Download Line Plots - Everyday Math

Line Plots
Objective To provide experience creating and interpreting line
plots with fractional units.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Identify equivalent fractions.
[Number and Numeration Goal 5]
• Identify fractions on a number line.
[Number and Numeration Goal 6]
• Add fractions and mixed numbers with
like and unlike denominators.
[Operations and Computation Goal 4]
• Create a line plot.
[Data and Chance Goal 1]
• Analyze a data set.
[Data and Chance Goal 2]
Family
Letters
Assessment
Management
Common
Core State
Standards
Curriculum
Focal Points
Ongoing Learning & Practice
Operations with Multidigit Whole
Numbers and Decimals
Math Journal 2, p. 242B
Students practice solving problems
involving operations with multidigit
whole numbers and decimals.
Math Boxes 7 10
Math Journal 2, p. 243
Students practice and maintain skills
through Math Box problems.
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Identifying Fractions on a Number Line
Math Masters, p. 211
Students label fractions on number lines.
EXTRA PRACTICE
Plotting Rain Gauge Data
Math Master, p. 213
Students read measures from pictures of rain
gauges, plot the data on a line plot, and then
answer questions about data landmarks.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 3. Key Activities
Students make a line plot to display and
analyze a data set of measurements in
fractions of a unit. Students use equivalent
fractions and operations of fractions
including addition and subtraction to solve
problems involving information presented in
line plots.
[Number and Numeration Goal 6 and
Operations and Computation Goal 4]
Study Link 7 10
Math Masters, p. 212
Students practice and maintain skills
through Study Link activities.
Materials
Math Journal 2, pp. 242 and 242A
Fraction Cards (Math Journal 2, Activity
Sheets 5–7)
Student Reference Book, pp. 119–121
(optional)
calculator Probability Meter Poster
(optional)
Advance Preparation
For Part 1, students need Fraction Cards (Math Journal 2, Activity Sheets 5–7), which were cut out
and used in Lesson 5-1.
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Unit 7
Exponents and Negative Numbers
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Getting Started
Mental Math and Reflexes
Math Message
Have students rename fractions as decimals and as
percents. Suggestions:
Sort the Fraction Cards to find the cards
3
1 _
1 _
equivalent to 0, _
4 , 2 , 4 , and 1. Use your slate to
record the number of cards in each group. Be ready
to justify your choices.
3 0.3; 30%
_
10
4
_
0.50; 50%
8
3
_ 0.75; 75%
4
1 0.3
_
⎯; 33.3
⎯%
3
2
_
0.40; 40%
5
1
_
0.125; 12.5%
8
3 0.375; 37.5%
_
8
2
_
0.6
⎯; 66.6
⎯%
3
4
_
1.00; 100%
4
Study Link 7 9 Follow-Up
Have partners compare answers and resolve
differences.
1 Teaching the Lesson
WHOLE-CLASS
ACTIVITY
▶ Math Message Follow-Up
(Math Journal 2, Activity Sheets 5–7)
Tell students that the number line will be used to create a line
plot displaying the results of the equivalent-fraction card sorting
activity.
Sorting Fraction Cards
Number of Cards
Draw a number line on the Class Data Pad, and label the
3 , and 1. Label the line plot Sorting Fraction
1, _
1, _
benchmarks 0, _
4 2 4
Cards, the x-axis Fractions, and the y-axis Number of Cards. Place
the title, Sorting Fraction Cards, above the number line, allowing
enough room for data to be added for a line plot.
0
1
4
1
2
3
4
1
Fractions
Ask students to share the results of their card sorting and justify
their choices as you record the results on the Class Data Pad.
Possible questions to ask include the following:
●
3, _
2, _
4,
How many cards show a fraction equivalent to 1? eight: _
2 3 4
5, _
6, _
8, _
10 , _
16
_
5 6 8 10 16
●
How do you know these fractions are all equivalent to 1?
Sample answers: The front of each of these cards is fully colored.
The numerator is equal to the denominator in each fraction.
3,
1 ? seven: _
1, _
2, _
How many cards show a fraction equivalent to _
2
2 4 6
5,_
6,_
8
4, _
_
●
8 10 12 16
●
How many cards show a fraction equivalent to
●
How many cards show a fraction equivalent to 0?
4
3?
_
4
4 8 12
3, _
6, _
9
three: _
4 8 12
0, _
0,_
0
three: _
5 10 16
Sorting Fraction Cards
Number of Cards
●
1?
How do you know these fractions are all equivalent to _
2
Sample answers: The denominator in each of these fractions is
twice the numerator. The number of spaces shaded blue on each
of these cards is equal to the number of spaces that are white.
3
1 ? three: _
1, _
2, _
How many cards show a fraction equivalent to _
●
X
X
X
X
X
X
X
X
X
X
X
X
X
0
1
4
1
2
X
X
X
3
4
X
X
X
X
X
X
X
X
1
Fractions
Lesson 7 10
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3, _
5 , and _
7 on the line plot.
1, _
Ask volunteers to label the fractions _
8 8 8
8
Ask students to explain their reasoning for the placement of each
fraction as it is recorded.
Number of Cards
Sorting Fraction Cards
X
X
X
0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1
8
1
4
3
8
1
2
X
X
X
X
X
X
X
5
8
3
4
7
8
X
X
X
X
X
X
X
X
1
Have students continue to sort the Fraction Cards to find those
that are equivalent to the fractions for eighths that were just
added to the number line. Continue discussing students’ findings
as you complete the line plot. Ask:
●
How many cards did you find for each new fraction we marked
1 is equal to _
2,
on the number line? There are 2 cards for each: _
8
16
3 is equal to _
6,_
5 is equal to _
10 , and _
7 is equal to _
14 .
_
8
16 8
16
8
16
●
How can you use the line plot to find the total number of cards
sorted? Count all the Xs in the line plot.
Fractions
▶ Using a Line Plot to
WHOLE-CLASS
ACTIVITY
Analyze Data
(Student Reference Book, pp.119–121)
Refer students to Student Reference Book, pages 119–121 to review
data landmarks, if necessary.
Number of Cards
Sorting Fraction Cards
X
X
X
0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1
8
1
4
3
8
1
2
minimum
X
X
X
X
X
X
X
5
8
3
4
7
8
mean
median
Fractions
X
X
X
X
X
X
X
X
Have students use slates to record information about the data on
the Sorting Fraction Cards line plot. Ask students to share their
thinking as they analyze the data. As they determine the various
landmarks, label them on the line plot on the Class Data Pad.
●
Which number on the line plot has the most equivalent fractions?
1 whole, or 1 What do we call the landmark for the value or values
that occur with the greatest frequency in a set of data? mode
●
What is the maximum value in the set of data? 1 What is the
minimum value in the set of data? 0
●
What is the range of data displayed on the line plot? 1 How
did you find the range? I subtracted the minimum from the
maximum: 1 – 0 = 1.
1 How did you find the median? I started
What is the median? _
1
mode and
maximum
●
2
at each end and then worked toward the center until I found the
middle number.
592
Unit 7
●
How many cards do we have in our data set? 32
●
If the blue shading on the cards represents blue liquid in a
beaker, for how many beakers do we have data? 32
●
What landmark would tell us how much liquid each beaker
would have if the liquid were distributed equally among all the
beakers? mean
●
If you actually had these beakers of liquid, what would you
do to distribute the liquid equally among all beakers? Sample
answer: I’d pour liquid from the beakers with more liquid into
the beakers with less liquid until the liquid levels in all of the
beakers were equal.
●
How do you find the mean for a set of data? Sample answer:
Add all of the data values, and then divide the sum by the
number of data values.
Exponents and Negative Numbers
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Student Page
PARTNER
ACTIVITY
▶ Finding the Mean
Date
Time
LESSON
7 10
Line Plots and Data in Fractional Units
Use the data in the table below to create a line plot.
Ask students to work with a partner to find the sum of the data
1 Ask students to share their
values using various strategies. 18_
2
strategy for finding the sum.
K I N E S T H E T I C
Yuma, Arizona
3
2_
4
Alamosa, Colorado
1
7_
8
Las Vegas, Nevada
1
4_
4
Reno, Nevada
1
7_
2
Bishop, California
3
5_
4
Winslow, Arizona
3
7_
4
Bakersfield, California
3
5_
4
El Paso, Texas
3
7_
4
Phoenix, Arizona
1
7_
8
Winnemucca, Nevada
3
7_
4
City and State
Annual Rainfall (in.)
Place an X on the line plot below to represent the annual rainfall in each of the 10 driest
cities in the United States. Label the line plot with the mixed numbers for the data.
1.
Rainfall in the Driest U.S. Cities
Students who need a visual model to find the sum
of the fractions may benefit from using the Fraction Cards.
Have students match cards that together add to a sum
7
1
_
of 1 whole. For example, _
8 and 8 add to 1 whole. Using
1
this method, all cards except for one of the _
2 cards has a
“match” to make 1 whole.
Annual Rainfall (in.)
Source: National Climatic Data Center
Adjusting the Activity
A U D I T O R Y
Rainfall in the Driest U.S. Cities
City and State
T A C T I L E
+
Number
of
Cities
X
2 34 3
2
X
4 14
4
X
X X
X XX
7
71 8
7 18 2 7 34
X
X
5 34 6
5
Annual Rainfall (in.)
Now analyze the data from the table and line plot to answer the questions
about the annual rainfall in the 10 driest U.S. cities.
V I S U A L
Students then use a calculator to find the mean of the set of data.
1 to a decimal and then use the calculator
Students may convert 18_
2
to divide the sum by 32 to find the mean. Ask students to round
the quotient in the calculator display to the nearest hundredth.
18.5 / 32 = 0.578125, or about 0.58 Ask:
●
Between which two fractions on your line plot does 0.58 fall?
5
1 and _
Between _
2
8
●
Which fraction on your line plot is 0.58 closest to? How do
5 because _
5 =
you know? Sample answer: 0.58 is closest to _
8
8
0.625, and 0.625 - 0.58 = 0.045. This is less than the distance
between 0.58 and 0.5, which is 0.08.
2_34
2.
What is the minimum amount of annual rainfall?
3.
What is the range of annual rainfall?
4.
What is the mode of annual rainfall?
5.
What is the median annual rainfall?
6.
What is the combined annual rainfall for the 10 driest cities?
7.
What is the mean annual rainfall for the 10 driest cities?
5
7_34
7_18
in.
in.
in.
in.
63_21
6.35 in.
in.
Math Journal 2, p. 242
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Students then use estimation to determine an approximate
placement on the line plot for the mean of the set of data.
Adjusting the Activity
Students who need a visual model to estimate the placement of the
mean on the line plot may benefit from referring to the Probability Meter Poster.
After determining the approximate location of the decimal on the decimal side
of the probability meter, students look on the opposite side of the meter to
determine the fraction that is closest to the one found on the line plot. Students
should notice that 0.58 is greater than 0.5 and less than 0.625, and that it is
closer to 0.625.
Student Page
Date
Time
LESSON
7 10
Line Plots and Data in Fractional Units
Rainfall Data
Day
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
cont.
The table below shows rainfall for 10 days in one of the driest cities. Organize
the data in a line plot. Then analyze the data to answer questions about the
plotted rainfall.
Rainfall (in.)
1
2
3
_
1
_
8
2
3
4
0
0
5
6
7
1
_
5
_
3
_
8
8
4
8
9
10
0
0
0
3 _
5 _
6
1 _
2 _
4 _
7
_
_
8. Label the approximate locations on the line plot for 8 , 8 , 8 , 8 , 8 , 8 , and 8 .
9.
Plot the rainfall data from the table.
Rainfall Data
▶ Displaying and Analyzing
PARTNER
ACTIVITY
Data on a Line Plot
Number
of
Days
(Math Journal 2, pp. 242 and 242A)
X
X
X
X
X
X
1
8
0
2
8
X
X
X
X
3
8
4
8
5
8
6
8
7
8
1
Rainfall (in.)
Students work with a partner. Have students solve the problems
on journal pages 242 and 242A involving plotting data points
on a line plot with fractional units and analyzing the data with
landmarks. Circulate and assist.
10.
Identify the following landmarks for the rainfall data:
0
a.
mode:
b.
range:
in.
c.
median:
d.
mean (as a decimal, rounded to the nearest hundredth inch):
6
3
_
_
8 or 4
in.
1
_
16
in.
0.24
in.
Math Journal 2, p. 242A
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Lesson 7 10
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Student Page
Date
Time
LESSON
7 10
1.
2.
2
º
$7,550 is shared equally among 25 people.
a.
Write an open number sentence to show how
much money each person gets.
+
7,550 ÷ 25 = m
b.
c.
3.
2 Ongoing Learning & Practice
Operations with Multidigit Whole Numbers and Decimals
Use the standard algorithm to complete the
multiplication problem shown at right.
0
7
5
4
828
1 0,3 5 0
1 1,1 7 8
4 º 207
50 º 207
▶ Operations with Multidigit
Whole Numbers and Decimals
Will a reasonable estimate for the quotient be
in the tens, hundreds, or thousands?
In the hundreds
Each person gets $ 302
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 242B)
.
In a store, Denny picks out jeans for $34.98 and a shirt for $16.49. He has $50 with him.
a.
Does he have enough money to buy the jeans and shirt?
b.
If not, how much more money does he need?
4. a.
no
$1.47
Students practice solving problems involving operations with
multidigit whole numbers and decimals.
The correct digits for the product are given. Write the decimal point in the product
without actually multiplying.
.
0.98 ∗ 39.39 = 3 8 6 0 2 2
b.
Explain how you decided where to place the decimal point.
Sample answer: 0.98 is almost 1, so I knew that the
product would be close to 39.
5. a.
▶ Math Boxes 7 10
Sample answer: The shading
shows 13 groups of 0.05 in 0.65.
b.
INDEPENDENT
ACTIVITY
Explain how you could use the shading in the grid to find
the quotient 0.65 ÷ 0.05.
(Math Journal 2, p. 243)
What whole number division problem has the same quotient?
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 7-7. The skills in Problem 6
previews Unit 8.
Sample answer: 65 ÷ 5
Math Journal 2, p. 242B
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Math Boxes
Problem 3
Ongoing Assessment
Recognizing Student Achievement
Use Math Boxes, Problem 3 to assess students’ ability to add fractions with unlike
denominators and to use benchmarks to compare fractions. Students are making
3
1
_
adequate progress if they can compare the fraction _
8 to 2 and find the sum of the
1
two fractions. Some students may be able to compare the fraction to _
4.
[Number and Numeration Goal 6 and Operations and Computation Goal 4]
Student Page
Date
Time
LESSON
Math Boxes
7 10
1.
Write the following number in
standard notation.
2.
Nine billion, one hundred two million,
three thousand, sixty-two
Fill in the blanks.
8
a.
(8 ∗ 7) + (8 ∗ 4) =
b.
23 ∗ (
–
)=
(23 ∗ 3.2) – (23 ∗ 2)
9,102,003,062
∗ (7 + 4)
3.2 2
c.
6
d.
(9 ∗
9
∗ (12 + 21) = (6 ∗ 12) + (6 ∗ 21)
11 ) – (9 ∗ 3
)=
∗ (11 – 3)
5
3.
3
Shade _
8 of the fraction stick.
a.
b.
219
4.
3 _
5
1 _
_
a. 4 , 4 , 4 ,
less
Is this more or less than _? more
1
Is this more or less than _
2?
3
_
c. 8
7
_
1
+_
2 =
Write the next two numbers in
each pattern.
1
4
8
4
6, 12, 24,
c.
–16, –13, –10,
A large jar of drink mix holds 1.75 kg.
How much drink mix will 12 jars of the
same size hold?
21 kg
,
–7
56
_
5
66 67
5.
4
,
48
b.
28
7 _
14 _
_
d. 5 , 5 , 5 ,
9
_
7
_
96
–4
,
112
_
,
5
230
6.
36 stamps per package. How many in . . .
27 stamps
30 stamps
_ of a package? 8 stamps
_ of a package? 21 stamps
_ of a package? 24 stamps
3
_
a. 4
of a package?
5
_
b. 6
of a package?
2
c. 9
7
d. 12
2
e. 3
38–40
75
Math Journal 2, p. 243
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Unit 7
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Exponents and Negative Numbers
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Study Link Master
INDEPENDENT
ACTIVITY
▶ Study Link 7 10
Name
STUDY LINK
7 10
(Math Masters, p. 212)
Date
Scouting for Insects
Some insects are harmful to
farmers’ crops. The insects listed
in this table are harmful to alfalfa
crops. Farmers scout their crops
and randomly collect sample plants.
They regularly observe the plants
and gather data to determine if the
insect population is growing or
remaining stable.
Home Connection Students practice making line plots
with fractional increments using insect data.
Time
Type of Insect
Average Length
of Insect (in.)
Number of
Insects
_3
8
4
Alfalfa Weevil
Larvae
1
1_4
Fall Armyworm
3
4
_1
8
_1
8
Pea Aphid
The table shows the result of
one farmer’s insect scouting.
1
_1
Meadow Spittlebug
Potato Leafhopper
6
6
Plot and label the lengths of the insects from the scouting sample on the
line plot below. Use the line plot to find the following data landmarks:
_1
3 Differentiation Options
8
1.
Minimum insect length
3.
Range of insect lengths
5.
Mean insect length
_1
in.
1_1
8
4
in.
2.
Maximum insect length
4.
Median insect length
1_14
_1
8
in.
in.
in.
Insect Lengths
SMALL-GROUP
ACTIVITY
READINESS
Number
of
Insects
5–15 Min
▶ Identifying Fractions on a
Number Line
(Math Masters, p. 211)
0
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
1
8
1
4
3
8
X
1
2
3
4
1 12
1 14
1
Average Length (in.)
Students label fractions on number lines.
Math Masters, p. 212
SMALL-GROUP
ACTIVITY
EXTRA PRACTICE
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5–15 Min
▶ Plotting Rain Gauge Data
(Math Masters, p. 213)
Students use rain gauge data to practice creating a line plot
with fractional increments and then answer questions about the
landmarks of the data set.
Teaching Master
Name
Date
LESSON
Teaching Master
Time
Name
Identifying Fractions on a Number Line
7 10
LESSON
7 10
Date
Time
Plotting Rain Gauge Data
Label each number line with the correct fractions.
in.
3
1.
0
1
3
1
2
3
X
2
0
1
2
Rainfall (in.)
1
3
2.
0
1
5
2
5
3
5
1
4
5
Example: Read the rain gauge pictured above and place an X on
the line plot to show how much rain has been collected.
1.
3.
0
4.
Draw and label the following points on this number line. The first one is done
for you.
2
A: 1_4
1
B: _4
B C
0
5.
Read each rain gauge to find out how much rain fell each day.
Write the amount of rain on the line below the gauge.
1
1 2 3 4 5 6 7
8 8 8 8 8 8 8
1
4
1
4
4
A
1 24
4
C: _4
8
D: _4
8
4
1 12
5
2
in.
3
Wed
in.
3
3
Thu
Fri
Sat
in.
in.
in.
3
3
3
2
2
2
2
2
2
2
1
1
1
1
1
1
1
2
4
2.
Jay Kay Mae
3
4
Tue
in.
3
_1
2 343
3
Jay, Kay, and Mae are in a 3-mile walk-a-thon. So far, Jay has walked _4 mi,
5
1
Kay has walked 1_2 mi, and Mae has walked _2 mi. Draw and label points on
the number line below to show their approximate locations.
0
Mon
in.
E: 2_34
D E
2
Sun
3.
3
_1
in.
Use the number line
to make a line plot
recording daily rainfall
for 1 week. Label the
tick marks on the
number line. Place an
X to represent each
rain amount.
4
in.
1_12 in. 0
_1
in.
4
_1
in.
4
_1
in.
2
in.
Daily Rainfall
X
X X
X X X
Number
of
Days
0
1
4
1
2
X
3
4
1
1 14 1 12 1 34
2
Rainfall (in.)
Analyze the rain gauge data to answer the questions below.
_1
a. What is the mode amount of rain that fell each day? 4 in.
_1
2
b. What is the range of the rainfall during the week?
in.
1
Math Masters, p. 211
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Math Masters, p. 213
2/25/11 9:20 AM
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Lesson 7 10
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3/21/11 1:20 PM
Name
Date
LESSON
7 10
Time
Identifying Fractions on a Number Line
Label each number line with the correct fractions.
1.
0
1
0
1
0
1
2.
3.
4.
Draw and label the following points on this number line. The first one is done
for you.
2
A: 1_4
1
B: _4
4
C: _4
8
D: _4
E: 2_34
Copyright © Wright Group/McGraw-Hill
A
0
5.
1
1 24
2
3
4
3
Jay, Kay, and Mae are in a 3-mile walk-a-thon. So far, Jay has walked _4 mi,
5
1
Kay has walked 1_2 mi, and Mae has walked _2 mi. Draw and label points on
the number line below to show their approximate locations.
0
3
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Name
STUDY LINK
7 10
Date
Time
Scouting for Insects
Some insects are harmful to
farmers’ crops. The insects listed
in this table are harmful to alfalfa
crops. Farmers scout their crops
and randomly collect sample plants.
They regularly observe the plants
and gather data to determine if the
insect population is growing or
remaining stable.
Type of Insect
Average Length
of Insect (in.)
Number of
Insects
_3
8
4
1
1_4
1
Alfalfa Weevil
Larvae
Fall Armyworm
_1
Meadow Spittlebug
4
_1
8
_1
8
Pea Aphid
The table shows the result of
one farmer’s insect scouting.
Potato Leafhopper
3
6
6
Plot and label the lengths of the insects from the scouting sample on the
line plot below. Use the line plot to find the following data landmarks:
1.
Minimum insect length
3.
Range of insect lengths
5.
Mean insect length
in.
in.
2.
Maximum insect length
4.
Median insect length
in.
in.
in.
Insect Lengths
Copyright © Wright Group/McGraw-Hill
Number
of
Insects
0
1
2
3
4
1
1 12
Average Length (in.)
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Name
Date
LESSON
7 10
Time
Plotting Rain Gauge Data
in.
3
2
0
1
2
Rainfall (in.)
1
3
Example: Read the rain gauge pictured above and place an X on
the line plot to show how much rain has been collected.
1.
Read each rain gauge to find out how much rain fell each day.
Write the amount of rain on the line below the gauge.
Sun
Mon
Tue
in.
in.
in.
3
Copyright © Wright Group/McGraw-Hill
3.
in.
3
3
Thu
Fri
Sat
in.
in.
in.
3
3
3
2
2
2
2
2
2
2
1
1
1
1
1
1
1
in.
2.
3
Wed
Use the number line
to make a line plot
recording daily rainfall
for 1 week. Label the
tick marks on the
number line. Place an
X to represent each
rain amount.
in.
in.
in.
in.
in.
in.
Daily Rainfall
Number
of
Days
0
1
2
Rainfall (in.)
Analyze the rain gauge data to answer the questions below.
a.
What is the mode amount of rain that fell each day?
b.
What is the range of the rainfall during the week?
in.
in.
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