Line Plots
Objectives To create and describe line plots; and to use
data
landmarks.
d
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ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Construct a line plot from collected data. [Data and Chance Goal 1]
• Use the spread and shape of a line
plot to draw conclusions about the data
it represents. [Data and Chance Goal 2]
• Identify landmarks of data sets. [Data and Chance Goal 2]
Key Activities
Students construct line plots from data they
have collected about themselves. Then
students match “mystery” line plots to each
category of collected data. They also identify
landmarks for each set of data.
Ongoing Assessment:
Recognizing Student Achievement
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing High-Number Toss
(Whole-Number Version)
Student Reference Book, p. 323
Math Masters, p. 454
per partnership: six-sided die
Students practice reading, writing, and
comparing numbers.
Math Boxes 1 2
Math Journal 1, p. 8
metric ruler
Students practice and maintain skills
through Math Box problems.
Curriculum
Focal Points
Differentiation Options
READINESS
Reviewing Line Plots
Student Reference Book, p. 134
Students review how to read and construct
a line plot.
ENRICHMENT
Examining the Effects of Outliers
Math Masters, p. 9
Students examine how an outlier affects
the mean and median of a data set.
ELL SUPPORT
Study Link 1 2
Building a Math Word Bank
Math Masters, p. 8
Students practice and maintain skills
through Study Link activities.
Differentiation Handbook, p. 130
Students add the terms minimum, maximum,
median, and mode to their Math Word Banks.
Use an Exit Slip (Math Masters,
page 404). [Data and Chance Goal 2]
Key Vocabulary
line plot mystery plot landmark minimum maximum median mode range
Materials
Student Reference Book, p. 134
Math Journal 1, pp. 6 and 7
Study Link 11
Math Masters, pp. 7 and 404
scissors 5 envelopes 10 stick-on notes
per group: marker, large sheet of paper
Advance Preparation
Assemble five envelopes for the mystery plot activity in Part 1. Use stick-on notes to prepare number-letter
labels 1–5 and A–E. Affix one label to each envelope. Prepare a correspondence between letters and
numbers for your reference only (A↔2, B↔4, and so on). Supply groups with one large sheet of paper
and copies of Math Masters, page 7.
Teacher’s Reference Manual, Grades 4–6 pp. 162–164
22
Unit 1
Interactive
Teacher’s
Lesson Guide
Collection, Display, and Interpretation of Data
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP6, SMP7
Getting Started
Content Standards
6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5a, 6.SP.5b, 6.SP.5c
Bold SMP = Guiding Questions at everydaymathonline.com
Mental Math and Reflexes
Math Message
Cut 1 copy of Math Masters,
page 7, into 5 pieces.
Complete the statements at the
top of journal page 6. Do not share
your answers.
Students solve multiplication problems. Suggestions:
How many 7s in 56? 8
How many 700s in 5,600? 8
How many 9s in 540? 60
How many 18s in 540? 30
How many 5s in 600? 120
How many 50s in 6,000? 120
Draw attention to problems in which the dividend and divisor are multiplied
by the same number and the quotient remains unchanged.
Study Link 1 1
Follow-Up
Remind students to look
in newspapers and magazines for
graphs they can add to the classroom
Graphs Museum.
NOTE Some students may benefit from
1 Teaching the Lesson
▶ Math Message Follow-Up
Bold = Focus of lesson
doing the Readiness activity before beginning
Part 1 of the lesson. See Part 3 for details.
WHOLE-CLASS
ACTIVITY
(Math Masters, p. 7; Math Journal 1, p. 6)
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
Have students copy their answers from the Math Message onto
the five pieces from Math Masters, page 7 as follows:
1. On one of the five pieces, each student circles his or her
answer to Statement A. (A blank has been provided for
students to write in responses greater than 40.)
2. Students give the completed pieces to you.
3. Place the responses in the envelope labeled A. Discard any
responses that have extra marks or labels.
Student Page
Date
Mystery Plots and Landmarks
Complete the following statements. Do not share your answers. Estimate if you do
not know the exact number.
Answers vary.
A.
I usually spend about
B.
There is a total of
C.
There are
D.
My shoe is about
E.
I watch about
minutes taking a shower or a bath.
letters in my first, middle, and last names.
people living in my home.
centimeters long (to the nearest centimeter).
hours of television per week.
Mystery Plots
136
You and your classmates will make line plots of the data from the Math Message
above. You will then try to figure out which line plot, or mystery plot, goes with
which statement in the Math Message.
Landmarks
After the class has agreed on the subject of each line plot, mark the number lines
for each statement on the next page to show the following data landmarks for
each statement set: minimum, maximum, median, and mode. Also record the range.
Number of
Students
0
X
X
X
X
X
X
X
X
X
5
10
X
X
X
X
X
X
X
X
X
15
20
25
maximum
Example:
mode
Ask whether the questions in the Math Message are statistical
questions. No. Each question is specific to individual students
and so every answer will be a single number. Ask how the Math
Message questions could be changed to be statistical questions.
Sample answer: Change the questions to be about the class, not
the individuals in the class. For example, “How many hours of
television does a typical student in our class watch each week?”
12
Math Message
median = 15
Tell students that a statistical question is one that is answered by
analyzing a set of data. That is, a statistical question anticipates
some variability in the data associated with it, so it is best
answered by giving the mean, median, range, or some other
statistical summary of the data set. For example, “How many
students are in our class?” is not a statistical question because the
answer is only one piece of data. However, “How many students are
in a typical class in our school?” is a statistical question because its
answer will be found by collecting and analyzing a set of data.
Time
LESSON
minimum
Repeat this procedure for Statements B–E. Out of students’ sight,
replace the letter-labels with the corresponding number-labels.
X
30
35
40
Number of Minutes to Get to School
range
30 min
Math Journal 1, p. 6
EM3cuG6MJ1_U01_1-44.indd 6
1/11/11 5:29 PM
Lesson 1 2
23
Student Page
Date
▶ Making and Discussing Line
Time
LESSON
12
Mystery Plots and Landmarks
continued
Answers vary.
0
A.
10
30
Shower/Bath Time (in minutes)
0
B.
20
10
Plots of the Data
SMALL-GROUP
ACTIVITY
ELL
(Student Reference Book, p. 134)
40
range
20
30
Number of Letters in First, Middle, and Last Names
Give each group a numbered envelope and a large sheet of paper.
To support English language learners, review the meaning of plot
in the context of this activity.
40
range
Groups proceed as follows:
0
C.
10
10
20
10
40
1. List the data in order from least to greatest.
range
30
Length of Shoe (to nearest cm)
0
E.
30
Number of People Living in Home
0
D.
20
2. Using markers and the large sheet of paper, draw a
line plot of the data.
40
range
20
30
Hours of Television Viewed per Week
3. Write the envelope number on the line plot.
4. Post the line plots around the classroom.
40
range
Math Journal 1, p. 7
EM3cuG6MJ1_U01_1-44.indd 7
1/11/11 5:29 PM
NOTE Some students may go to great
lengths to try to identify their own responses
while deciding which statement goes with
which data set. You might consider switching
envelopes with another class.
5. Decide which line plot goes with which statement (A–E)
in the Math Message. Groups should be ready to defend
their answers.
▶ Matching Line Plots with
Statements and Landmarks
WHOLE-CLASS
DISCUSSION
PROBLEM
PRO
P
R
RO
ROBLEM
B EM
SOLVING
(Math Journal 1, pp. 6 and 7)
Pose questions such as the following:
Links to the Future
The activities in this lesson provide students
with a foundation for this year’s experiences
using graphs to represent and communicate
data. Analyzing and interpreting data is an
Everyday Mathematics program goal.
NOTE Line plots are also called dot plots.
●
Which mystery plot matches each statement? Why?
●
Is there a statement that definitely does not go with a
certain line plot? Why?
●
Which statement was easiest to identify by line plot?
Which was most difficult? Why?
Students may offer reasoning similar to the following: “Minutes of
shower/bath and hours of watching television could easily have the
same range. However, shower/bath minutes will probably be below
15, while television hours will probably have values above 20.”
Encourage students to consider the spreads and shapes of the line
plots. After some discussion, reveal the correct statement for each
line plot.
Adjusting
the Activity
ELL
Landmarks are notable features of a locale in
the same way that they are notable features
of a data set. To support English language
learners, discuss the similarities between
the everyday and mathematical meanings of
landmark. Label the landmarks on the group
charts as shown in the example on journal
page 6.
AUDITORY
24
Unit 1
KINESTHETIC
TACTILE
Have students find the number of data points shown on each line
plot. Ask: What do you notice? They all have the same number
of data points. Why? Each data point represents the answer of
a student in the class. All students should have answered each
question, so there should be the same number of data points on
each line plot.
Ask students to identify the following landmarks for each set
of data: minimum, maximum, median, mode, and range.
Have them turn to journal page 7 and record these landmarks.
VISUAL
Collection, Display, and Interpretation of Data
Game Master
Ongoing Assessment:
Recognizing Student Achievement
Exit Slip
Name
Date
Time
High-Number Toss Record Sheet
HundredMillions
TenMillions
Millions
,
HundredTenThousands Thousands Thousands
Player 1
Use an Exit Slip (Math Masters, p. 404) to assess students’ understanding of
landmark terms. (See next paragraph.) Students are making adequate progress
if their methods and meanings demonstrate knowledge of an accurate definition.
1 2
4 3
323
,
Hundreds
Tens
Ones
Player 2
(Name)
(Name)
Round
Player 1
>, <, =
Player 2
Sample
1 3 2 | 6
132,000,000
⬎
3 5 6 | 4
3,560,000
Pose the following informal assessment item to students: Suppose a friend has
trouble remembering the definitions for minimum, maximum, median, mode, and
range. Describe a way to remember the meaning of each landmark term.
|
|
|
|
|
|
|
|
|
|
1
[Data and Chance Goal 2]
2
3
2 Ongoing Learning & Practice
▶ Playing High-Number Toss
4
PARTNER
ACTIVITY
5
(Whole-Number Version)
Math Masters, p. 454
(Student Reference Book, p. 323; Math Masters, p. 454)
This is the whole-number version of the game introduced in
Fourth Grade Everyday Mathematics. Have students read the
game directions on page 323 in the Student Reference Book. Play a
round against the class before having students play on their own.
Provide each partnership with a six-sided die and record sheet
(Math Masters, page 454). Circulate and observe to get a sense of
students’ ability to read, write, and compare whole numbers to the
hundred-millions place.
NOTE Games are integral to the Everyday Mathematics program. They provide
an effective and interactive way to reinforce skills described in Grade 6 Goals.
Establish a games routine during Unit 1 and maintain it throughout the year.
Make sure all students are given time to play the games, especially those who
find traditional drill and practice tedious.
Student Page
Date
▶ Math Boxes 1 2
Time
LESSON
INDEPENDENT
ACTIVITY
䉬
1.
(Math Journal 1, p. 8)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lessons 1-4 and 1-5a. The skills in
Problems 4 and 5 preview Unit 2 content.
Math Boxes
12
Draw line segments having the following
lengths.
2.
Find the minimum, maximum, median,
mode, and range for the set of numbers.
a.
4.2 cm
105, 100, 111, 94, 105
b.
51 mm
minimum
maximum
c.
42 mm
median
mode
range
94
105
17
111
105
136
3.
Subtract.
a.
Writing/Reasoning Have students write their responses to the
following: Explain how you can check your answer to Problem 4
without using a calculator. Sample answer: I can multiply my
answer choice by 7 to see if I would get 882.
900 ⫺ 3 ⫽
897
b.
5,182 ⫺ 2,637 ⫽
2,545
c.
7,360 ⫽ 8,035 ⫺ 675
15–17
4.
Which is the quotient 882 and 7?
5.
Fill in the circle next to the best answer.
Complete.
a.
A.
93.6
b.
B.
126
c.
C.
12.6
d.
D.
127
e.
90 ⫽ 54,000
7,200 ⫽ 80 ⴱ 90
400 ⴱ 80 ⫽ 32,000
800
560,000 ⫽ 700 ⴱ
40 ⴱ 700 ⫽ 28,000
600 ⴱ
18
22–24
Math Journal 1, p. 8
Lesson 1 2
25
Study Link Master
Name
Date
STUDY LINK
▶ Study Link 1 2
Time
Mystery Line Plots and Landmarks
12
䉬
Draw a line plot for the following spelling test scores.
1.
134–136
INDEPENDENT
ACTIVITY
(Math Masters, p. 8)
100, 100, 95, 90, 92, 93, 96, 90, 94, 90, 97
X
X
X
X
X
X
X
X
X
X
X
Home Connection Students draw a line plot to represent
a given set of data and use it to identify landmarks. You
may want to send the Student Reference Book home
with students.
90 91 92 93 94 95 96 97 98 99 100
90
2.
The mode of the above data is
3.
Draw a line plot below that represents data with the following landmarks.
Use at least 10 numbers.
range: 7
minimum: 6
median: 10
Sample answer:
X
X
X
X
X
X
X
6
7
8
5
.
9
modes: 8 and 11
X
X
X
X
X
X
X
X
X
X
X
X
10
11
12
13
Describe a situation in which the data in the above line plot might occur.
4.
Sample answer: The data might represent
the results of a survey on weekly allowance.
5. Give the line plot a title and a unit. Sample answers given.
Title Weekly Allowance
Unit Dollars
3 Differentiation Options
Practice
90
120
6.
540 ⫼ 6 ⫽
8.
84,000 ⫼ 700 ⫽
80
7.
7,200 ⫼ 90 ⫽
9.
400,000 ⫼ 5,000 ⫽
Consider assigning the Practice problems that appear at the
bottom of most Study Links. Because these problems provide fact
and computation practice, students should not use calculators to
solve them. They may work the problems on the back of the page.
80
READINESS
8
▶ Reviewing Line Plots
Math Masters, p. 8
SMALL-GROUP
ACTIVITY
5–15 Min
(Student Reference Book, p. 134)
To provide experience with line plots, have students read page 134
of the Student Reference Book and complete Problem 2 of Check
Your Understanding. Review answers.
ENRICHMENT
▶ Examining the Effects
INDEPENDENT
ACTIVITY
5–15 Min
of Outliers
(Math Masters, p. 9)
Teaching Master
Name
Date
LESSON
12
䉬
Time
Outliers and Gaps
The data value of 39 is an outlier.
It is very different from the rest
of the data values.
X
X
X
X
X
X X
X X
5
10
15
X
X
X
There are no data values
from 19 to 38. This is a gap.
X
20
25
30
35
40
The effect of an outlier on the mean depends on the number of data values in
the set and the size of the gap between the outlier and the other data values.
1.
Find the mean and median for the data set above.
mean
2.
13
median
10
▶ Building a Math Word Bank
10.8
median without outlier
10
Explain the effect of the outlier on the mean of the set.
Suppose the outlier of the data set were 30 instead of 39.
a.
Predict the value of the mean.
predicted mean
b.
Answers vary.
Now calculate the mean. Round it to the nearest tenth.
mean
5–15 Min
To provide language support for data landmarks, have students
use the Word Bank template found on Differentiation Handbook,
page 130. Ask students to write the terms minimum, maximum,
median, and mode and then represent the terms with pictures and
other words that describe them. See the Differentiation Handbook
for more information.
12.3
Math Masters, p. 9
26
INDEPENDENT
ACTIVITY
(Differentiation Handbook, p. 130)
Sample answer: The mean is much higher
with the outlier than without.
4.
ELL SUPPORT
Find the mean and median for the data set above without the outlier.
Round each landmark to the nearest tenth.
mean without outlier
3.
To extend students’ knowledge of mean and median, have them
find the mean and median of a data set with and without the
outlier. Students compare the results and draw conclusions about
the effect of an outlier on the mean and median of a data set.
Unit 1
Collection, Display, and Interpretation of Data