Download 8.12A Plan7.Cent.Tend - Texarkana Independent School District

Focus Plan
Texarkana Independent School District
GRADING
PERIOD:
Teacher:
2nd 6 Weeks
PLAN CODE:
Winton
Course/subject:
Mathematics
Grade(s):
8
Time allotted
for instruction:
1 – 1 ½ hours
Title:
Understanding Mean, Median, Range, and Mode
Lesson TOPIC:
Central Tendency
TAKS Objective:
Objective 5: The student will demonstrate an understanding of
probability and statistics.
FoCUS TEKS and
Student Expectation:
(12) Probability and statistics. The student uses statistical procedures
to describe data. The student is expected to:
(A) select the appropriate measure of central tendency to describe a
set of data for a particular purpose.
(14) Underlying processes and mathematical tools. The student
applies Grade 8 mathematics to solve problems connected to everyday
experiences, investigations in other disciplines, and activities in and
outside of school. The student is expected to:
(A) identify and apply mathematics to everyday experiences, to
activities in and outside of school, with other disciplines, and with
other mathematical topics.
Supporting TEKS and
Student Expectations:
Concepts
Mean
Median
Mode
Measures of Central
Tendency
Range
Enduring Understandings/Generalizations/Principles
The student will understand that
The mean is the sum of the numbers in a set of data divided by the number
of pieces of data.
The median is the middle number in a set of data when the data are
arranged in numerical order. If the data has an even number, the median is
the mean of the two middle numbers.
The mode is the number(s) or item(s) that appear most often in a set of
data.
Measures of central tendency are numbers of pieces of data that can
represent the whole set of data.
The range is the difference between the greatest number and the least
number in a set of data.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
I.
Sequence of Activities (Instructional Strategies)
A.
Focus/connections
Place the following hourly wage amounts on the board:
$8.00, $9.00, $12.00, $12.50, $9.50, $13.00, $9.50, $14.50, $17.00
Ask each student to get out a piece of paper for which to take notes. Have students place the hourly
wage amounts that are on the board on their paper going from least to greatest. Discuss that the ability
to understand and use measures of central tendency are important math skills. Tell your students that
this lesson will help them understand how the same set of data can be interpreted in a variety of ways.
B.
Instructional activities
(demonstrations, lectures, examples, hands-on experiences, role play, active
learning experience, art, music, modeling, discussion, reading, listening, viewing,
etc.)
Have students write the following terms on their notes page: Mean, Median, Mode, Range, and Measure
of Central Tendency. Ask them to leave enough room to write the definitions of each word on their page.
Give students the definitions as listed above. Next demonstrate how to find the mean, median, range,
and mode of the data. As you demonstrate, have your students record their calculations on their notes
page. Now ask the following questions: “Would you rather work for the mean, median, or mode
amount?”, “If someone wanted to complain about low wages, what figure would they quote?”, “If a
company wanted to brag about higher than average wages, what figure would they quote?” Discuss how
numbers can sometimes be interpreted for different purposes.
C.
Guided activity or strategy
Place students in groups of 2 – 3. Give each student a Practicing with Mean, Median, Range, and Mode
Worksheet. Allow students to complete the guided activity. Once ample time has passed, go over
correct answers with students, answering questions as they arise.
D.
Accommodations/modifications
Students requiring modifications may be paired with a peer to complete the guided activity.
E.
Enrichment
Students requiring enrichment may reteach the steps to obtain the mean, median, range, and mode to a
peer requiring modifications.
II.
STUDENT PERFORMANCE
A.
Description
Students will complete the Mean, Median, Range, and Mode Worksheet individually.
iii.
B.
Accommodations/modifications
C.
Enrichment
Assessment of Activities
A.
Description
Individual student grades may be taken on the Mean, Median, Range, and Mode Worksheet.
B.
Rubrics/grading criteria
Grades may taken based on the Mean, Median, Range, and Mode Worksheet Answer Key/Grading
Rubric.
C.
Accommodations/modifications
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
D.
Enrichment
Question #6 on the Mean, Median, Range, and Mode Worksheet can be used for enrichment purposes.
E.
IV.
Sample discussion questions
 What real world applications do you utilize mean, median, mode, and range?
 How can numbers be manipulated to make opposite points?
TAKS Preparation
A.
Transition to TAKS context
The teacher will lead the students in a discussion of how central tendency problems may look in test
format by placing the TAKS questions below on the overhead/board.
B.
Sample TAKS questions
1. The Webster Junior High faculty includes 37 teachers. The principal’s and teachers’ annual salaries
total $1,266,140. If the principal’s salary is $54,250, which equation can be used to find s, the average
salary for a teacher at Webster Junior High?
F. s = (1,266,140 + 54,250) / 37
G. s = 1,266,140 + 54,250 / 37
H. s = 1,266,140 - 54,250 / 37
J. s = (1,266,140 - 54,250) / 37
2. The following table shows the number of pages in novels that Chloe read for pleasure each month
during the school year.
Month
Number
of Page
Read
Sept.
Oct.
Chloe’s Novel Reading
Nov.
Dec.
Jan.
Feb.
March
April
370
393
380
372
385
391
376
396
If Chloe read only 125 pages during the month of May, which measure of data changed the most?
A. The mean
B. The median
C. The mode
D. All measures were affected equally.
V.
Key Vocabulary
Mean, Median, Mode, Measures of Central Tendency, Range
VI.
Resources
A.
Textbook
Glencoe Mathematics ~ Applications and Connections Course 3
Chapter 4: Statistics: Analyzing Data
 Measures of Central Tendency, pp. 158 – 161
B.



Supplementary materials
Practicing with Mean, Median, Range, and Mode Worksheet
Mean, Median, Range, and Mode Worksheet
Mean, Median, Range, and Mode Worksheet Answer Key/Grading Rubric
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District
C.
Technology
For additional practice, students may utilize the following web sites:
http://www.mathgoodies.com/lessons/vol8/challenge_vol8.html
http://regentsprep.org/Regents/math/mean/Pmeasure.htm
http://www.aaamath.com/sta.html
VII.
follow up activities
(reteaching, cross-curricular support, technology activities, next lesson in sequence, etc.)
Bring in newspaper/magazine articles dealing with prices, wages, and production. Search for references
to mean, median, range, and mode.
VIII.
Teacher Notes
Junior High students really like working with anything dealing with food. There are many ways to use
individual packs of M&Ms or Skittles. With the candy, each student can estimate the number in his or her
own individual pack. Students can then open the packs, count each piece, and sort by color. The full
class data can be collected and each student can then find the mean of each color, the mean number of
pieces per bag, and a number of other statistics.
 Division of Curriculum and Instruction  School Improvement Department  Texarkana Independent School District