The Median
Objectives To review how to display a set of data with a
line plot; and to review how to find the median of a set
of data.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Create a line plot. [Data and Chance Goal 1]
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
• Find the maximum, minimum, range, mode,
median, and mean for a set of data. [Data and Chance Goal 2]
• Use data landmarks and representations to
answer questions and draw conclusions. [Data and Chance Goal 2]
Key Activities
Students construct a line plot to organize
and summarize data about the sizes of their
families. They find the minimum, maximum,
range, mode, and median for the data.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 40. [Data and Chance Goal 2]
Key Vocabulary
line plot median
Materials
Playing Subtraction Top-It
(Extended-Facts Version)
Student Reference Book, pp. 263
and 264
Math Masters, p. 506
per partnership: 4 each of number
cards 1–10 (from the Everything Math
Deck, if available)
Students practice subtraction fact
extensions.
Math Boxes 2 6
Math Journal 1, p. 41
Students practice and maintain skills
through Math Box problems.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Finding the Middle Value
Math Masters, p. 55
deck of number cards (the Everything Math
Deck, if available)
Students order number cards and find
the median.
ENRICHMENT
Comparing Family-Size Data
Math Masters, p. 56
Students organize and compare family-size
data for two or more classes.
ELL SUPPORT
Study Link 2 6
Building a Math Word Bank
Math Masters, p. 54
Students practice and maintain skills
through Study Link activities.
Differentiation Handbook, p. 140
Students add the term median to their Math
Word Banks.
Ongoing Assessment:
Informing Instruction See page 117.
Math Journal 1, p. 40
Student Reference Book, p. 71
Study Link 2 5
3-inch-square stick-on notes tape (optional) slate
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 160–169
112
Unit 2
Using Numbers and Organizing Data
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Getting Started
Mental Math and Reflexes
Math Message
Write the problem 50 - 26 on the board. Ask students to solve it mentally and
write the answer on their slates. Have students share their strategies. Present
the following counting-up strategy if it is not brought up during discussion:
Find the line plot on page 71
of your Student Reference Book.
Write two things you notice about
students’ scores on Mr. Jackson’s
spelling test.
Start at 26. Add up to the next 10 and then to 50:
26 + 4 = 30, and 30 + 20 = 50. That is 4 + 20 = 24.
26
Study Link 2 5
Follow-Up
⫹20
⫹4
30
Ask partners to compare answers to
Problems 2–6. Check to see that all
students know the number of people in
their families (or the number of radios,
televisions, pets, or smoke detectors in
their home).
50
Pose additional problems such as the following:
40 - 27 = 13
30 - 16 = 14
60 - 33 = 27
67 - 10 = 57
51 - 20 = 31
84 - 30 = 54
110 - 52 = 58
180 - 143 = 37
240 - 136 = 104
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Student Reference Book, p. 71)
Invite volunteers to share observations about the data shown in
the “Scores on a 5-Word Spelling Test” line plot. Have students
stand up if they made a similar observation.
Student Page
Investigating the Sizes
WHOLE-CLASS
ACTIVITY
ELL
of Students’ Families
(Math Journal 1, p. 40; Study Link 2 5)
PROBLEM
PR
PRO
P
RO
R
OB
BLE
BL
L
LE
LEM
EM
SOLVING
SO
S
OL
O
LV
VIN
IIN
NG
Data and Probability
Organizing Data
Once the data have been collected, it helps to organize them to
make them easier to understand. Line plots and tally charts
are two methods of organizing data.
Mr. Jackson’s class got the following scores on a five-word spelling test.
Make a line plot and a tally chart to show the data below.
Tell students that in this lesson they will organize data about
the number of people in their families. Then they will identify
landmarks in the data.
Reviewing Students’ Family-Size Data
Remind students that in conducting their survey, all people living
at home now and any siblings living elsewhere are to be included.
Resolve any questions students might have. For example:
●
●
Do I count my brother who is away at college? yes
We have a boarder who has rented a room for the last 10 years.
We think of her as part of the family. Should I count her? yes
5 3 5 0 4 4 5 4 4 4 2 3 4 5 3 5 4 3 4 4
Scores on a 5-Word
Spelling Test
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
2
3
4
5
Number
of
Students
x
0
1
Number Correct
In this line plot, there are
4 Xs above the number 3.
In this tally chart, there are 4 tallies to
the right of 3.
Four students got a score of 3 on the test.
Four students got a score of 3 on the test.
Both the line plot and the tally chart help to organize the data.
They make it easier to describe the data. For example,
♦
♦
♦
♦
Five students had 5 words correct.
4 correct is the score that came up most often.
0 correct and 2 correct are scores that came up least often.
No student got exactly 1 correct.
Here are the number of hits made by 14 players in a baseball game.
4 1 0 2 1 3 2 1 0 2 0 2 0 3
Organize the data.
1. Make a tally chart.
2. Make a line plot.
Check your answers on page 341.
Student Reference Book, p. 71
Lesson 2 6
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●
My parents are divorced. I live with my mother during the
school year and with my father during summer vacations. How
should I count them? Count only those people living in your
present household.
●
I have a cousin who lives in France. Should he be counted? no
After questions have been resolved, students may need to revise
their family lists. Then have students record their family size in
Problem 1 on journal page 40 and on a stick-on note.
Constructing a Line Plot
Draw a number line on the board. Ask students to attach their
stick-on notes in the appropriate places above the number line,
creating a line plot. To support English language learners,
discuss the everyday as well as the mathematical meaning of the
word plot.
4
NOTE A line plot is a quick and easy way to
organize and display data. You can think of it
as a rough sketch of a bar graph. If graphing
software is available, have students create
their line plots using the software.
3
4
3
4
5
2
3
4
5
2
3
4
5
6
2
3
4
5
6
2
3
4
5
6
9
7
8
9
10
11
12
Number of People in Family
After everyone’s stick-on note has been posted on the board,
students copy the line plot on their journal pages. Have them use
Xs in place of the stick-on notes.
Analyzing the Data
Ask students to complete Problem 3 on journal page 40 on their
own. Then have students share their observations about the data.
In discussing the data landmarks, students can use informal
terms, but you should refer to these terms as maximum,
minimum, range, and mode.
Adjusting the Activity
ELL
As you discuss each landmark, have a volunteer label the number on
the class line plot. Consider having students do the same on journal page 40.
A U D I T O R Y
114
K I N E S T H E T I C
T A C T I L E
V I S U A L
Unit 2 Using Numbers and Organizing Data
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Student Page
Here are some other questions for discussion:
Date
Time
LESSON
●
How are the landmarks reflected in the shape and distribution
of the data in the line plot? Sample answers: The mode is the
family size that occurs most frequently. The number with the
most stick-on notes is the mode. If two or more family sizes
have the tallest columns of stick-on notes, they are all modes.
2 6
Follow your teacher’s directions and complete each step.
1.
How many people are in your family?
Write the number on a stick-on note.
2.
Make a line plot of the family-size data for the class.
Use Xs in place of stick-on notes.
Answers vary.
71 73
74
people
Class Data on Family Size
Where are the clusters, bumps, holes, and far-out numbers?
Answers vary.
Ongoing Assessment:
Recognizing Student Achievement
Family Size
Number of Families
●
䉬
Journal
page 40
Problem 3
Use journal page 40, Problem 3 to assess students’ understanding of data
landmarks. Students are making adequate progress if they are able to identify
the maximum, minimum, range, and mode of the data set. Some students may
be able to identify the mean.
2
夹
3.
[Data and Chance Goal 2]
4.
3
4
5
6
7
8
9
10
11
12
13
Number of People in Family
Find the following landmarks for the class data:
a.
What is the maximum (largest) number of people in a family?
b.
What is the minimum (smallest) number of people in a family?
people
c.
What is the range? (Subtract the minimum from the maximum.)
people
d.
What is the mode (most frequent family size)?
people
What is the median family size for the class?
people
people
Math Journal 1, p. 40
Finding the Median of the Class Data
Review ways of finding a middle value for family size; that is,
about half the families should be smaller and half should be larger
than this middle number. Remind students that the middle
number is called the median. Here is one way to find the median:
1. List all the data from smallest to largest (or largest to
smallest).
NOTE Stem-and-leaf plots
are covered in Grade 5.
If your curriculum requires
that this concept be
covered in Grade 4, see
www.everydaymathonline.com.
2. Count from each end to the number (or pair of numbers)
in the middle.
3. If two numbers are in the middle, the median number is the
average of the two numbers. This happens when there is an
even number of data.
Ages of 5 boys:
9
10
↓
11
11 12
The median age of the boys is 11.
↓
Ages of 6 girls:
9
10
10
11 11
12
The median age of the girls is 10 _12 — the value
halfway between the two middle numbers.
Lesson 2 6
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To find the median family size for the class, you can remove the
stick-on notes from the line plot and line them up single file in
ascending order on the board. (Have tape available to secure stickon notes that fall off.) Then have two students remove the stick-on
notes two at a time, one from each end, until only one or two notes
are left on the board. Students then record the median on journal
page 40, Problem 4.
last note remaining
2 2 2 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 6 6 9
Adjusting the Activity
ELL
Instead of lining up stick-on notes on the board, have each student take
a stick-on note and line up in order. Model finding the median by asking one
student from each end of the line to come together as a pair and then sit down.
Repeat this until one or two students are left standing and identify the median.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
After finding the median family size for your class, ask the
following questions:
●
Are the median and the mode for family size the same?
●
How does your own family size compare with the median size?
Is your family size equal to the median size? Less than the
median size? Greater than the median size?
Explain that the median is the most useful landmark for
describing the middle point of a data set, and it is often called a
typical value.
Adjusting the Activity
Ask students to find the mean of the data set and explain how the
mean is similar to or different from the median. Then ask them to explain which
landmark they think better represents the data.
A U D I T O R Y
116
K I N E S T H E T I C
T A C T I L E
V I S U A L
Unit 2 Using Numbers and Organizing Data
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Student Page
2 Ongoing Learning & Practice
Date
Time
LESSON
䉬
Add mentally.
a.
Playing Subtraction Top-It
b.
PARTNER
ACTIVITY
c.
(Extended-Facts Version)
d.
e.
(Student Reference Book, pp. 263 and 264;
Math Masters, p. 506)
f.
3.
Students play an extended-facts version of Subtraction Top-It to
develop automaticity with subtraction fact extensions. See Lesson
1-4 for additional information. Consider having students record
several rounds of play on Math Masters, page 506.
b.
147
⫺ 56
Find the median of the data set.
3, 45, 13, 15, 3, 7, 19
Fill in the circle next to the best answer.
A
3
B
13
C
15
D
45
73
10 11
4.
Write 4,007,392 in words.
four million, seven
thousand, three
hundred ninety-two
531
⫺ 246
285
91
4
12–15
5.
2.
9
90
20 ⫹ 70 ⫽
900
200 ⫹ 700 ⫽
12 ⫽ 8 ⫹ 4
120 ⫽ 80 ⫹ 40
1,200 ⫽ 800 ⫹ 400
2⫹7⫽
Subtract mentally or with a paper-andpencil algorithm.
a.
Math Boxes 2 6
Math Boxes
2 6
1.
A royal python can be 35 feet long. An
anaconda can be 28 feet long. What would
be their combined length, end-to-end?
63
6.
Tell whether each number sentence is
true or false.
a.
14 ⫹ 7 ⫽ 22
b.
36 ⫽ 15 ⫹ 5
c.
45 ⫺ 12 ⫽ 33
d.
27 ⫽ 40 ⫺ 13
feet
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 41)
false
false
true
true
148
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 2-8. The skills in Problems 5 and 6
preview Unit 3 content.
Math Journal 1, p. 41
Writing/Reasoning Have students write a response to the
following: Suppose the data set in Problem 2 represents the
number of hours each volunteer at an animal shelter
worked during the month of July. What was the median number of
minutes worked? 780 minutes Explain how you found your answer.
Sample answer: There are 60 minutes in an hour, so 60 × 13 =
780. Do you think it makes make more sense to report data like this
in hours or in minutes? Why? Sample answer: It makes more sense
to report it in hours. I understand what 13 hours feels like, but
780 minutes doesn’t mean as much to me. The larger unit makes
more sense.
Study Link Master
INDEPENDENT
ACTIVITY
(Math Masters, p. 54)
Home Connection Students construct a line plot from
data given in a tally chart. Then they find landmarks of
the data set.
Date
STUDY LINK
26
䉬
Line Plots
The students in Sylvia’s class estimated
how much time they spend watching
television each week. The tally chart
below shows the data they collected.
Number of Hours
per Week Spent
Watching TV
1.
17
71
Number of
Students
18
////\ /
////\ ////
/
////\
//
19
20
21
Watch for students who think that the median number of hours spent watching
television is 19.5. Students need to order the actual numbers of hours reported
by Sylvia’s class to find the median of the data set.
22
23
2.
3.
Construct a line plot for the data.
Student Data on
Television Time
///
///
16
Ongoing Assessment: Informing Instruction
Time
Number of Students
Study Link 2 6
Name
16
17
18
19
20
21
22
Find the following landmarks for the data:
a.
The maximum number of hours spent watching television each week.
b.
minimum
c.
range
d.
mode
e.
median
16 hours
20 hours
23
Number of Hours Spent
Watching Television Each Week
7 hours
20 hours
23
hours
Answers vary.
Estimate the amount of time that you watch television each week.
hours
Try This
4.
Calculate the mean number of hours Sylvia and her classmates spent
watching TV each week.
19.7 hours
Practice
5.
7.
110
130 ⫽ 70 ⫹ 60
80 ⫹ 30 ⫽
6.
8.
180 ⫽ 90 ⫹ 90
150
120 ⫹ 30 ⫽
Math Masters, p. 54
Lesson 2 6
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Teaching Master
Name
Date
Time
3 Differentiation Options
Find the Median Number
LESSON
26
䉬
The number in the middle of an ordered set of data is called the middle value,
or median.
73
For Problems 1–3,
Arrange the cards in order from smallest to largest.
䉬
Record the numbers in the boxes below.
䉬
Circle the number in the middle.
5
7
5
5
8
7
5
2
9
8
2
0
13
9
Example:
READINESS
0
smallest
Finding the Middle Value
18
13
Draw nine cards from a deck of number cards.
䉬
18
䉬
smallest
The median of my nine cards is
.
The median of my nine cards is
.
The median of my nine cards is
.
To provide experience with finding the median of a data set using
a concrete model, have students order number cards and find the
middle value.
largest
2.
smallest
largest
smallest
largest
3.
4.
Describe how you found the middle number in the problems above.
Sample answer: With 9 cards total, the
middle card has 4 cards on each side
of it. So the fifth card is the middle one.
5.
15–30 Min
(Math Masters, p. 55)
largest
Answers vary.
1.
PARTNER
ACTIVITY
ENRICHMENT
Comparing Family-Size Data
If you arranged the cards in Problem 1 in order from largest to smallest,
would the middle number stay the same?
Explain.
yes
The order of the numbers would be
reversed, but the middle number would
remain the same.
PARTNER
ACTIVITY
30+ Min
(Math Masters, p. 56)
To further investigate organizing and summarizing data,
have students compare the family-size data of their class
with those of other fourth-grade classes. If graphing
software is available, encourage students to use it to create
their displays.
Math Masters, p. 55
ELL SUPPORT
Building a Math Word Bank
SMALL-GROUP
ACTIVITY
5–15 Min
(Differentiation Handbook, p. 140)
To provide language support for data landmarks, have students
use the Word Bank Template found on Differentiation Handbook,
page 140. Ask students to write the term median, draw a picture
representing the term, and write other related words. See the
Differentiation Handbook for more information.
Teaching Master
Name
LESSON
26
䉬
1.
Date
Time
Comparing Family-Size Data
Create a display that compares the family-size data from your class with those
of other fourth-grade classes.
70–75
Answers vary.
2.
Compare the maximum, minimum, range, mode, and median for family size
for each class. Write about the similarities and differences. Use the back of
this page if you need more space.
Combine and organize the data from all of the classes. Then answer the following questions.
3.
What is the median family size for all of the classes?
4.
How does your class median compare with the larger sample?
5.
What is the mean family size for all of the classes?
6.
If you had to predict the family size of a student from your school that you did
not know, what would you predict? Explain your answer.
people
people
Math Masters, p. 56
118
Unit 2 Using Numbers and Organizing Data
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