This four-question practice should be
completed quickly by students. The teacher can then lead a class discussion to identify the answers.

Closure: How will the teacher assist students in organizing the knowledge gained in the
lesson?
The teacher should have a quick whole-class review after going over the extra practice worksheet. Then the
attached homework worksheet should be passed out for students to complete and turn in the next day.

Summative Assessment
For the summative assessment, students will complete attached homework worksheet. This assessment is
used to determine whether students have learned what they were expected to learn in class.

Formative Assessment
o
Using a PowerPoint presentation (attached) and worksheet, the teacher provides several data
values and asks students to work in pairs calculating mean, and standard deviation using
technology. The teacher observes group activities walking around the room and assist with
correction of errors in reasoning. If more than two groups are making errors the teacher may want
to stop and bring the whole group together for clarification.
o

The teacher should also review vocabulary such as sample mean, median, mode, and standard
deviation verbally through questioning on their meanings.
Feedback to Students
The students will receive feedback following the warm-up and throughout the lesson. After the warm-up,
the teacher will verbally review the result with the whole class and correct any misconceptions.
Also, students will receive feedback after guided and independent practices when answers are discussed.
ACCOMMODATIONS & RECOMMENDATIONS

Accommodations:
o
o

ESOL and other students with accommodations will be paired with a peer to check their work
and/or help with technology; they will also be given extended time to complete assignments
and/or tasks.
Data lists can be shortened if helpful for completion of work.
Extensions:
Students can collect their own data (via research, experiment, or survey) and:


o create a box plot
o relative frequency histogram
o find standard deviation using formulas and TI-84
o decide if data is normal
o interpret percentages of data intervals if data is normal
Suggested Technology: Graphing Calculators, Computer for Presenter, LCD Projector
Special Materials Needed:
o
o
Tape measure
Graphing calculators
Additional Information/Instructions
By Author/Submitter
Math Practices:



Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others.
SOURCE AND ACCESS INFORMATION
Contributed by: lianet rodriguez
Name of Author/Source: lianet rodriguez
District/Organization of Contributor(s): Miami-Dade
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.S-ID.1.4:
Description
Use the mean and standard deviation of a data set to fit it to a
normal distribution and to estimate population percentages.
Recognize that there are data sets for which such a procedure is
not appropriate. Use calculators, spreadsheets, and tables to
estimate areas under the normal curve. ★