Mystery Plots
Objective To provide experiences with data presented
in line plots and stem-and-leaf plots.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Interpret line plots and stem-and-leaf plots. [Data and Chance Goal 2]
• Use landmarks to identify data sets. [Data and Chance Goal 2]
• Use landmarks to draw conclusions about
data sets. [Data and Chance Goal 2]
Key Activities
Students interpret and then match the data
in line and stem-and-leaf plots to given data
descriptions.
Ongoing Assessment:
Informing Instruction See page 396.
Ongoing Assessment:
Recognizing Student Achievement
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Finish First
Math Journal 1, pp. 170 and 171
per partnership: 4 each of number
cards 4–8 (from the Everything Math
Deck, if available)
Students continue to collect data by
playing Finish First.
Math Boxes 6 4
Math Journal 1, p. 179
Students practice and maintain skills
through Math Box problems.
Study Link 6 4
Math Masters, p. 164
Students practice and maintain skills
through Study Link activities.
Use journal page 176. Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Finding the Median
Math Masters, p. 429
scissors
Students explore finding the median using
a concrete model.
ENRICHMENT
Analyzing Spelling Test Scores
Math Masters, p. 166
Students find the median and the mean to
analyze their relationship to the data set.
EXTRA PRACTICE
Matching Mystery Plots
Math Masters, p. 165
Students practice matching line plots with
data descriptions.
[Data and Chance Goal 2]
Ongoing Assessment:
Informing Instruction See page 397.
Materials
Math Journal 1, pp. 176–178
Study Link 63
Math Masters, p. 163
slate calculator
Advance Preparation
For the Math Message, make several copies of Math Masters, page 163 and cut them in half. For the optional
Readiness activity in Part 3, cut Math Masters, page 429 (1-inch grid paper) into 1 inch by 9 inch strips.
Teacher’s Reference Manual, Grades 4–6 p. 169
Lesson 6 4
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Getting Started
Mental Math and Reflexes
Math Message
Use the following problems to practice rounding numbers. Students write
decimals from dictation then round the decimals to a specified place.
Suggestions:
Take a Math Message half-sheet of
paper. Use the stem-and-leaf plot to find
the landmarks.
Thirty-two and six hundredths to the nearest whole number 32.06; 32
Four and thirty-eight hundredths to the nearest tenth 4.38; 4.4
Seven and eighteen hundredths to the nearest whole number 7.18; 7
Seven and eighteen hundredths to the nearest tenth 7.18; 7.2
Eighty-six and fifty-five hundredths to the nearest ten 86.55; 90
Nine thousandths to the nearest hundredth 0.009; 0.01
Study Link 6 3
Follow-Up
Ask partners to compare their answers and
resolve any differences.
1 Teaching the Lesson
Unit: Inches
Stems
▶ Math Message Follow-Up
Leaves
(10s)
(1s)
(Math Masters, p. 163)
4
4 7
5
0 0 6 8
6
1 3 5
Ask volunteers to name the nine data items shown in the
stem-and-leaf plot. List the numbers in order on the board. 44, 47,
50, 50, 56, 58, 61, 63, and 65 Ask students to identify the
minimum 44 in., maximum 65 in., range 21 in., median 56 in.,
and mode 50 in. Circle and label these numbers in the data list.
Stem-and-leaf plot for the Math Message,
with leaves in numerical order
Draw a second version of the stem-and-leaf plot by rewriting each
row of leaves in numerical order. (See margin.) Ask students
which version of the stem-and-leaf plot makes it easier to find the
landmarks and why. The second version because data is ordered.
Teaching Master
Name
Date
Time
Math Message
LESSON
64
䉬
Ongoing Assessment: Informing Instruction
Find the minimum, maximum, range, mode, and median for this stem-and-leaf plot.
Unit: inches
Stems
(10s)
Leaves
(1s)
4
4 7
5
0 8 6 0
6
1 5 3
Watch for students who have difficulty finding the median. Have them write the
ordered data list from the board and cross off number pairs, one at each end,
until they reach the middle number. This is the median. Then have them copy
the second version of the stem-and-leaf plot and cross off pairs of leaves in the
same way, by crossing off one leaf from the top and one leaf from the bottom, to
identify the median.
44 in.
maximum 65 in.
range 21 in.
mode 50 in.
median 56 in.
minimum
Name
Date
Time
Math Message
LESSON
64
䉬
▶ Identifying Mystery
Find the minimum, maximum, range, mode, and median for this stem-and-leaf plot.
Unit: inches
Stems
(10s)
Line Plots
Leaves
(1s)
4
4 7
5
0 8 6 0
6
1 5 3
maximum
range
mode
median
Math Masters, p. 163
Unit 6
PARTNER
ACTIVITY
PROBLEM
PRO
P
RO
R
OB
BLE
BL
L
LE
LEM
EM
SOLVING
SO
S
OL
O
L
LV
VIN
V
ING
(Math Journal 1, pp. 176 and 177)
minimum
396
WHOLE-CLASS
DISCUSSION
163
Assign partners to complete journal pages 176 and 177 by
matching the four sets of described data with the appropriate line
plot. Emphasize that students are looking for the matches that
make the most sense. Tell them that no plot is used more than
once, and one of the plots is not used at all. Circulate and assist.
Using Data; Addition and Subtraction of Fractions
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Student Page
Date
After ten to fifteen minutes, gather the class and discuss
the answers:
LESSON
6 4
䉬
Data Set 1, hours of TV watched, is represented by Plot #2.
Data Set 2, ages of younger siblings, is represented by Plot #5.
None of the other plots could describe Data Sets 1 or 2 because
the numbers in those other plots are too large.
If Plot #5 represented TV hours, then more than half of the
students watched TV for 5 or more hours the previous night.
That’s possible, but unlikely. However, Plot #5 could represent
hours on a nonschool day or when there is a significant national or
international event, such as the Olympics.
If Plot #2 represented sibling ages, then no fifth grader would
have a sibling aged 7 through 10. That’s possible, but unlikely.
Data Set 3, heights, is represented by Plot #1.
Time
Mystery Plots
There are five line plots on page 177. Each plot shows a different set of data about a
fifth-grade class.
Match each of the following four data set descriptions with one of the five plots. Then
fill in the unit for each matched graph on page 177.
1.
The number of hours of TV each fifth grader watched last night
2.
The ages of the younger brothers and sisters of the fifth graders
Plot
3.
The heights, in inches, of some fifth graders
Plot
#2
#5
#1
4.
The ages of some fifth graders’ grandmothers
Plot
#3
Plot
夹
5.
Explain how you selected the line plot for Data Set 4.
Sample answer: Plot #1 and Plot #3 show reasonable
numbers for grandmothers’ ages. But Plot #3 shows
numbers in the 70s and 80s and is more reasonable for
showing grandmothers’ ages.
夹
6.
Tell why you think the other line plots are not correct for Data Set 4.
Sample answer: Some or all of the numbers in Plots
#2, #4, and #5 are too small to represent ages of fifth
graders’ grandmothers. If Plot #3 represents fifth graders’
heights, then 6 of them would be taller than 6 ft. So Plot #1
represents heights, which means Plot #3 must represent
grandmothers’ ages.
Data Set 4, ages of grandmothers, is represented by Plot #3.
Plot #3 cannot represent heights because the largest numbers are
too large. (Some students would be nearly 7 feet tall!) It does,
however, show a reasonable range for grandmothers’ ages.
Math Journal 1, p. 176
Plot #4 does not represent any of the data described on journal
page 176. Ask students to describe any data that could be
represented by Plot #4. Sample answers: Ages of the students’
mothers; average time in minutes spent on homework each night
Ongoing Assessment:
Recognizing Student Achievement
Journal page 176
Problems
5 and 6
Use journal page 176, Problems 5 and 6 to assess students’ facility with
interpreting data displayed in line plots. Students are making adequate progress
if their writing demonstrates an understanding of the data’s meanings in relation
to data descriptions. Some students may refer to data landmarks in their
explanations.
[Data and Chance Goal 2]
Student Page
Date
LESSON
6 4
䉬
Plot #1
▶ Identifying Mystery
PARTNER
ACTIVITY
Stem-and-Leaf Plots
Time
Mystery Plots
inches
Unit:
52
53
54
x
x
x
x
x
x
x
x
x
x
x
Plot #3
55
56
57
58
59
60
61
62
66
x
x
x
0
1
2
3
4
5
6
x
x
x x
x x x
years
26
x
x
x
52
54
56
58
60
x
x
62
64
66
68
70
72
x
x
x
74
76
x x
x
80
82
78
NA
Unit:
x x
28
30
32
x
x
x
x x x
x
x
x x x
x
34
38
42
36
40
44
46
x
x
48
50
x
52
54
years
Unit:
x
0
65
x
x
x
Plot #5
64
x
x
x
x
x
x
Unit:
Ongoing Assessment: Informing Instruction
63
x
x
x
x
x
x
x
Plot #4
x
x
x
x
x
x
50
Watch for students who have difficulty reading the leaves as separate numbers
in the stem-and-leaf plots. Have them list the numbers from the plot, use the list
to help them answer the questions, and verify their selection of the median.
x
x
x
hours
Unit:
(Math Journal 1, p. 178)
In this activity, similar to the previous one, students match data
with stem-and-leaf plots instead of line plots. Students identify a
data set that reasonably represents arm reach and then a data set
for standing jump distances.
x
x
Plot #2
continued
1
x
x
x
2
3
4
x
x
x
x
x
x
x
x
5
6
7
8
x
9
10
Math Journal 1, p. 177
Lesson 6 4
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Student Page
Date
Time
LESSON
Most students will correctly identify Plot #1 as standing-jump
distance and Plot #2 as arm reach. Expect a variety of
explanations.
Reaching and Jumping
6 4
䉬
Some fifth-grade students measured
how far they could reach and jump.
Each student stood with legs together,
feet flat on the floor, and one arm
stretched up as high as possible.
Arm reach was then measured
from top fingertip to floor.
arm
reach
Examples:
The smallest number in Plot #2 is in the 60s. That’s more than
5 feet, and many kids can’t jump that far. So Plot #2 must be
arm reach.
In the standing jump, each student
stood with knees bent and then
jumped forward as far as possible.
The distance was then measured from
the starting line to the point closest to
where the student’s heels came down.
The smallest numbers in Plot #1 are in the 40s. Four feet is
48 in., so the smallest numbers are about 4 ft. Those numbers
are too small to be arm reaches.
jump
distance
The students made stem-and-leaf plots of the results.
Which stem-and-leaf plot below shows arm reach?
1. a.
Plot
What is the median arm reach?
b.
Which stem-and-leaf plot below shows standing-jump distances? Plot
2. a.
What is the median standing-jump distance?
b.
Plot #1
Unit: Inches
Stems
(10s)
#2
74
#1
57
I just held my arm up, and I found that I can reach about
15 in. above the top of my head. If you take 15 away from each
number in Plot #2, you get numbers that are possible fifth
graders’ heights in inches. So Plot #2 is arm reach.
in.
in.
Plot #2
Unit: Inches
Leaves
(1s)
Stems
(10s)
Leaves
(1s)
4
4 6 8
6
7
5
003345677889
7
0122223344666899
6
001338
8
0347
2 Ongoing Learning & Practice
Math Journal 1, p. 178
▶ Playing Finish First
PARTNER
ACTIVITY
(Math Journal 1, pp. 170 and 171)
Partners continue to collect data by playing Finish First.
They record their results on journal page 171 and on the
classroom tally sheet. For detailed instructions, see Lesson 6-2.
NOTE Remind students that the game data will be used in Lesson 6-6, so they
must play their designated number of games by that time.
▶ Math Boxes 6 4
Student Page
Date
Math Boxes
6 4
䉬
3.
(Math Journal 1, p. 179)
Time
LESSON
1.
Solve.
Solution
a.
8 ⴱ d ⫽ 80
d ⫽ 10
b.
5,500 ⫽ 55 ⴱ t
t ⫽ 100
c.
r ⫺ 79 ⫽ 180
r ⫽ 259
d.
t/9⫽7
t ⫽ 63
e.
217 ⫹ m ⫽ 300
m ⫽ 83
2.
218 219
222
Write a 9-digit numeral with
6
1
8
9
4
5
3
in
in
in
in
in
in
in
4.
the thousands place,
the hundreds place,
the ones place,
the thousandths place,
the hundred-thousands place,
the tenths place, and
all other places.
4 3 6
1 3 8
,
.
Write the numeral in words.
96 R2
a.
386 ⫼ 4 ➝
b.
673 ⫼ 9 ➝
c.
68 ⴱ 50 ⫽
3,400
d.
299 ⴱ 15 ⫽
4,485
e.
295 ⫼ 4 ➝
74 R7
Writing/Reasoning Have students respond to the
following: Explain your method for finding the savings
1 , so I
in Problem 5. Sample answer: I know that 20% is _
5
divided each regular price by 5 to find the savings amount.
73 R3
21
Complete the table.
Standard Notation
Exponential Notation
100,000
1,000,000,000
105
109
106
104
1,000,000
10,000
10,000,000
5 3 9
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 6-2. The skill in Problem 4 previews
Unit 7 content.
Multiply or divide mentally.
▶ Study Link 6 4
107
four hundred thirty-six thousand,
one hundred thirty-eight, and five
hundred thirty-nine thousandths
INDEPENDENT
ACTIVITY
(Math Masters, p. 164)
5
4 28
5.
INDEPENDENT
ACTIVITY
1
4 ᎏᎏ
2
A store is giving a 20% discount on all items. 6. Nigel has 2 dogs. One dog eats
pounds
1
Find how much is saved on each item.
of food each week, and the other eats 2ᎏᎏ
8
pounds.
Regular Price
Savings
5
How
much
do
they
$45
$9
ᎏᎏ
8 lb
eat in one week?
$5.80
$1.16
Home Connection Students match descriptions of data
sets with line plots.
6
$320
$93.75
$64
$18.75
51
70
Math Journal 1, p. 179
398
Unit 6
Using Data; Addition and Subtraction of Fractions
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Study Link Master
Name
3 Differentiation Options
Date
Time
How Much Do Students Spend?
STUDY LINK
64
䉬
A fifth-grade class collected data about class spending per
month on various items. Below are some of the results.
117 118
䉬 A median amount of $6 per month was spent for books and magazines.
READINESS
▶ Finding the Median
SMALL-GROUP
ACTIVITY
15–30 Min
䉬 A median amount of $10 per month was spent for tapes and CDs.
䉬 A median amount of $8 per month was spent for movie tickets.
The number-line plots below display the data. Match the plots with the
items: books and magazines, tapes and CDs, and movie tickets.
Tapes and CDs
1.
(Math Masters, p. 429)
To explore finding the median using a concrete model, have students
prepare and fold grid paper. Record the data set below on the board
or a transparency. Give students 1 in. by 9 in. strips of 1-inch grid
paper. They will use these strips to find the median of the data set.
1
2.
2
3
4
x
x
1
x
6
7
x
x
x
x
x
9
10
11
12
13
14
15
16
12
13
14
15
16
12
13
14
15
16
8
x
2
3
x
x
x
x
x
x
x
x
x
4
5
6
7
8
9
10
11
x
x
x
x
x
x
x
x
9
10
11
x
Movie tickets
3.
Have students complete the following steps:
1
2. Record the ordered numbers on the grid paper. Write one
number in each cell, left-to-right. Cut off any cells that do not
contain a value.
x
x
x
x
x
Books and magazines
Spelling Scores: 100, 83, 94, 93, 85, 70, 96, 94
1. Write the numbers in the data set in order from smallest to
largest on scrap paper.
5
x
x
2
3
4
x
x
x
x
x
x
x
x
x
5
6
7
8
Practice
4.
119 ⴱ 47 6.
9冄5
苶,2
苶4
苶1
苶∑
5,593
5.
9,402
7,137
16,539
582R3
7.
9,487 ⴱ 8 75,896
Math Masters, p. 164
3. Fold the grid-paper strip in half.
More Mystery Plots
4. Find the median. Explain that if a data set has an odd number
of values, the number in the cell with the folded line is the
median. If a data set has an even number of values, there will
be two numbers separated by the folded line. The number
halfway between these two numbers is the median.
When they have finished, ask students to describe how this
strategy uses the definition of median. The median is the middle
value in a data set. By folding the grid-paper strip in half, the fold
is in the middle and identifies the middle of the data set.
Plot A
Unit: minutes
Plot B
Unit: books
Plot C
Unit: days
Plot D
Unit: years
Math Masters, p. 165
Teaching Master
ENRICHMENT
▶ Analyzing Spelling Test Scores
SMALL-GROUP
ACTIVITY
Name
LESSON
64
䉬
15–30 Min
(Math Masters, p. 166)
Date
Time
Making the Grade
Ms. Hallaran has her students collect their spelling test scores for 9 weeks. She asks
students if they want her to record the median or mean of their scores. For each set of
scores below, which landmark should they choose?
After finding the landmarks for each student, circle the better score.
To apply students’ understanding of the relationship between the
median and the mean, have students analyze data to describe
which is greater without actually finding the landmarks. When
students have finished the Math Masters page, discuss
their solutions.
1.
Eliezer’s scores: 0, 70, 95, 85, 90, 70, 95, 100, 80
median
2.
median
3.
EXTRA PRACTICE
▶ Matching Mystery Plots
INDEPENDENT
ACTIVITY
80
mean
About 88
80
mean
About 73
80
mean
About 87
How can they decide which landmark to choose without finding the median
and the mean?
Sample answer: If a student’s scores are all
close to being the same, then the mean is
the better choice. If there is one score that
is much lower or higher than the other scores,
then the median is the better choice.
15–30 Min
(Math Masters, p. 165)
Students match line plots to data descriptions. When they are
finished, ask students to share their reasoning.
About 76
Kiyada’s scores: 75, 80, 95, 80, 100, 80, 95, 100, 80
median
5.
mean
Charlene’s scores: 80, 80, 70, 65, 60, 80, 60, 80, 80
median
4.
85
Miles’ scores: 100, 80, 80, 80, 95, 80, 95, 100, 80
6.
An outlier is a data point that is located far from the rest of the data.
What score is the outlier in the spelling score data?
Eliezer’s score of 0
Math Masters, p. 166
Lesson 6 4
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