Unit 9 - Professional Development

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Unit 9 - Professional Development
Unit 9
Common Core
How Long Can You Stand on
One Foot?
Mathematical Practices (MP)
Domains
• Number and Operations in Base Ten (NBT)
• Number and Operations – Fractions (NF)
• Measurement and Data (MD)
INVESTIG ATION 1
Comparing Balancing Data Day
1 1.1
Session
Balancing on One Foot
SESSION FOLLOW-UP
Daily Practice and
Homework
2
1.2
Common Core Adaptation
Common Core Standards
MP3, MP6, MP7
Family Letter: Make copies of C105–C106, Family Letter, as a 5.MD.2
replacement for M11–M12 Family Letter.
Mystery Balancers
SESSION FOLLOW-UP
Daily Practice and
Homework
Family Letter: Make copies of C107, Family Letter, as a
replacement for M13–M14 Family Letter.
1.3
5
Comparing Student and
Adult Data
1.4 Who Can Balance Longer
on One Foot?
1.5A Fractions on a Line Plot
See p. CC160.
6
1.6A End-of-Unit Assessment
3
4
CC158 See p. CC165.
MP3, MP6, MP7
5.MD.2
MP3, MP6, MP7
5.NBT.5, 5.NBT.6, 5.MD.2
MP3, MP6, MP7
5.NBT.5, 5.MD.2
MP7
5.NBT.5, 5.NBT.6, 5.NF.6,
5.MD.2
MP1, MP2, MP7
5.NBT.5, 5.NBT.6, 5.NF.6,
5.MD.2
UNIT 9 How Long Can You Stand on One Foot?
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INVESTIG ATION 2
Collecting Data from Experiments Skip this Investigation.
Day
2.1
2.2
2.3
2.4
2.5
2.6
Session
Assessment: Students’
Experiment Projects and
Designing an Experiment
Assessment: Analyzing
the Data
Collecting and
Representing Data from
Experiments
What Makes a Good
Representation?
Analyzing Experiment
Data
What Did You Find Out?
Common Core Adaptation
Common Core Standards
Common Core Adaptation
Common Core Standards
INVESTIG ATION 3
Fair and Unfair Games Skip this Investigation.
Day
3.3
Session
One-Half-Green Spinner
Experiment
Comparing Spinner
Experiments
Race to the Top
3.4
Designing a Fair Game
3.5
End-of-Unit Assessment
3.1
3.2
The End-of-Unit Assessment is now Session 1.6A.
Instructional Plan INV12_TE05_U09.indd 159
CC159
6/27/11 2:53 PM
session 1.5A
Fractions on a Line Plot
Math Focus Points
Making a line plot to display a data set of measurements
involving fractions
Using operations on fractions to solve problems involving
information given in line plots
Today’s Plan
Materials
activity
•Student Activity Book, pp. 17A–17B or
Grasshopper Lengths
C108–C109, Grasshopper Lengths Make
copies. (as needed)
50 Min Class Individuals
Discussion
•Student Activity Book, pp. 17A–17B or
Grasshopper Lengths
C108–C109 (completed)
10 Min Class
Session Follow-Up
•Student Activity Book, p. 17C or
Daily Practice
C110, Comparing Rainfall Data Make
copies. (as needed)
Student Math Handbook, pp. 81–88
•
Ten-Minute Math
Estimation and Number Sense: Closest Estimate Show Problems 7–9 on Estimation
and Number Sense: Closest Estimate (T86), one at a time. Give students approximately
30 seconds to look at the three possible estimates and determine which is the closest
to the actual answer. Have two or three students explain their reasoning for each
problem. Ask students:
• How did you break the numbers apart?
• How did you determine the magnitude of the answer?
• If you changed the numbers in the problem, how did you change them and why?
Also, ask if the closest estimate is greater than or less than the actual answer and how
students know.
CC160 Investigation 1 Comparing Balancing Data
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1 Activity 2 Discussion 3 Session Follow-Up Name
Date
How Long Can You Stand on One Foot?
AC TIVIT Y
50 Min
Grasshopper Lengths
class individuals
Grasshopper Lengths (page 1 of 2)
A scientist collected two types of grasshoppers and
recorded their lengths in the boxes below. Show the lengths
on the line plots.
Lengths of Clear-Winged Grasshoppers (inches)
Have students look at Student Activity Book page 17A or C108. Ask
them to tell in their own words what the boxes of data show. Then
ask them what they notice about these data that is different from
the balancing data. (These data contain fractions.)
1 1_4
3
_
4
1
1 1_4
1
1 3_8
1 1_4
1 1_2
7
_
8
1
_
2
1 3_8
1 1_8
5
_
8
1 1_8
3
_
4
Lengths of Two-Striped Grasshoppers (inches)
5
_
8
1 3_8
0
2 1_4
1 7_8
3
_
4
1 7_8
1
1 3_4
1 1_2
1 1_2
2
2 3_8
1 3_4
1 3_8
2
1 1_4
1
1 3_4
3
Lengths of Clear-Winged Grasshoppers (inches)
On the board, draw a number line like those on page 17A
or C108. Ask students how they can show halves, fourths,
and eighths on the number line.
0
1
2
3
Lengths of Two-Striped Grasshoppers (inches)
© Pearson Education 5
Students might say:
“To show half inches, you have to divide the
space between the numbers in half. Then
divide each of those spaces in half again
to show fourths. Then divide those spaces
in half again to show eighths.”
1 7_8
Session 1.5A
Unit 9
17A
▲ Student Activity Book, Unit 9, p. 17A;
Resource Masters, C108
INV12_SE05_U9.indd 1
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“I’d just do eighths right away. Then every
two eighths is a fourth, and four eighths is
a half.”
Have volunteers draw tick marks on the number line to indicate
halves, fourths, and eighths, and label the halves.
You’re going to represent the data about the lengths of the
grasshoppers on two line plots. Let’s do the first two lengths for
the clear-winged grasshopper together.
Call on volunteers to mark the first two lengths, 1​ _14 ​inches and 1​ _78 ​
inches, on the line plot.
x
0
1
2
1
x
1 12
2
2 12
3
Lengths of Clear-Winged Grasshoppers (inches)
Session 1.5A Fractions on a Line Plot INV12_TE05_U09_S1.5A.indd 161
CC161
6/27/11 2:56 PM
1 Activity 2 Discussion 3 Session Follow-Up Name
Give students 10–15 minutes to mark the data on the line plots on
Student Activity Book page 17A or C108.
Date
How Long Can You Stand on One Foot?
Grasshopper Lengths (page 2 of 2)
Use the information in the line plots on the previous page to solve the
following problems. Show your work.
Then discuss how the two data sets compare.
1. a. What is the range of the clear-winged grasshopper
data?
How do the lengths of the clear-winged grasshoppers compare to
the lengths of the two-striped grasshoppers? Think about the
aspects of the standing-on-one-foot data sets that we compared.
b. What is the range of the two-striped grasshopper
data?
c. Which range is larger? How much larger?
2. If all the 1 3_4 -inch grasshoppers were lined up end to
end, how long would they be?
If students only describe what they notice about one data set, ask
them to compare the two data sets.
3. If the 3_4 -inch two-striped grasshopper and the 1 _81 -inch
clear-winged grasshoppers were lined up end to end,
how long would they be?
4. Which is longer, the longest clear-winged grasshopper
or the longest two-striped grasshopper? How much
longer?
17B
Unit 9
© Pearson Education 5
5. Which is shorter: the shortest clear-winged grasshopper
or the shortest two-striped grasshopper? How much
shorter?
Session 1.5A
▲ Student Activity Book, Unit 9, p. 17B;
Resource Masters, C109
INV12_SE05_U9.indd 2
6/13/11 12:57 PM
Based on our comparisons, would you say that clear-winged
grasshoppers are longer or two-striped grasshoppers are longer?
Ask students to cite evidence from the data to support their
conclusions about which kind of grasshopper is longer.
Then ask students to look at Student Activity Book page 17B or
C109.
You are going to solve some problems based on the information
you gathered from these two data sets.
Remind students that the range of a set of data is the difference
between the highest value and the lowest value.
Ongoing Assessment: Observing Students at Work
Students represent a data set of measurements involving
fractions on a line plot. They use the data in the line plot to solve
problems involving fractions.
• Do students accurately mark the fractions on the line plot?
• Do students accurately represent the data on the line plot?
• Can students use the information on the line plot to solve
addition, subtraction, and multiplication problems
involving fractions?
• What strategies are students using to solve the addition,
subtraction, and multiplication problems?
differentiation: Supporting the Range of Learners
Some students may have difficulty transferring
data from the line plots to the word problems. Help these
students identify each of the numbers needed to solve the
problem. Some students may find subtracting or adding fractions
with unlike denominators or multiplying fractions challenging. Encourage these students to draw representations or to use the
number line in the line plot to help them.
CC162 Investigation 1 Comparing Balancing Data
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1 Activity 2 Discussion 3 Session Follow-Up Students who easily solve these problems can be
asked to make up their own problems using the grasshopper
length data. Encourage them to use fractions with unlike
denominators.
Discussion
Grasshopper Lengths
10 Min
class
Math Focus Points for Discussion
Using operations on fractions to solve problems involving
information given in line plots
Let’s start with Problem 1a. Was this an addition, subtraction,
multiplication, or division situation? How did you know?
Ask students to share their solutions for Problem 1a.
Students might say:
“The problem was a subtraction problem,
but I used addition. I knew it was ​ _12 ​ inch
more to 1 inch, and then another ​ _78 ​ inch
to 1​ _78 ​ inches. So I add ​ _12 ​ and ​ _78 ​. ​ _78 ​ plus
one more eighth is 1, so there is ​ 3_8 ​ left
from the ​ _12 ​. So ​ _12 ​ ∙ ​ _78 ​ is 1​ _38 ​. The range is
1​ _38 ​ inches.”
“I knew ​ _12 ​ is the same as ​ _48 ​. ​ _78 ​ minus ​ _48 ​ is ​ _38 ​.
The range is 1​ _38 ​ inches.”
Let’s look at Problem 2. Was this an addition, subtraction,
multiplication, or division situation? How did you know?
Ask students to share their solutions for Problem 2.
Students might say:
“It was a multiplication problem. There is a
total of three 1​ _34 ​ grasshoppers. I did
3 ∙ 1 which is 3 and then 3 ∙ ​ _34 ​ which is 3
groups of ​ _34 ​ which is ​ _94 ​. ​ _94 ​ is 2​ _14 ​. 3 plus 2​ _14 ​ is
5​ _14 ​.”
Session 1.5A Fractions on a Line Plot CC163
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1 Activity 2 Discussion 3 Session Follow-Up Name
Date
How Long Can You Stand on One Foot?
Session Follow-Up
Daily Practice
Comparing Rainfall Data
Daily Practice
note Students represent two sets of data in line plots and compare the data.
The table gives data for the cities of Eureka,
California and Gainesville, Florida. Show
the data on the line plots.
Average Monthly Rainfall, 1971–2000 (inches)
Jan. Feb. Mar. Apr. May Jun.
Eureka
6
5​2_1 ​ 5​2_1 ​ 2​8_7  1​8_5 
5
_
​8
 
Daily Practice: For reinforcement of this unit’s content,
have students complete Student Activity Book page 17C
or C110.
Jul. Aug. Sep. Oct. Nov. Dec.
1
_
​8
 
3
_
​8
 ​
7
_
​8
 
2​8_3 ​ 5​4_3 ​ 6​8_3 ​
Gainesville 3​2_1 ​ 3​8_3 ​ 4​4_1 ​ 2​8_7  3​4_1 ​ 6​4_3 ​ 6​8_1  6​8_5  4​8_3 ​ 2​2_1 ​ 2​8_1  2​2_1 ​
0
1
2
3
4
5
6
Eureka Average Monthly Rainfall (inches)
7
0
1
2
3
4
5
6
Gainesville Average Monthly Rainfall (inches)
7
Student Math Handbook: Students and families may use
Student Math Handbook pages 81–88 for reference and
review. See pages 147–150 in the back of Unit 9.
© Pearson Education 5
Compare the rainfalls in the two cities. Write three statements about how
they compare. Explain how the data support your statements.
Session 1.5A
Unit 9
17C
▲ Student Activity Book, Unit 9, p. 17C;
Resource Masters, C110
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CC164 6/8/11 1:55 PM
Investigation 1 Comparing Balancing Data
INV12_TE05_U09_S1.5A.indd 164
6/27/11 2:57 PM
session 1.6A
End-of-Unit Assessment
Math Focus Points
Comparing sets of data using the shape and
spread of the data
Drawing conclusions based on data
Using operations on fractions to solve problems involving
information given in line plots
Today’s Plan
Materials
Assessment Activity
End-of-Unit Assessment
•C111–C112, End-of-Unit Assessment Make
Activity
Grasshopper Collections
copies. (1 set per student)
30 Min Individuals
•Student Activity Book, pp. 17D–17E or
C113–C114, Grasshopper Collections Make copies. (as needed)
30 Min Individuals PAIRS
SESSION FOLLOW-UP
Daily Practice
•Student Activity Book, p. 17F or
C115, Crickets Make copies. (as needed)
•Student Activity Book, p. 17G or
C116, Collecting and Describing Data Make
copies. (as needed)
Student Math Handbook, pp. 81–88
•
Ten-Minute Math
Estimation and Number Sense: Closest Estimate Show Problems 10–12 on Estimation
and Number Sense: Closest Estimate (T86), one at a time. Give students approximately
30 seconds to look at the three possible estimates and determine which is the closest
to the actual answer. Have two or three students explain their reasoning for each
problem. Ask students:
• How did you break the numbers apart?
• How did you determine the magnitude of the answer?
• If you changed the numbers in the problem, how did you change them and why?
Also, ask if the closest estimate is greater than or less than the actual answer and how
students know.
Session 1.6A End-of-Unit Assessment CC165
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1 Assessment Activity 2 Activity 3 Session Follow-Up
Professional Development
1 Teacher Note: the Data, p. 122
Assessment: Analyzing
Name
Date
End-of-Unit Assessment (page 1 of 2)
A fifth-grade class conducted an experiment on how long people
could hold their breath. They wanted to answer this question:
Who can hold their breath longer, fifth graders or adults?
Here are the data they collected from fifth graders and adults.
Number of Students
6
5
4
3
2
1
20
25
30
35
40
45
50
55
60
65
70
75
80
70
75
80
Time in Seconds
Amount of Time Adults Held Their Breath
7
Number of Adults
6
5
4
3
2
1
0
15
20
25
30
35
40
45
50
55
60
65
Time in Seconds
Unit 9 Session 1.6A
C111
30 Min individuals
In this unit, students interpret bar graphs only for homework.
However, students should be familiar with bar graphs from their
work in Grades 3 and 4. This assessment will give you an
opportunity to see whether students can gather information from a
bar graph, make comparisons on the basis of the data, and support
their conclusions with evidence from the data. This assessment
addresses Benchmarks 1 and 2. Benchmark 1: Describe major
features of a set of data represented in a line plot or bar graph, and
quantify the description by using the median or fractional parts of
the data. Benchmark 2: Draw conclusions about how two groups
compare based on summarizing the data for each group.
Amount of Time Fifth Graders Held Their Breath
7
15
End-of-Unit Assessment
Students work individually on the End-of-Unit Assessment (C111–
C112). In this assessment, students compare data about two groups
represented in bar graphs, and come to conclusions that use
evidence from the data. 1
How Long Can You Stand on One Foot?
0
A ssessment Ac tivit y
© Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
▲ Resource Masters, C111
INV12_BLM05_U9.indd 111
4/28/11 5:01 PM
Ongoing Assessment: Observing Students at Work
Name
Students compare data about two groups represented in bar
graphs.
Date
How Long Can You Stand on One Foot?
End-of-Unit Assessment (page 2 of 2)
• What aspects of the data do students compare? Do
1. Write 3 statements about how long the fifth graders held
their breath, compared with the adults. As you write your
comparison, consider aspects of the data, such as where the
data are concentrated, the ranges, any outliers, and the medians.
a.
b.
c.
students find the medians correctly? Do they describe the
ranges, outliers, areas of concentration?
• Are students able to draw conclusions about the two
groups from their comparisons? Do they support their
conclusions with evidence from the data?
2. Who would you say are better at holding their breath,
fifth graders or adults? Explain what evidence from
the data supports your conclusion.
differentiation: Supporting the Range of Learners
Unit 9 Session 1.6A
C112
© Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
▲ Resource Masters, C112
INV12_BLM05_U9.indd 112
CC166 4/28/11 5:01 PM
Some students may still be unsure how to
compare two sets of data. Ask them to start with the first bar
graph about the fifth graders and describe certain aspects of the
data such as median, least value, greatest value, and range. Then
have them describe each of these same aspects for the data
about adults shown in the second bar graph.
Investigation 1 Comparing Balancing Data
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1 Assessment Activity 2 Activity 3 Session Follow-Up
AC TIVIT Y
Grasshopper Collections
Name
Date
How Long Can You Stand on One Foot?
30 Min individuals pairs
Grasshopper Collections (page 1 of 2)
Olivia and Terrence collected grasshoppers for a science project. The
lengths of their grasshoppers are shown in the line plots below.
X
X XX
Introduce Student Activity Book pages 17D–17E or C113–C114.
When you’re done with the problems, share your work with a
partner. See if you and your partner solved the problems in the
same way. Did you get the same answers? If not, see if you can
figure out who made a mistake. Check to see if you chose the
right operation. Check to see if your strategy for working with
fractions makes sense.
0
1
1 12
X X
X
X X X X X X
2
2 12
3 12
3
4
Lengths of Olivia’s Grasshoppers (inches)
X
X
XXX X
1
2
0
1
1 12
X
XXX X
2
X
2 12
3
3 12
4
Lengths of Terrence’s Grasshoppers (inches)
Solve each problem. Show your work or explain how you found
each answer.
1. What is the range of the lengths of Olivia’s grasshoppers?
2. What is the range of the lengths of Terrence’s grasshoppers?
© Pearson Education 5
Now you’re going to do some more work with grasshopper data.
This time, the data are already shown in two line plots. Your job
will be to carefully read the data and use them to solve the
problems. These data contain fractions, just like the previous
grasshopper data. So you’ll have to remember your strategies for
adding, subtracting, multiplying, and dividing fractions.
1
2
17D
Unit 9
Session 1.6A
▲ Student Activity Book, Unit 9, p. 17D;
Resource Masters, C113
INV12_SE05_U9.indd 4
Name
6/8/11 1:57 PM
Date
How Long Can You Stand on One Foot?
Ongoing Assessment: Observing Students at Work
Grasshopper Collections (page 2 of 2)
Refer to the line plots on the previous page showing the
lengths of the grasshoppers Olivia and Terrence collected.
Solve each problem. Show your work or explain how you
found each answer.
Students use operations on fractions to solve problems involving
information given in line plots.
3. What is the median length of Olivia’s grasshoppers?
• Do students accurately read the data? Can they interpret the
4. How much longer is Olivia’s longest grasshopper than
Terrence’s longest grasshopper?
Xs even when the tick marks are not labeled?
• Do students use the right operation? Do they know which
5. Olivia read that some grasshoppers can jump 20 times
their body length. How many inches can Olivia’s
longest grasshopper jump if it jumps 20 times its
body length?
computations to do to find the ranges? Can they choose the
right operations for the other problems?
and accurate strategy for adding, subtracting, multiplying, and
dividing fractions?
© Pearson Education 5
• Do students compute accurately? Do they use an efficient
6. Terrence’s shortest grasshopper jumped 14 inches. How
many times its body length did that grasshopper jump?
Session 1.6A
17E
▲ Student Activity Book, Unit 9, p. 17E;
Resource Masters, C114
INV12_SE05_U9.indd 5
differentiation: Supporting the Range of Learners
Unit 9
6/8/11 1:57 PM
Some students may be uncertain which operation
to use in each problem, and others may have difficulty doing
computation with fractions. Discuss each problem with the
students and help them decide which operation to use to solve
the problem. Encourage them to use representations to help
them solve the problems.
Session 1.6A End-of-Unit Assessment INV12_TE05_U09_S1.6A.indd 167
CC167
6/10/11 11:37 AM
1 Assessment Activity 2 Activity 3 Session Follow-Up
Name
Date
How Long Can You Stand on One Foot?
1
4
0
1
2
3
4
X
X X
1
1 14
Daily Practice
note Students use data in a line plot to
solve problems involving measurements in
fractions of a unit.
Nora collected crickets for a science project.
The lengths of the crickets are shown in the line
plot below.
X
X
X
X X X X
Session Follow-Up
Daily Practice
Crickets
X
X X
1 12
Daily Practice: For reinforcement of this unit’s content,
have students complete Student Activity Book page 17F or
C115. For enrichment, have students complete Student
Activity Book page 17G or C116.
X
1 34
2 14
2
Lengths of Nora’s Crickets (inches)
Solve each problem. Show your work or explain how you found
each answer.
1. What is the range of the lengths of Nora’s crickets?
Student Math Handbook: Students and families may use
Student Math Handbook pages 81–88 for reference and
review. See pages 147–149 in the back of Unit 9.
2. What is the mode of the data about the lengths of Nora’s crickets?
4. Nora read that some crickets can jump to a height that is 30 times their
body length. How many inches high can Nora’s shortest cricket jump if it
jumps 30 times its body length?
17F
Unit 9
© Pearson Education 5
3. How many of Nora’s crickets were more than twice as long as her
shortest cricket?
Session 1.6A
▲ Student Activity Book, Unit 9, p. 17F;
Resource Masters, C115
INV12_SE05_U9.indd 6
6/13/11 12:58 PM
Name
Date
How Long Can You Stand on One Foot?
Daily Practice
Collecting and Describing
Data
note Students collect, represent, and describe data in line plots.
Measure a set of 10–20 similar items. Possibilities
include leaves, sharpened pencils, books, or classmates’ shoes.
1. Measure the length of each item to the nearest eighth
inch. Record the measurements below. Make a line plot
of the data on another sheet of paper.
Items I measured:
Lengths to the nearest eighth inch:
2. Complete the following. (You might need to write
“none” for some answers.)
Shortest:
Range:
Mode (most common):
in.
Longest:
in.
in.
Median length:
Outlier(s):
in.
in.
© Pearson Education 5
in.
Session 1.6A
Unit 9
17G
▲ Student Activity Book, Unit 9, p. 17G;
Resource Masters, C116
INV12_SE05_U9.indd 7
CC168 6/8/11 2:00 PM
Investigation 1 Comparing Balancing Data
INV12_TE05_U09_S1.6A.indd 168
6/15/11 7:37 PM
Name
Date
How Long Can You Stand on One Foot?
Family Letter
About the Mathematics in This Unit (page 1 of 2)
Dear Family,
Our class is starting a new mathematics unit about data called How Long Can
You Stand on One Foot? During this unit, students collect, represent, describe, and
interpret data.
Throughout the unit, students work toward these goals:
Benchmarks/
GOALS
Describe major
features of a set of
data represented in
a line plot or bar
graph, and quantify
the description by
using the median or
fractional parts of
the data.
Examples
How many years have 5th graders been at this school?
1
2
3
4
5
6
7
8
Number of Years
9
Most of the data are in two clumps. Almost half (​ ___
  ​) 
21
have been here 1 or 2 years, and an equal
number have been here for 5 or 6 years. Only
one person (the teacher) has been at this school
for 8 years.
(continued)
Unit 9 Session 1.1
INV12_BLM05_U9.indd 105
C105
© Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
5/18/11 7:52 PM
Name
Date
How Long Can You Stand on One Foot?
Family Letter
About the Mathematics in This Unit (page 2 of 2)
Number of Trials
Benchmarks/
Examples
GOALS
Draw conclusions
Which coin will spin longer, a penny or a quarter?
about how two groups
Spinning Coins
compare based on
3
summarizing the data
for each group.
2
1
0
1 to 5
6 to 10
11 to 15
16 to 20
21 to 25
26 to 30
Number of Seconds
Penny
Quarter
The data show that overall, quarters spin longer than
pennies. About half (7 out of 13) of the quarters spun
for more than 15 seconds. Almost all (11 out of 13) of
the pennies spun for 20 seconds or less.
Please look for more information and activities about How Long Can You Stand on
One Foot? that will be sent home in the coming weeks.
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How Long Can You Stand on One Foot?
Family Letter
Related Activities to Try at Home
Dear Family,
The activities below are related to the mathematics in the unit How Long Can You
Stand on One Foot? You can use the activities to enrich your child’s mathematical
learning experience.
Data in the Media We live in an information-rich society, and it is important for
students to begin to experience the variety of ways that information is communicated
and represented in the world. Much of the data we read and hear about every day
involves comparisons— of everything from automobiles to cold remedies. As you
are reading either the newspaper or a magazine, point out various graphs and
charts to your child. Talk about how you make sense of the data, what they mean,
and why you are interested in them. This is an opportunity for you to show your
child how graphs communicate important information to you and your family.
Math and Literature Here is a suggestion of a children’s
book that contains relevant mathematical ideas about
data. Look for this book at your local library.
Pappas, Theoni. Math for Kids & Other People Too!
24084_003v
Unit 9 Session 1.2
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Grasshopper Lengths (page 1 of 2)
A scientist collected two types of grasshoppers and
recorded their lengths in the boxes below. Show the
lengths on the line plots.
Lengths of Clear-Winged Grasshoppers (inches)
1​ _14 ​ 1​ _78  ​ 3_4 ​ 1 1​ _14 ​ 1 1​ _38 ​ 1​ _14 ​ 1​ _12 ​ ​ 7_8  ​ 1_2 ​ 1​ _38  1​ _18  ​ 5_8  1​ _18  ​ 3_4 ​
Lengths of Two-Striped Grasshoppers (inches)
5
 ​_
8  0
1​ _38 ​ 2​ _14 ​ 1​ _78  ​ 3_4 ​ 1​ _78  1​ _34 ​ 1​ _12 ​ 1​ _12 ​ 2 2​ _38 ​ 1​ _34 ​ 1​ _38 ​ 1​ _14 ​ 1 1​ _34 ​
1
2
3
Lengths of Clear-Winged Grasshoppers (inches)
0
1
2
3
Lengths of Two-Striped Grasshoppers (inches)
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Grasshopper Lengths (page 2 of 2)
Use the information in the line plots on the previous page to solve the
following problems. Show your work.
1. a. W
hat is the range of the clear-winged grasshopper
data?
b. W
hat is the range of the two-striped grasshopper
data?
c. Which range is larger? How much larger?
2. If all the 1​ 3_4 ​-inch grasshoppers were lined up end to
end, how long would they be?
3. If the ​ _34 ​-inch two-striped grasshopper and the 1​ _18 -inch
clear-winged grasshoppers were lined up end to end,
how long would they be?
4. Which is longer, the longest clear-winged grasshopper
or the longest two-striped grasshopper? How much
longer?
5. Which is shorter: the shortest clear-winged grasshopper
or the shortest two-striped grasshopper? How much
shorter?
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Daily Practice
Comparing Rainfall Data
The table gives data for the cities of Eureka,
California and Gainesville, Florida. Show
the data on the line plots.
note Students represent two
sets of data in line plots and compare
the data.
Average Monthly Rainfall, 1971–2000 (inches)
Jan. Feb. Mar. Apr. May Jun.
Eureka
6
5​ _12 ​ 5​ _12 ​ 2​ _78  1​ _58 
5
 ​_
8 
Jul. Aug. Sep. Oct. Nov. Dec.
1
 ​_
8 
3
 ​_
8 ​
7
 ​_
8 
2​ _38 ​ 5​ 4_3 ​ 6​ _38 ​
Gainesville 3​ 1_2 ​ 3​ _38 ​ 4​ 1_4 ​ 2​ 7_8  3​ 1_4 ​ 6​ 3_4 ​ 6​ 1_8  6​ 5_8  4​ 3_8 ​ 2​ 1_2 ​ 2​ _81  2​ 1_2 ​
0
1
2
3
4
5
6
Eureka Average Monthly Rainfall (inches)
7
0
1
2
3
4
5
6
Gainesville Average Monthly Rainfall (inches)
7
Compare the rainfalls in the two cities. Write three statements about how
they compare. Explain how the data support your statements.
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End-of-Unit Assessment (page 1 of 2)
A fifth-grade class conducted an experiment on how long people
could hold their breath. They wanted to answer this question:
Who can hold their breath longer, fifth graders or adults?
Here are the data they collected from fifth graders and adults.
Amount of Time Fifth Graders Held Their Breath
Number of Students
7
6
5
4
3
2
1
0
15
20
25
30
35
40
45
50
55
60
65
70
75
80
70
75
80
Time in Seconds
Amount of Time Adults Held Their Breath
Number of Adults
7
6
5
4
3
2
1
0
15
20
25
30
35
40
45
50
55
60
65
Time in Seconds
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End-of-Unit Assessment (page 2 of 2)
1. Write 3 statements about how long the fifth graders held
their breath, compared with the adults. As you write your
comparison, consider aspects of the data, such as where the
data are concentrated, the ranges, any outliers, and the medians.
a.
b.
c.
2. Who would you say are better at holding their breath,
fifth graders or adults? Explain what evidence from
the data supports your conclusion.
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Grasshopper Collections (page 1 of 2)
Olivia and Terrence collected grasshoppers for a science project. The
lengths of their grasshoppers are shown in the line plots below.
X
X XX
0
1
2
1
1 12
X X
X
X X X X X X
2 12
2
3 12
3
4
Lengths of Olivia’s Grasshoppers (inches)
X
X
XXX X
0
1
2
1
1 12
X
XXX X
2
2 12
X
3
3 12
4
Lengths of Terrence’s Grasshoppers (inches)
Solve each problem. Show your work or explain how you found
each answer.
1. What is the range of the lengths of Olivia’s grasshoppers?
2. What is the range of the lengths of Terrence’s grasshoppers?
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Grasshopper Collections (page 2 of 2)
Refer to the line plots on the previous page showing the
lengths of the grasshoppers Olivia and Terrence
collected. Solve each problem. Show your work or
explain how you found each answer.
3. What is the median length of Olivia’s grasshoppers?
4. How much longer is Olivia’s longest grasshopper
than Terrence’s longest grasshopper?
5. Olivia read that some grasshoppers can jump 20 times
their body length. How many inches can Olivia’s
longest grasshopper jump if it jumps 20 times its
body length?
6. Terrence’s shortest grasshopper jumped 14 inches.
How many times its body length did that
grasshopper jump?
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Daily Practice
Crickets
note Students use data in a line
plot to solve problems involving
measurements in fractions of a unit.
Nora collected crickets for a science project.
The lengths of the crickets are shown in the
line plot below.
X
X
X
X X X X
0
1
4
1
2
3
4
X
X X
1
1 14
X
X X
1 12
1 34
X
2
2 14
Lengths of Nora’s Crickets (inches)
Solve each problem. Show your work or explain how you found
each answer.
1. What is the range of the lengths of Nora’s crickets?
2. What is the mode of the data about the lengths of Nora’s crickets?
3. How many of Nora’s crickets were more than twice as long as her
shortest cricket?
4. Nora read that some crickets can jump to a height that is 30 times
their body length. How many inches high can Nora’s shortest cricket
jump if it jumps 30 times its body length?
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Daily Practice
Collecting and
Describing Data
note Students collect, represent,
and describe data in line plots.
Measure a set of 10–20 similar items. Possibilities include leaves,
sharpened pencils, books, or classmates’ shoes.
1. Measure the length of each item to the nearest
eighth inch. Record the measurements below. Make
a line plot of the data on another sheet of paper.
Items I measured:
Lengths to the nearest eighth inch:
2. Complete the following. (You might need to write
“none” for some answers.)
Shortest:
Range:
Mode (most common):
in.
in.
Unit 9 Session 1.6A
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Longest:
in.
Median length:
in.
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Outlier(s):
in.
in.
© Pearson Education, Inc., or its affiliates. All Rights Reserved. 5
6/22/11 8:32 AM
Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Carta a la familia
HOGAR
Sobre las Matemáticas de esta unidad (página 1 de 2)
Estimada familia:
Nuestra clase está comenzando una nueva unidad de Matemáticas sobre datos
llamada ¿Cuánto tiempo puedes mantenerte en un pie? En el transcurso de esta unidad,
los estudiantes recopilan, representan, describen e interpretan datos.
A lo largo de esta unidad, los estudiantes trabajarán para lograr los siguientes
objetivos:
PUNTOS DE
REFERENCIA/
EJEMPLOS
OBJETIVOS
Describir las
¿Cuántos años llevan los estudiantes de quinto grado
principales
en esta escuela?
características de un
conjunto de datos
representados en un
diagrama de puntos o
en una gráfica de
barras y cuantificar la
descripción usando la
1
2
3
4
5
6
7
8
mediana o partes
fraccionarias de los
Número de años
datos.
La mayoría de los datos está en dos grupos. Casi la
9
  ​)  ha estado aquí 1 o 2 años y una
mitad (​ ___
21
misma cantidad ha estado aquí 5 o 6 años. Sólo una
persona (el maestro) ha estado en la escuela
8 años.
(continúa)
Unidad 9 Sesión 1.1
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Carta a la familia
HOGAR
Sobre las Matemáticas de esta unidad (página 2 de 2)
Número de intentos
PUNTOS DE
REFERENCIA/
EJEMPLOS
OBJETIVOS
¿Qué moneda girará más tiempo, la de 1¢ o la
Sacar conclusiones
de 25¢?
sobre cómo se
comparan dos grupos
Monedas giratorias
teniendo en cuenta un
3
resumen de los datos
de cada uno de los
2
grupos.
1
0
1a5
6 a 10
11 a 15
16 a 20
21 a 25
26 a 30
Número de segundos
Moneda de 1¢
Moneda de 25¢
Los datos muestran que las monedas de 25¢ giran más
tiempo que las de 1¢. Aproximadamente la mitad (7 de
13) de las monedas de 25¢ giraron por más de 15
segundos. Casi todas (11 de 13) las monedas de 1¢
giraron por 20 segundos o menos.
En las próximas semanas le enviaremos más información y actividades sobre
¿Cuánto tiempo puedes mantenerte en un pie?
Unidad 9 Sesión 1.1
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Carta a la familia
HOGAR
Actividades relacionadas para hacer en el hogar
Estimada familia:
Las actividades que siguen están relacionadas con las Matemáticas de la unidad
¿Cuánto tiempo puedes mantenerte en un pie? Puede usar estas actividades para
enriquecer la experiencia del aprendizaje de las matemáticas de su hijo/a.
Datos en los medios de comunicación Vivimos en una sociedad con pleno
acceso a todo tipo de información. Es importante para los estudiantes que comiencen
a prestar atención a la variedad de maneras en que la información se comunica y se
representa alrededor del mundo. Mucha de la información que leemos y escuchamos
todos los días incluye comparaciones que van desde las características de un
automóvil hasta los diferentes remedios para la salud. Mientras lee el periódico o una
revista, señálele a su hijo/a varias gráficas y tablas. Háblele sobre cómo interpretar
los datos, lo que significan y por qué está interesado en ellos. Ésta es una
oportunidad para mostrarle a su hijo/a cómo las gráficas comunican información
importante para usted y su familia.
Matemáticas y literatura Aquí tiene una sugerencia de un libro
para niños que contiene ideas matemáticas relevantes
sobre datos. Búsquelo en la biblioteca de su vecindario.
Pappas, Theoni. El encanto de las matemáticas.
24084_003v
Unidad 9 Sesión 1.2
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Longitudes de saltamontes (página 1 de 2)
Un científico coleccionó dos tipos de saltamontes y
registró sus longitudes en las cajas de abajo. Muestra
las longitudes en el diagrama de puntos.
Longitudes de saltamontes de alas transparentes (pulgadas)
1​ _14 ​ 1​ _78  ​ 3_4 ​ 1 1​ _14 ​ 1 1​ _38 ​ 1​ _14 ​ 1​ _12 ​ ​ 7_8  ​ 1_2 ​ 1​ _38  1​ _18  ​ 5_8  1​ _18  ​ 3_4 ​
Longitudes de saltamontes birrayados (pulgadas)
5
 ​_
8  0
1​ _38 ​ 2​ _14 ​ 1​ _78  ​ 3_4 ​ 1​ _78  1​ _34 ​ 1​ _12 ​ 1​ _12 ​ 2 2​ _38 ​ 1​ _34 ​ 1​ _38 ​ 1​ _14 ​ 1 1​ _34 ​
1
2
3
Longitudes de saltamontes de alas transparentes (pulgadas)
0
1
2
3
Longitudes de saltamontes birrayados (pulgadas)
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Longitudes de saltamontes (página 2 de 2)
Usa la información del diagrama de puntos de la página anterior para
resolver los siguientes problemas. Muestra tu trabajo.
1. a. ¿ Cuál es el rango de los datos del saltamontes
de alas transparentes?
b. ¿ Cuál es el rango de los datos del saltamontes
birrayado?
c. ¿Qué rango es mayor? ¿Cuánto mayor?
2. Si se alinearan de extremo a extremo todos los
saltamontes de 1​ _34 ​-pulgadas ¿qué longitud tendrían?
3. Si el saltamontes birrayado de ​ _34 ​ de pulgada y los
saltamontes de alas transparentes de 1​ _18  pulgadas
se alinearan de extremo a extremo, ¿qué longitud
tendrían?
4. ¿Cuál es más largo: el saltamontes de alas
transparentes más largo o el saltamontes
birrayado más largo? ¿Cuánto más largo es?
5. ¿Cuál es más corto: el saltamontes de alas
transparentes más corto o el saltamontes
birrayado más corto? ¿Cuánto más corto es?
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Práctica diaria
Comparar datos de
precipitación
La tabla da información sobre las ciudades de
Eureka, California y Gainesville, Florida. Muestra
los datos en los diagramas de puntos.
notA Los estudiantes representan
dos conjuntos de datos en los
diagramas de puntos y comparan
los datos.
Promedio de precipitación mensual, 1971-2000 (pulgadas)
Ene. Feb. Mar. Abr. May. Jun.
Eureka
6
5​ _12 ​ 5​ _12 ​ 2​ _78  1​ _58 
5
 ​_
8 
Jul. Ago. Sep. Oct. Nov. Dic.
1
 ​_
8 
3
 ​_
8 ​
7
 ​_
8 
2​ _38 ​ 5​ 4_3 ​ 6​ _38 ​
Gainesville 3​ _12 ​ 3​ _38 ​ 4​ _14 ​ 2​ _78  3​ _14 ​ 6​ _34 ​ 6​ _18  6​ _58  4​ _38 ​ 2​ _12 ​ 2​ _81  2​ _12 ​
1
2
3
4
5
6
7
0
Promedio de precipitación mensual en Eureka (pulgadas)
0
1
2
3
4
5
6
7
Promedio de precipitación mensual en Gainesville (pulgadas)
Compara la precipitación en ambas ciudades. Escribe tres
enunciados sobre las comparaciones que hiciste. Explica cómo
los datos apoyan tus enunciados.
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Evaluación final de la unidad (página 1 de 2)
Una clase de quinto grado realizó un experimento para
determinar cuánto tiempo pueden contener la respiración algunas
personas. La clase quería contestar la siguiente pregunta: ¿Quién
puede contener más tiempo la respiración, los estudiantes de
quinto grado o los adultos? Aquí están los datos que recopilaron:
Número de estudiantes
Tiempo que los estudiantes de quinto grado contuvieron la respiración
7
6
5
4
3
2
1
0
15
20
25
30
35
40
45
50
55
60
65
70
75
80
Tiempo en segundos
Tiempo que los adultos contuvieron la respiración
Número de adultos
7
6
5
4
3
2
1
0
15
20
25
30
35
40
45
50
55
60
65
70
75
80
Tiempo en segundos
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Evaluación final de la unidad (página 2 de 2)
1. Escribe 3 enunciados comparando el tiempo que los estudiantes de
quinto grado contuvieron la respiración y el tiempo que contuvieron
la respiración los adultos. Al escribir los 3 enunciados debes tener
en cuenta algunos aspectos de los datos, como por ejemplo: dónde
están concentrados los datos, los rangos, cualquier valor extremo y
las medianas.
a.
b.
c.
2. ¿Quién contiene mejor la respiración, los estudiantes de
quinto grado o los adultos? ¿Qué pruebas basadas en los
datos apoyan tu conclusión?
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Colecciones de saltamontes (página 1 de 2)
Olivia y Terrence coleccionaron saltamontes para un proyecto de
ciencias. Las longitudes de sus saltamontes se muestran en los
diagramas de puntos de abajo.
X
X XX
0
1
2
1
1 12
X X
X
X X X X X X
2 12
2
3 12
3
4
Longitudes de los saltamontes de Olivia (pulgadas)
X
X
XXX X
0
1
2
1
1 12
X
XXX X
2
2 12
X
3
3 12
4
Longitudes de los saltamontes de Terrence (pulgadas)
Resuelve cada problema. Muestra tu trabajo o explica cómo hallaste
cada respuesta.
1. ¿Cuál es el rango de las longitudes de los saltamontes de Olivia?
2. ¿Cuál es el rango de las longitudes de los saltamontes de Terrence?
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Colecciones de saltamontes (página 2 de 2)
Usa como referencia los diagramas de puntos de la
página anterior, que muestran la longitud de los
saltamontes que recolectaron Olivia y Terrence.
Resuelve cada problema. Muestra tu trabajo o explica
cómo hallaste cada respuesta.
3. ¿Cuál es la longitud mediana de los saltamontes
de Olivia?
4. ¿Cuánto más largo es el saltamontes más largo de
Olivia que el saltamontes más largo de Terrence?
5. Olivia leyó que algunos saltamontes pueden saltar
20 veces el tamaño de la longitud de su cuerpo.
¿Cuántas pulgadas puede saltar el saltamontes
más largo de Olivia, si salta 20 veces la longitud
de su cuerpo?
6. El saltamontes más corto de Terrence saltó 14
pulgadas. ¿Cuántas veces la longitud de su cuerpo
saltó ese saltamontes?
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Práctica diaria
Grillos
Nora colecciona grillos para un proyecto de
ciencias. Las longitudes de los grillos se
muestran en el diagrama de puntos de abajo.
X
X
X
X X X X
0
1
4
1
2
3
4
X
X X
1
1 14
notA Los estudiantes usan los
datos de un diagrama de puntos
para resolver problemas que incluyen
medidas en fracciones de una unidad.
X
X X
1 12
1 34
X
2
2 14
Longitudes de los grillos de Nora (pulgadas)
Resuelve cada problema. Muestra tu trabajo o explica cómo hallaste
cada respuesta.
1. ¿Cuál es el rango de las longitudes de los grillos de Nora?
2. ¿Cuál es la moda de los datos sobre las longitudes de los grillos
de Nora?
3. ¿Cuántos de los grillos de Nora tenían más de dos veces la longitud
que su grillo más corto?
4. Nora leyó que algunos grillos pueden saltar a una altura que es
30 veces el tamaño de la longitud de su cuerpo. ¿Cuántas pulgadas
de alto puede saltar el grillo más corto de Nora, si salta 30 veces la
longitud de su cuerpo?
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Nombre
Fecha
¿Cuánto tiempo puedes mantenerte en un pie?
Práctica diaria
Reunir y describir datos
Mide un conjunto de 10 a 20 artículos similares.
Las posibilidades incluyen hojas, lápices afilados,
libros o los zapatos de tus compañeros de clase.
notA Los estudiantes reúnen,
representan y describen datos en
diagramas de puntos.
1. Mide la longitud de cada artículo al octavo de
pulgada más cercano. Registra las medidas abajo.
Haz un diagrama de puntos de los datos en una
hoja aparte.
Artículos que medí:
Longitudes al octavo de pulgada más cercano:
2. Completa lo siguiente: (Es posible que tengas que
escribir “ninguno” para algunas respuestas).
Más corto:
Rango:
Moda (más común):
pulg.
Más largo:
pulg.
Longitud mediana:
pulg.Valor(es) extremo(s):
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C116
pulg.
pulg.
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