Lesson
7 Decimal Numbers
Problem Solving:
Drawing Box-and-Whisker Plots
Lesson7 SkillsMaintenance
Lesson Planner
Vocabulary Development
Date
Unit 1
Name
SkillsMaintenance
FractionOperations
rational number
Activity1
Solvethemixoffractionoperations.Remembertolookcarefullyto
determinethecorrectstrategy.Simplifytheanswersifnecessary.
Skills Maintenance
1.
3 2
5+9
2.
4 3
8·5
Building Number Concepts:
3.
5 2
6·3
Decimal Numbers
4.
5 1
7÷7
5.
2 1
3−4
6.
2 1
3÷2
Fraction Operations
Students learn to convert fractions to
decimal numbers.
37
45
12
40
10
18
35
7
5
12
4
3
Simplify
Simplify
Simplify
Simplify
Simplify
Simplify
37
45
3
10
5
9
5
5
12
11
3
Objective
Students will convert fractions to
decimal numbers.
Problem Solving:
rawing Box-and-Whisker
D
Plots
Students learn a four-step method for
drawing box-and-whisker plots.
Objective
Students will draw box-and-whisker plots.
Unit1•Lesson7
17
Homework
Students convert fractions to decimal
numbers, answer questions about decimal
numbers, and answer questions about data.
In Distributed Practice, students perform
operations with whole numbers and fractions.
Skills Maintenance
Fraction Operations
(Interactive Text, page 17)
Activity 1
Students add, subtract, multiply, and divide fractions
and simplify the answers.
Unit 1 • Lesson 7 71
Lesson 7
Lesson
Building Number Concepts:
7
Decimal Numbers
Problem Solving:
Drawing Box-and-Whisker Plots
Decimal Numbers
Decimal Numbers
Vocabulary
How are decimal numbers like fractions?
How are decimal numbers like
fractions?
(Student Text, page 48)
1
4
1
2
3
4
0.25
0.5
0.75
Fraction
Connect to Prior Knowledge
Remind students that we have already worked
with fractions and decimal numbers on number
lines.
Decimal Number
Link to Today’s Concept
In today’s lesson, we look at how fractions and
decimal numbers both represent fractional
locations between the whole numbers. Explain to
students that they are both part of the system of
numbers we call rational numbers .
Decimal Number
Demonstrate
Engagement Strategy: Teacher Modeling
Demonstrate how we locate fractions and
decimal numbers on a number line in one of the
following ways:
: Use the mBook Teacher
Edition for Student Text, page 48. ​
Overhead Projector: Display
Transparency 6, and modify
as discussed.
Board: Draw the number line on the
board, and modify as discussed.
•Show the number line. Remind students
that fractions occur between two whole
numbers. Mark and label the positions of the
1
4
fractions 1
4 , 1 3 , and 2 5 . ​
•Mark and label the decimal numbers 0.25,
1.33, and 2.8 on the number line. Point out
that these are the same locations as the
fractions we just looked at. For example,
0.25 is another name for 1
4 . ​
72 Unit 1 • Lesson 7
rational number
We have learned a lot about fractions in this unit. We will now
focus on decimal numbers. Fractions and decimal numbers are
both rational numbers . These are numbers that can be written
as fractions. We can think about fractions and decimal numbers
as different names for the same location on the number line.
0
Fraction
Decimal Number
0
Fraction
0
1
3
2
3
0.33
0.67
1
1
1
5
2
5
3
5
4
5
0.2
0.4
0.6
0.8
1
We use decimal numbers because they are easier to work with
than fractions. Imagine if you had to add the following three
fractions together.
3
4
14
5 + 10 + 15
The answer, 58
30 , is a large fraction that is difficult to understand. We
know that it is bigger than 1 because 30
30 = 1. But how much bigger is it?
Understanding this problem is easier if we convert the fractions to
decimal numbers and then add them.
48
48
Unit 1 • Lesson 7
•Have students look at the problem
4
14
3
5 + 10 + 15 . Tell the students that the
answer is 58
30 .
•Point out that it is difficult to solve this problem
in its fraction form because we need to find the
least common denominator for 5, 10, and 15. If
we convert these numbers to decimal numbers,
the problem becomes easy to solve, as we see on
the next page. ​
Lesson 7
How do we convert fractions to
decimal numbers?
How do we convert fractions to
decimal numbers?
Example 1 shows how to convert fractions to decimal numbers and then
round them to the hundredths place.
Example 1
(Student Text, pages 49–50)
Convert the fractions to decimal numbers and solve the problem.
3
4
14
5 + 10 + 15
Demonstrate
•Turn to page 49 of the Student Text, and
direct students’ attention to Example 1 .
Point out that we convert the fraction to a
decimal number by dividing the fraction.
To get the decimal numbers, we divide the fractions.
0.6
5q3
Fractions
Decimal numbers
•Rewrite the fraction 35 as the division
0.4
10q4
0.93
15q14
3
5
+
4
10
+
14
15
=
58
30
0.6
+
0.4
+
0.93
=
1.93
When we convert fractions to decimal numbers, we change the fraction
into the base-10 system. Each place value for a decimal number is a
power of 10.
Thousandths
Hundredths
Tenths
problem 5q3.
•Convert all the fractions, then add them in
0.375
decimal number format.
3
8 = 8q3
•Have the students compare the decimal
Finally, it is important to remember that when we convert fractions into
decimal numbers, the numbers still have the same value or quantity.
The fraction and the decimal number are equivalent.
number, 1.93, to the fraction, 58
30 .
Ask:
Which number is easier to understand?
Listen for:
Unit 1 • Lesson 7
58
•I can tell 30
is greater than 1 because the
numerator
is larger than the denominator.
•It is hard to tell at a glance how much
greater the fraction is than 1.
•It’s easy to see at a glance that 1.93 is only
0.07 away from 2; so 1.93 is very close to 2.
•Point out that when we convert a fraction to
a decimal number, the decimal number is in
the base-10 system. Analyze with students
the conversion of 3
8 to a decimal number.
•Note that 38 is equivalent to 0.375. The digit
3 is in the tenths place, the digit 7 is in
the hundredths place, and the digit 5 is in
the thousandths place. Remind students
that fractions and decimal numbers are
equivalent.
49
49
Check for Understanding
Engagement Strategy: Pair/Share
Have students partner with another student. Have
one student convert the fraction 2
5 to a decimal
number (0.4). Have the other student convert 5
8
(0.625). Have pairs exchange their papers to check
each other’s work. When students finish, have pairs
volunteer to share their reasoning and answers.
Reinforce Understanding
If students need further practice, have them convert
the following fractions to decimal numbers:
3
5 (0.6)
3
4 (0.75)
Unit 1 • Lesson 7 73
Lesson 7
Lesson 7
Example 2
How do we convert fractions to
decimal numbers? (continued)
Use area models to show that 3
4 and 0.75 are equivalent.
3
4 = 4q3 = 0.75
Demonstrate
•Have students look at Example 2 on page
50 of the Student Text. Show students
visually that fractions and decimal numbers
are equivalent. It is important for students
to see this relationship.
Part
Whole
•Examine the area models for 34 and 0.75. In
3
4
0.75
3
4
75
100
Both fractions and decimal numbers are part-to-whole relationships.
both models, the same area of the shape is
shaded. When we shade 3 out of 4 parts of
a shape, it represents the same area as 75
out of 100.
The models show that 3
4 and 0.75 have the same area.
•If time allows, draw the two area models,
and superimpose one model over the top of
the other. Some students need this visual
demonstration to see that fractions and
decimal numbers are equivalent.
•Finally, have students summarize in their
own words the relationship between decimal
numbers and fractions.
Listen for:
•They are both rational numbers.
•They both represent part-to-whole
relationships.
•We can show any fraction and the
equivalent decimal number as a point on a
number line.
•Some students might give examples: 34 =
1
1
0.75, 41 = 0.25, 21 = 0.5, 10
= 0.1, 100
= 0.01.
•Tell students that they need to be able work
flexibly with both types of numbers. This
ability will help them as they move into
higher-level math.
74 Unit 1 • Lesson 7
Apply Skills
Turn to Interactive Text,
page 18.
50
50
Unit 1 • Lesson 7
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Lesson7 ApplySkills
Name
Apply Skills
Date
ApplySkills
DecimalNumbers
(Interactive Text, page 18)
Activity1
PlaceanXonthenumberlineintheapproximatelocationofeachofthe
decimalnumbers.Thenexplainwhyyouchosethelocation.
Have students turn to page 18 in the Interactive
Text and complete the activities.
1.
Where would you find 0.78?
1
4
0
1
2
3
4
1
2
3
4
X
1
Sample answer: 3 = 0.75 Since 0.78 is just a
4
Explain
little bigger than 0.75, I decided to put the X right next to
Activity 1
Students place an X on a number line to show the
location of a given decimal number. Then they
explain their reasoning.
it on the number line.
2.
Where would you find 0.10?
X
0
1
4
1
Sample answer: 1 = 0.25 Since 0.10 is just about
4
Explain
half of 0.25, I decided to put the X between it and 0 on
Activity 2
Students convert fractions to decimal numbers
and decimal numbers to fractions.
the number line.
Activity2
Convertthefractionstodecimalnumbersanddecimalnumbersto
fractions.Ifneeded,youmayuseacalculator.
Monitor students’ work as they complete the
activities.
1.
4.
Watch for:
3
5=
0.6
5
6=
0.833
2.
5.
1
10
3
4
= 0.10
= 0.75
3.
6.
1
4=
0.25
1
3
= 0.33
•Can students find the approximate location
of the decimal numbers on the number line?
•Can students explain their strategy for
placing the numbers on the number line
(e.g., 0.78 is near 0.75, which is the same as
3
3
4 ; you put 0.78 just a little to the right of 4
on the number line)?
•Can students convert fractions to decimal
18
Unit1•Lesson7
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the online
mBook Study Guide.
numbers without the use of a calculator
(e.g., students should recognize the common
1
3
conversions: 10
= 0.10, 1
4 = 0.25, 4 = 0.75,
1
1
3 = 0.33, 2 = 0.50)?
•If students use a calculator to convert, do
they understand how to use it (e.g., 3
5 is
converted by the computation 3 ÷ 5)?
•Do students use the concept of place value
to convert decimal numbers to fractions
1
(e.g., 0.10 means one tenth or 10
, or it could
10
mean ten hundredths, or 100
)?
Unit 1 • Lesson 7 75
Lesson 7
Lesson 7
Problem Solving: Drawing Box-and-Whisker Plots
How do we create box-and-whisker plots?
Problem Solving:
Drawing Box-and-Whisker Plots
How do we create box-and-whisker
plots?
(Student Text, pages 51–54)
Connect to Prior Knowledge
Begin by asking students to draw a blank boxand-whisker plot on the board. Have students
discuss how we use a box-and-whisker plot to
analyze data.
The method for creating box-and-whisker plots is simple. It involves
medians. Let’s look at another event at Sports Day—the high jump. Here
is how everyone did.
Student
Brittany
Joshua
Autumn
Marcus
Erica
Oscar
Ryan
Pablo
Amber
Tracey
Mikaela
Lamar
DeAnne
Seth
Paige
Height (in inches)
45
49
50
53
54
54
55
56
57
58
60
62
64
64
65
median = 56
Listen for:
•It helps us organize the data visually.
•You can find the min and max just by
looking at the plot.
•You can easily calculate the range, mean,
and median.
Link to Today’s Concept
In today’s lesson, students learn to create boxand-whisker plots on their own.
Demonstrate
•Have students look at the data on page 51
in the Student Text. Use these data to create
a box-and-whisker plot. The data is from
another event at Sports Day—the high jump.
•Have students look through the data for
all the students. Point out that the data
are arranged in numeric order from lowest
to highest jump. Make sure students
understand why the median is 56.
76 Unit 1 • Lesson 7
Unit 1 • Lesson 7
51
51
Lesson 7
We start with the median and divide the list into two groups. The first
group is the group below, or lower than, the median. The second group
is the group above, or higher than, the median. We find the median of
each of these groups.
Demonstrate
•Turn to page 52 of the Student Text, and
look at the data in the two tables. Point out
that to create a box-and-whisker plot, we
first organize the data. We start with the
median and divide the list into two groups.
•Have students look at the example where
the data are divided. The first group is
below the median, and the second group is
above the median. We then find the median
of both these groups, 53 for the first group
and 62 for the second group.
•Be sure students understand how we got
Student
Brittany
Joshua
Autumn
Marcus
Erica
Oscar
Ryan
Pablo
Group 1
Height (in inches)
45
49
50
53
54
54
55
56
Student
Amber
Tracey
Mikaela
Lamar
DeAnne
Seth
Paige
Group 2
Height (in inches)
57
58
60
62
64
64
65
min
median for group 1 (lower) = 53
median for the whole group = 56
min
median for group 2 (upper) = 62
max
each of the numbers in the illustration.
Explain to students that once we divide the
data, we are ready to draw the box.
52
52
Unit 1 • Lesson 7
Unit 1 • Lesson 7 77
Lesson 7
How do we create box-and-whisker
plots? (continued)
Demonstrate
•Next have students turn to page 53 of
the Student Text. There are four steps
for drawing the box-and-whisker plot. Go
through the steps as outlined.
Lesson 7
Now we are ready to draw the box-and-whisker plot. Follow these
four steps.
Steps for Drawing a Box-and-Whisker Plot
Step 1
Draw vertical lines for the min and the max.
45
min
65
max
STEP 2
Use the lower and upper median numbers to make the sides of the box.
Draw the rest of the box.
•Remind students that the whisker pointing
to the left represents the lowest 1
4 of the
data, and the whisker pointing to the
right represents the highest 1
4 of the data.
•Explain that in this example, the numbers
represent the different distances that the
students jumped.
Step 1
•Draw a number line that will contain all the
data. In this case, a number line from 45
to 65 will contain all the data. Show how to
draw vertical lines for the min at 45 and the
max at 65.
Step 2
•Show how to use the lower- and uppermedian numbers to make the sides of the
box. In this case, the median for the lower
group is at 53. Label 53 on the number line,
and draw one side of the box at 53. The
median for the upper group is at 62. Label
62 on the number line, and draw the other
side of the box at 62. Then draw the rest of
the box.
Step 3
•Show how to draw the horizontal lines that
connect the min and the max to the box.
78 Unit 1 • Lesson 7
45
min
53
62
65
max
Step 3
Draw horizontal lines that connect the min and the max to the box.
45
min
53
62
65
max
Step 4
Put a mark for the median of the entire group of numbers in the box.
45
min
53
62
65
max
Unit 1 • Lesson 7
53
53
Step 4
•Show how to put in the median for the entire
group of numbers in the box. The median for the
whole group is 56. Locate 56 on the number line,
and draw a mark at that location.
Lesson 7
Remember, the whisker on the left of the box contains the lowest 1
4 of
the numbers. The box represents the middle 1
2 of the numbers, and the
1
whisker on the right contains the highest 4 of numbers. In this example,
the numbers stand for different heights that students jumped.
Demonstrate
•Turn to page 54 of the Student Text. With
students, read the material that describes
how to use the box-and-whisker plot to
make sense of data.
Once we have the box-and-whisker plot, we can make sense of all the
high jumps.
• Ericajumped54inches.Sheisnearthebottomofthemiddlehalf
of numbers. She also isn’t that far below the median of 56.
• HerfriendDeAnnejumpedmuchhigher.Sheisnearthetopofthe
highest 1
4 of heights. DeAnne is well above the median.
•Go over each of the points, making sure that
• Finally,Pablojumped56inches.Heisnearthecenterofthe
middle group of numbers and right on the median.
students understand where the jumps that
Erica, DeAnne, and Pablo made are located
in the box-and-whisker plot.
•Have students use the box-and-whisker plot
to make statements about Autumn, Ryan,
and Seth.
Listen for:
•Autumn jumped 50 inches. Her jump is in
the lowest 41 .
•Ryan jumped 55 inches. His jump is in the
middle 21 .
•Seth jumped 64 inches. His jump is in the
highest 41 .
Check for Understanding
Engagement Strategy: Think, Think
Ask students to use the box-and-whisker plot to
make a statement about Amber. Tell students
that you will call on one of them to give a
statement. Tell them to think about the answer
and to listen for their name. Allow time for
students to write a statement. Then call on a
student by name.
Problem-Solving Activity
Turn to Interactive Text,
page 19.
54
54
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 7
Reinforce Understanding
If students need further practice, have them make
statements about the following jumpers:
Joshua (49 in, lower 41 )
Lamar (62 in, upper 41 median)
Listen for:
•Amber jumped 77 inches.
•Her jump is in the middle 21 of the data.
•Her jump is close to the median.
Unit 1 • Lesson 7 79
Lesson 7
Lesson7 Problem-SolvingActivity
Problem-Solving Activity
Problem-SolvingActivity
DrawingBox-and-WhiskerPlots
(Interactive Text, page 19)
IsabelMartinezistheAssistantPrincipalatViegaMiddleSchool.She
islookingoverattendancedata.Sheisparticularlyinterestedinone
classwhereanumberofstudentsareabsentonaregularbasis.Thetable
showsalistofdatafortheclassandthenumberofdaysthatstudents
wereabsentforSeptember,October,andNovember.Usethisinformation
andthebox-and-whiskerplottoanswerthequestions.
Have students turn to Interactive Text, page
19, and complete the activity. Students answer
questions about information in a table and a boxand-whisker plot.
0
1.
Watch for:
2.
•Can students tell if a data point is typical
or not?
•Can students identify data that are
not typical?
3.
3
Juan
0
Carmen
20
Sara
6
2
22
Hector
2
Jessica
4
Eva
1
Pedro
1
Sample answer: No, he is outside the box of typical
James
3
absenteeism.
Julie
4
Violeta
2
Carlos
2
4
6
8
10
12
14
16
18
20
22
24
Is Mica absent a typical amount of time? Explain your thinking
using the box-and-whisker plot.
Carlos thinks he has a much better attendance rate than the rest
of the students in his class. He has only been absent two times in
the first three months. He tells his teacher this, but she says, “No,
you’ve missed about the same amount as everyone else.” Explain
why the teacher is right using the box-and-whisker plot.
Marshall
5
Cristina
24
Rena
3
Cyndie
2
Sample answer: The box represents the most typical
Michael
0
pattern, and 2–5 absences is typical.
Adam
4
Alberto
2
Cara
6
Jennifer
3
Mica
4
Jana
5
What three students should the assistant principal bring into her
office? Explain why.
brought in because they have far more days absent
and fall on the far right of the plot.
ReinforceUnderstanding
Use the mBook Study Guide to review lesson concepts.
Unit 1 • Lesson 7
Amelia
Malena
2
Sample answer: Christina, Carmen, and Melina should be
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
Number
Student
of Days
Name
Absent
Luisa
median = 3
Monitor students’ work as they complete
this activity.
80 Date
Unit 1
Name
Unit1•Lesson7
19
Lesson 7
Homework
Activity 1
Homework
Go over the instructions for each activity on
pages 55–56 of the Student Text.
Convert the fractions to decimal numbers.
1.
1
2
4.
1
4
0.5
4
0.8
3.
2
3
0.67
6. 8
2. 5
0.25
5.
3
4
0.75
3
0.375
Activity 2
Select the best answer for each of the questions about decimal numbers.
place. b
1. The decimal number 0.35 has a 3 in the tenths place and a 5 in the
Activity 1
Students convert fractions to decimal numbers.
Activity 2
Students identify the best answer for a question
about decimal numbers.
(a) thousands
(b) hundredths
(c) thousandths
4
2. We can check that 5 = 0.8 by doing this computation on the calculator.
a
(a) 4 ÷ 5
(b) 4 + 5
(c) 4 · 5
3. The decimal number 0.87 is the same as what fraction?
(a)
(b)
(c)
c
8
7
87
10
87
100
4. What are the fraction/decimal number equivalents for “three hundredths”?
b
3
(a) 0.3 = 10
3
(b) 0.03 = 100
3
(c) 0.003 = 1,000
Unit 1 • Lesson 7
Unit 1 • Lesson 7 55
55
81
Lesson 7
Lesson 7
Homework
Activity 3
Look at the data. Imagine how it would look in a box-and-whisker plot. Answer
the questions about the data and how it would be arranged in the plot.
Homework
Data Set: 45, 34, 55, 87, 62, 79, 39, 75, 95
Go over the instructions for each activity on
page 56 of the Student Text.
1. What number represents the median of this data? Is this the same as or
different than the actual midpoint of the data? 62, different
3. What is the min?
Activity 3
5. What is the max?
95
Activity 4 • Distributed Practice
Solve.
1. 120 ÷ 12
10
2. 437 + 223
Activity 4 • Distributed Practice
3. 15 · 8
Students practice operations with whole numbers
and fractions.
3
4
+ 18
7
1
7.
5
11
1
2
8.
3
4
5.
6. 9 − 3
·
÷ 18
4
1
5
9
1
6
10.
56
56
−
Unit 1 • Lesson 7
660
120
4. 601 − 379
9. 5 ÷ 5
Unit 1 • Lesson 7
34 or 39
1
87 or 95
34
4. Write a number that falls in the upper 4 .
Students imagine data in a box-and-whisker plot
and answer questions about it.
82 1
2. Write a number that falls in the lower 4 .
7
8
4
9
5
22
6
4
7
18
222