Collecting, Organizing and Working with Data

Contributed by:
Diego
In this pdf, we will be collecting, organizing, and analyzing data. Data handling is gathering and recording information and then presenting it in a way that can be understood easily and used by other people. Data collection is gathering the facts and figures needed for the research.
1. The learner will understand and
4
Notes and textbook
references
use graphs and data analysis.
4.01 Collect, organize, analyze, and display
data (including stem-and-leaf plots) to solve Notes and textbook
references
A. Collect data using a variety of quick collection activities
involving timing things to do in one minute. Complete the collect, The step of collecting
organize, analyze, and display cycle. Example- How many X’s can you data is often not
experienced by students
draw in one minute with your right hand? Your left hand? Organize and
since many tasks already
display the data on an appropriate graph. Analyze factors that may have provide the data.
contributed to the discrepancies in the data or any outliers you may have. Students need
Why were some people able to draw more X’s with their left hand? Would opportunities to work
this data be appropriate for a stem plot? A line plot? A line graph? throughout the entire
data collection process;
pose a question, collect
the data, analyze and
interpret the data, and
B. Hold a class discussion on data collection and the display it. Allowing
students to collect data
importance of controlling all variables. Ask the students what they would and make the different
need to do to help define the question before collecting data for the number representations will
of times a fifth grader can jump rope. For example: Can I jump as long as I increase their
want, anyway that I want, should someone else turn the rope, should I turn understanding of using
data to solve problems.
the rope, etc? Would we get an accurate answer to our question if some
people skipped and others jumped with their feet together or if students
were allowed to count their own jumps? Does everyone need to use the
same type rope? It is important that students understand all factors that may
lead them astray. Posing questions to ensure the data collected answers the
question is more difficult than most students realize. Collect, analyze, and
display the data.
Grade 5 Classroom Strategies 65
2. Notes and textbook C. Survey the class collecting data on the number of buttons on
references a student’s clothing or the number of pencils in a student’s desk. Display
the data using an appropriate graph. Have students explain their graph and
why they chose that representation.
D. Ask the students to collect graphs from newspapers and
magazines. Working in groups of two to four, ask the students to study the
graphs and make a list of questions which had to be answered to make the
graphs. Have each group report to the class about their findings.
Determine the questions that were alike/similar and make a list of decisions
to be made before gathering data.
E. From the list below, have students determine how to graph
the data given. Why are some types of graphs more appropriate than
others?
• If the kindergarten students were measured each month to chart
growth
• Number and different type of books in the library
• How students spend their allowance
• Number of free throws successfully completed by two people
• How students get to school - car, bus, foot
• The attendance of each fifth grade class for one week - displayed
on one graph
• Student’s age and shoe size (data on same graph)
• Student’s height and weight (same graph)
• Daily grades on homework assignments for two weeks
• Favorite soft drink (from choice of three)
• Temperature in your city and temperature in another city for a
two-week period
• Number of students in each grade compared to entire school
F. Give each pair of students data from real-life situations.
Have the students generate a list of decisions to be made about arranging
the data in graphic form. Ask the class to compile a list of different types
of graphs and appropriate times to use each type of graph. Have the
students determine which type of graph would fit their data.
66 Grade 5 Classroom Strategies
3. G. Assign class a data project by groups: Notes and textbook
references
1. In groups of four, write an opinion question. For example,
“Do you prefer Coke™, Pepsi™, or RC Cola™? Do you prefer
Hardees™, McDonalds™, or Wendy’s™? Which team will you
root for - N. C. State, Carolina, or Duke?”
2. Develop a plan to gather data. Decide how many people to
survey. What would be an appropriate sample?
3. After gathering data, organize it and decide how to represent the
information in graphic form.
4. Create the graph.
5. Present graphs to the class and explain to the class why you
chose that type of data display.
H. Have students collect data by hopping on their right foot for
45 seconds, while a partner counts and records the number of hops. Then,
partners change places and repeat the same procedure. After gathering the
data, students list the decisions that the class needs to make to organize the
data into an appropriate display. What have you learned?
I. Continue the activity explained in 4.01 H . Once students
have brainstormed a list of decisions that need to be made when
representing data, they need many opportunities to gather, organize, display
and interpret data. Spend time discussing how to be systematic about
collecting data. If a group of students is working together to collect
information, they need a system for knowing whether or not an individual
has already been included in a data sample. Once a sample group is
chosen, they need a system for making sure that everyone in the group is
included. This might be a good time to introduce the idea of sampling and
making generalizations about larger populations based on a sample. How
does one determine whether or not a sample is representative of a total
If the questions that students brainstormed while working on 4.01 H
need expanding in order to include a wider variety of content areas, this
would be an appropriate time to extend the list of questions.
Grade 5 Classroom Strategies 67
4. Notes and textbook
references
Fifth graders might be interested in comparing themselves to
some AMERICAN AVERAGES. Here are some interesting
data from a book by the same name written by Mike Feinsilber
and William B. Mead.
The average person:
* blinks 25 times a minute
* laughs 15 times a day
* makes 1,029 phone calls a year
* reads 16 books a year
* eats 5 times a year at Kentucky Fried Chicken
* eats 92 hotdogs a year
* eats 4 pounds of food a day
* drinks about 1 bottle of soda a day (12oz.)
* watches 3 hours of TV on an average weekday if 18 or older
* watches 25,000 TV commercials a year if under 18
* spends a day a year in a federal park
The Average American Household:
* has the TV on 45.5 hours a week
* washes 8 loads of clothes a week
* receives 13 letters& bills, 2 magazines, & 4 ads a week
* has 3 family members
How are all these data gathered and analyzed?
J. Research to find the population of five major cities in Canada,
the United States, and Latin American countries. Have students organize the
information and determine how to display data. Then, have students present
information to another fifth grade class.
K. Is one paper towel better than another? What are the criteria
for “better?” Is it strength? Is it the ability to absorb the most liquid? In
working groups, choose a factor and design an experiment to gather data.
Different groups can examine different factors and then share their data in
class presentations.
68 Grade 5 Classroom Strategies
5. L. To help students understand the importance of clear titles Notes and textbook
and accurate labeling of their graphs, display the following and ask references
students to write sentences interpreting the data:
CARS
X X
X X X
X X X X
X X X X X X
X X X X X X X X X
2 3 4 5 6 7 8 9 10
PEOPLE
After students try to interpret the graph, talk about why these labels
are not clear enough. Does the graph describe the number of passengers
who can ride in your car? Does it describe the number of cars people have
brought over the past 10 years? The number of cars in your family? How
people rated a given new car?
M. Have students bring to class a variety of food package labels
to obtain nutritional data. Students are to collect data from the labels
pertaining to calories per serving and fat grams per serving. Fill in the
chart (Blackline Master IV - 1) from the data collected. Students can
determine the amount of fat calories in a serving of each food.
Procedure: Multiply the number of fat grams per serving by 9 (calories
per 1 gram of fat). Students can analyze the data to generalize which foods
are healthier choices in their diet. Categorize foods by the food pyramid
N. Have students watch television for specific hours and specific
stations. Graph the number of commercials per hour. Compare Saturday
mornings from 10-11 AM with Tuesday evenings from 6-7 PM or Friday
nights from 8-9 PM.
Grade 5 Classroom Strategies 69
6. Notes and textbook O. Before constructing graphs, students need to collect data to
references represent in a graph. Having them gather their own data is not only more
engaging than taking already gathered information but also accomplishes
objective 4.03.
Brainstorm a list of questions that students might like to answer
about themselves. These questions might include the following:
• How long is a fifth grader’s standing broad jump?
• How much taller is a fifth grader than a first grader?
• How many fifth graders fit into the principal’s office at one time?
• What is a fifth grader’s resting pulse?
• What is a fifth grader’s exercise pulse?
• What is the typical family size of a fifth grader?
• How many sit ups can a fifth grader do in one minute?
• How many times can a fifth grader jump rope before missing?
• Try to encourage the inclusion of some questions that require the
gathering of data over a period of time. For example, how many servings
of fruit does a fifth grader eat in one week?
Choose one of these questions as a beginning point. Work as a
whole class to plan a strategy for collecting the data in an organized
fashion. Focus on questioning strategies in relationship to gathering
information. For example, it is easier to gather and organize data when
asking “Do you prefer hotdogs, hamburgers, or pizza?” than when asking
“What is your favorite lunch?”
After the class has gathered a set of data, have small groups of
students decide how they would display these data and be ready to justify
their display. As each group explains and justifies its display, some issues
or questions may emerge. Discuss the differences between the displays
and what kinds of decisions that need to be made when creating a display.
For example, What kind of graph will be used (line plot, stem and leaf, bar,
circle, etc.)? How will the graph be labeled? What value will be assigned
to each symbol? This list might become a poster that stays up as a
reminder or kind of self checklist as students continue to create more
graphs.
70 Grade 5 Classroom Strategies
7. P. Have students create charts and graphs showing the data that Notes and textbook
they have organized from activity 4.01 F. On each graph, they could also references
write a sentence that summarizes the information, ask a question, or draw
some kind of conclusion. For example, a group that has charted or graphed
data related to how students get to school might write: “Most of the students
in this class ride a car to school,” or “What might be the effect if the school
buses didn’t run one day?”, or “If the school buses didn’t run one day, half
of our class wouldn’t come to school.” It is more important to discuss cause
and effect statements, like the last example here. Other factors may also
need to be considered. For example, bus riders might walk or get a car ride
with a friend if the buses didn’t run. Cause and effect statements appear in
the media daily. In order to behave like responsible citizens, students need
to recognize and question such relationships. Students might be asked to
find examples of this kind of reporting in the newspaper and bring them in
for discussion.
Q. Additional opportunities for charting and graphing data might
come from organizing collections of various kinds. Bags of bean mix, candy
hearts, M&M’s™, colored paper clips, etc. could be sorted and organized
by color or type. This information could then be used to construct a chart or
graph showing the number of each color, etc. Have students summarize
results. Students might be asked to bring in their own collections for sorting.
R. Have students record the outside temperature each day at 11
a.m. Allow them to organize and display the data weekly as part of an on-
going investigation. Do you notice any patterns in the weather? What
could be a contributing factor - high pressure, low pressure, cold front?
Then, have students write an article for their class newspaper telling what
they discover. Also, ask students to record monthly electric bills and the
average temperature.
S. Have students record the names and ages of people at their
death from an almanac. Direct them to graph their data in a stem-and-leaf
plot. Have a second group of students collect data from current newspaper
obituaries and graph that information. What comments can you make about
each set of data?
Grade 5 Classroom Strategies 71
8. Notes and textbook T. Model for students how to quickly collect data using a stem-
references and-leaf plot. Then help them organize the data (order it) and make
summarizing statements. For example, draw the start of two stem-and-leaf
plots on the board or overhead. Have students estimate the total number of
pages they have read (any books) during the past week. Record their data.
If the first 12 students gave the following numbers as their estimates, your
quick graph would look like the sample on the left: 18 ,6, 9, 4, 15, 21, 19,
37, 28, 24, 33, 15. The data, when organized, would look like the stem-
and-leaf plot on the right.
0 6, 9, 4, 0 4, 6, 9
1 8, 5, 5, 9 1 5, 5, 8, 9
2 1, 8, 4 2 1, 4, 8
3 7, 3 3 3, 7
4 4
5 5
U. Have students keep an hour by hour log for a 24 hour period.
Ask the class to determine categories for their data (sleep, school, eating,
play, and so on). Students need to round their categories to the nearest half
hour or hour (nearest half hour is more precise, but may be very difficult for
some students). Have each child construct a circle graph. (See pages 80 - 85,
a section about creating graphs.) Use these graphs to create a bulletin board
and have students write about their day.
72 Grade 5 Classroom Strategies
9. V. Stem-and-Leaf Plot: (also called stem-plot) is an easy way Notes and textbook
to represent a set of data. A stem and leaf plot works best for data with a references
range of several decades, since the plot is most frequently organized by
tens. For example, here is a collection of data showing arm lengths in
91, 77, 81, 78, 82, 64, 78, 69,
79, 77, 71, 71, 80, 54, 65
To make a stem and leaf plot of this set of data, divide each value into tens
and units. The tens become the “stem” of the plot, and the units are the
54
6 4 ,5, 9
7 1, 1, 7, 7, 8, 8, 9
8 0, 1, 2
91
In this plot, the first line shows one data point in the fifties: 54. The
second line shows three data points in the sixties: 64, 65, 69.
Notice that the leaves in each decade are arranged in order. It is now easy
to see many things. The range is the difference between 91 and 54, or 37.
These data create an interesting pattern with a cluster in the seventies , and
a form of a “bell curve.”
W. Ask the students to bring
in charts and graphs from newspapers
and magazines (USA Today, Newsweek,
Science Digest).
In groups, ask the students to review
the charts/graphs and look for patterns
and trends. Have the groups report
their findings to the class.
Grade 5 Classroom Strategies 73
10. Notes and textbook X. Work with a partner. Roll a pair of dice. Using the attribute
references chart label one circle on the Venn diagram with the attribute listed below
the sum of the dice. For example, if you roll 3 your attribute is odd, 7
attribute - factors of 24, and 8 attribute - multiples of 5. See the chart
below for all the categories.
This activity should be repeated several times. See Blackline Master IV - 2.
Attributes
2 3 4 5
even odd one digit is 3 multiples of 7
6 7 8
factors of 12 factors of 24 multiples of 5
9 10 11 12
one digit is 5 prime multiples of 3 factors of 40
odd factors of 24
7
9 3 2 6 4
11 13 17 8 12
1 24
21 39 23
27 29 37
31 33 5
15 25 32 43
14 16 35 34
22 10 20
26 38
30
18 26 36
40
28 multiples of 5 24
74 Grade 5 Classroom Strategies
11. Y. Roll a die twice to get two of these attributes. If you get the Notes and textbook
same number on the second roll, keep rolling until you get a number references
different from the first. See Blackline Master IV - 3. Use the diagram to
sort the numbers 1 to 20 according to the two attributes you rolled. For
example, if you rolled 1 (odd numbers) and 4 (factors of 100), your
diagram would look like the diagram below. Repeat the above steps two
more times to make two different sortings of the numbers 1 to 20.
Extension: Have students work in pairs and assign the same tasks with the
numbers 20 to 50, 40 to 70, 60 to 90 or 70 to 100.
Attributes
1 2 3
odd even factors of 25
4 5
6
factors of 100 multiples of 4
composites
odd numbers factors of 100
3 7 2 4
9 11 1
19 10 20
13 15 5
17
18 6
16 8 12 14
Grade 5 Classroom Strategies 75
12. Notes and textbook Z. Venn Diagrams provide many opportunities for organizing
references complex sets of information. The relationships among ideas, animals, and
objects can be graphically displayed. A Venn diagram can be used to show
characteristics that are shared and/or not shared. The use of Venn diagrams
can be personalized in classroom activities.
Begin with one idea, for example wearing a watch. Draw a circle
on the chalkboard or a large piece of paper. Label this circle “wearing a
watch.” Explain that students who are wearing a watch will sign in the
circle and those not wearing a watch will sign outside the circle.
After students have responded to the Venn, ask a few simple
Students begin questions about the data. How many students responded to the Venn?
working with Venn What fraction or percent of those who responded were wearing a watch?
diagrams in 1st grade. Suggest that it might be interesting to find out whether more boys or girls
wear watches. Demonstrate how to draw a Venn Diagram that would
generate this information. There are several ways to accomplish this. One
is to have girls sign in one color and boys with another.
wearing a 1234
1234
12345 123456 1234
watch12345
12345
123456
123456
12345
12345
12345
12345
1234
1234
1234
123412345
12345 1234
12345 1234
1234
1234
12345
12345
boys 12345
12345 girls
Another way to gather these data would be to draw two separate circles,
one for boys and a second for girls. Then a third circle is drawn which
overlaps both of these. This diagram creates four areas: A= boys not
wearing watches, B= boys wearing watches, C= girls wearing watches,
D= girls not wearing watches. Of course, if circles are used, there are
some areas in which nothing really belongs, unless something other than
girls and boys (male or female) wear watches. This can be “corrected” by
using rectangles instead of circles. Venn Diagrams can be drawn with
shapes other than circles, although circles are traditional.
A third way to draw this Venn would be to go back to the single
circle and draw a horizontal line separating it and the area around it. Then
label the top half with girls and the bottom with boys (or draw a vertical
line and use left and right labels). Continue posting Venn Diagrams for
student response. Have students brainstorm ideas for Venn diagrams. If a
magnetic board is available, each student could have a small magnet with
his/her name on it to place on each Venn. There may be times when a
76 Grade 5 Classroom Strategies
13. sensitive question is asked. Students could respond in an anonymous Notes and textbook
manner by marking “X” marks or placing a colored circle label in the references
appropriate place.
Provide many opportunities for students to label and organize information
on increasingly more complex Venn Diagrams. After exploring two circle
diagrams, move on to three. How many different ways can three circles be
drawn? Provide lists of categories for students to diagram, for example,
factors of 18 and factors of 24; birds, frogs, plants, and living things; math
papers, playing soccer, and homework; people who travel, pilots, people
who fly in airplanes, and people; sandals, boots, and shoes, etc. Reverse
the process also by supplying Venn Diagrams and asking students to
provide labels.
Venn Diagrams also provide a good strategy for solving problems.
Here is a sample: One day a zoologist spotted 30 animals in the jungle.
Seventeen had fur, 21 had tails, and 2 had neither. Of the animals she saw,
how many had both fur and a tail? By setting up four regions on a Venn
and then moving markers around into the regions until all the information
fits, one can solve this problem. The regions are: A= animals with fur and
no tail, B= animals with a tail and no fur, C= animals with fur and a tail,
D= animals with neither fur nor a tail. If 2 animals had neither, then 30 - 2
= 28 animals that belong in regions A, B, and C. How can 28 be grouped
into these regions so that a total of 17 are in A and C together and 21 are in
B and C together?
GET IT TOGETHER by EQUALS and Cooperative Problem Solving with
Calculators by Creative Publications both contain more problems of this
Grade 5 Classroom Strategies 77
14. Notes and textbook AA. Keep a set of laminated Venn diagram posters like these:
references
On a weekly basis, change the names of the circles and have the students
put their names or the item in the appropriate sets. At the end of the week,
discuss what the diagrams show. Examples:
logo on shirt wearing jeans
10 years old
stories by stories about
women animals
stories about
long ago
78 Grade 5 Classroom Strategies
15. Notes and textbook
4.02 Compare and contrast different references
representations of the same data; discuss the
effectiveness of each representation.
A. Use the class survey sheet from week one of the Week-by-
Week Essentials to gather data on each of your students. Allow students the
opportunity to graph the results for one of the questions using multiple
representations. Note: Let the students spend time grappling with making
these graphs. It is a great tool to help them realize which graphs are good for
which kinds of data. Hold a class discussion on the types of graphs and what
kinds of data are most effectively displayed on them. Discuss pros and cons
for each graph.
B. Ask the students questions to assess their understanding of
this objective. Example: If everyone in our class scores between 90-99 on
the graphing test, would a stem-and-leaf be a good graph to display the
data? (No, since all the data falls on the same leaf.) Which graph would
work well?
C. Each student gets a box of raisins. Estimate, then count the
number of raisins in each box. Put the results of the number of raisins in
each box on a line plot. Use another brand of raisins and repeat the process
except place the data on a stem-and-leaf graph. Use a third brand of raisins
and repeat the process but construct a bar graph. Discuss the three types of
graphs and draw some conclusions about the graphs.
D. Double Bar Graphs vs. Double Pie Charts - (Blackline
Master IV - 4 through IV - 5) Students interpret information from a double
bar graph and use it to create two pie charts. As the students answer the
associated questions, they should find that some information is more easy
to obtain from one form of the graph than the other.
E. Bar Graph vs. Line Graph - (Blackline Master IV - 6)
Students interpret data from a bar graph and use it to create a line graph.
As the students answer questions associated with the data, they should find
that some information is easier to obtain from one form of the data than the
Grade 5 Classroom Strategies 79
16. Notes and textbook
references
4.03 Solve problems with data from a
single set or multiple sets of data using
median, range, and mode.
A. Have students collect data on their heights. Divide students
into groups of three or four. Each group makes an index card set (one card
It is critical that for each person’s height). Color-code the cards; blue markers for boys’
students understand the height cards and red markers for the girls’ cards. Each group works together
difference with to display the cards to determine the range, mode, and median for the boys’
categorical and height data set and girls’ height data set. Each group needs to share its
numerical data before strategies for determining the measures of central tendency and the range.
attempting to find the
median, range and After a class discussion, ask students how the measures and ranges would
mode of a data set. change if a new student (indicate a girl or boy) walked into our class. Allow
Categorical data deals the students to determine what the new student’s height might be to change
with categories or the mode of our data? The range? The median? For example, the teacher
words. For example: may ask the following questions:
data displaying favorite
foods is categorical
since the data is in word • How tall would the student need to be to change the range?
form; pizza, steak, • What height might the student be if the median changed?
enchiladas, etc. • Name a possible height for the new student that would
Numerical data deals change the current mode. Would any other heights work?
with numbers. Since
words cannot be • Have students share their solutions.
subtracted, there can be
no range. Categorical
data can also not have a
median because there is B. Using a county or city map, ask the students to develop multi-
no middle number! Note
step problems related to measurement, graphing, and statistics. Example:
that students may try to
use the y-axis (count) to Compare the number of intersections of streets (roads) in two one-mile squares
find the range and/or on the map.
median. This
misconception needs to
be corrected
immediately when it
C. Pretend that you are a stock broker. One of your clients
would like you to invest her money by selecting a stock from the New York
Stock Exchange. Record the progress of the stock that you selected for ten
trading days. Graph the progress of your client’s stock. Then, write a
report to your client informing her of the stock’s progress including the
range, median, and mode. Was this a good investment? Explain why or
why not.
80 Grade 5 Classroom Strategies
17. D. Survey the class to determine the number of members in Notes and textbook
each student’s family. Students need to define “family” as a class references
discussion. Identify the range, median and mode. Graph data.
E. Using a data chart from your school system or your social
studies book, ask the students to develop multi-step problems related to the
data. Have them work in pairs or groups. Trade problems among the
groups until the students have worked on all the problems.
F. Ask students questions and have them determine whether the
question would collect categorical or numerical data. Example: Numerical -
“How many pets do students in class have?” Categorical - “What kinds of
pets do students in our class have?” Chart the class results for types of
numerical and categorical questions. Be sure to identify and discuss the
measures of central tendency.
G. Collect data for one of each question type, numerical and
categorical. Have students make bar graphs of the data and determine the
mode, range, and median, when appropriate. Be sure students do not confuse
the range of y-axis with the data points.
H. Have students gather sport statistics (i.e., baseball cards).
With these statistics, rank data from least to greatest and determine range,
median, and mode. Sets of data can be plotted and compared using a
variety of graphic organizers which include line graphs to study trends,
bar graphs, and stem-and-leaf plots.
I. Ask the students to bring in information from newspaper
and catalogue advertisements about buying a television. Include the price,
size, length of warranty and other pertinent information. Arrange the data
in various ways so that the students (in groups) can make generalizations.
Establish criteria to help determine the best buy. Discuss measures of
central tendency. Predict which television might be the best seller.
Grade 5 Classroom Strategies 81
18. Notes and textbook Some thoughts on graphing . . .
references
We live in an information age. Rapidly expanding bodies of
knowledge combined with increased uses of technology clearly indicate that
we as adults and the children currently enrolled in elementary grades will
need to be able to evaluate and use vast amounts of data in personal and
job-related decisions.
Skills in gathering, organizing, displaying, and interpreting data are
important for students within all content areas. Graphing activities
incorporate knowledge and skills from a variety of mathematical topics and
integrate geometric ideas with computational skills, and classification tasks
with numeration understandings.
Graphs provide a means of communicating and classifying data.
They allow for the comparison of data and display mathematical
relationships that often cannot easily be recognized in numerical form. The
traditional forms of graphs are picture graphs, bar graphs, line graphs, and
circle graphs. New plotting techniques include line plots, stem-and-leaf
plots, and box plots.
The following discussion is paraphrased and condensed by
permission from the National Council of Teachers of Mathematics from
Developing Graph Comprehension, pages 1-9. Information on newer
techniques is for the teacher’s benefit, since most applications of these
techniques are more appropriate for upper elementary and middle grades
rather than fifth grade.
82 Grade 5 Classroom Strategies
19. Traditional Graph Forms Notes and textbook
references
Bar graphs. Used horizontally or vertically, bar graphs (also called bar
charts) compare discrete quantities expressed by rectangular bars of
uniform width. The heights (or lengths) are proportional to the quantities
they represent. The bars are constructed within perpendicular axes that
intersect at a common reference point, usually zero. The axes are labeled.
Books We Read
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Multiple or double bar graphs are used to compare discrete stratified date
(i.e., data collected from particular groups). For example, when asking
children to vote for their favorite pets, colors, or favorite games to play,
organize the results according to boys’ responses and girls’ responses.
Do you like yogurt?
Yes
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0 Girls Boys Girls Boys
Grade 5 Classroom Strategies 83
20. Notes and textbook
references
Books We Read
Juan
Toni
Sara
Lee
= 2 books
Picture graphs. Picture graphs (pictographs) use the pictures to depict
quantities of objects or people with respect to labeled axes. They are used
when the data are discrete (i.e., noncontinuous). The symbols (ideographs)
need to be the same size and shape. These symbols may represent real
objects (e.g., a stick figure to represent a person or a carton to represent
milk drunk by students) or they may take the form of something more
abstract (e.g., a triangle or square).
In picture graphs without a legend, the ideograph and the item it
represents are in a one-to-one correspondence. When a legend is used, the
ratio of each ideograph to the number of objects it represents must be taken
into consideration when interpreting the graph. Fractional parts of
ideographs (e.g., one-half of a picture) may cause some difficulties for
children. Data presented in picture graphs are usually appropriate for bar
graphs. Converting picture graphs to bar graphs is one way to help
children move from semiconcrete representations of data to more abstract
forms.
84 Grade 5 Classroom Strategies
21. Line graphs. A line graph (broken-line graph) is used to compare Notes and textbook
continuous data. Points are plotted within perpendicular axes to represent references
change over a period of time or any linear functional relationship. The
labeled axes intersect at a common point, usually zero. The units of division
on each axis are equally spaced, and the graphed points are connected by
straight or broken lines. When children keep a record over a period of time
of their own height or weight, of the daily average temperature, and so on,
line graphs are appropriate displays.
Multiple line graphs are used to compare two or more sets of
continuous data: for example, to compare the heights or weights of two
children over a period of time (e.g., four months or one year), or the heights
of two (or more) plants over a period of time (e.g., one to two months after
planting seeds).
Absences from 10/6 to 10/14
6 •
4 •
3 •
2 • •
1 • •
Mon. Tues. Wed. Thur. Fri. Mon. Tues.
Grade 5 Classroom Strategies 85
22. Notes and textbook Circle graphs. The area of the circle graph (pie graph, pie chart, area
references graph) is divided into sections by lines emanating from the center of the
circle. Circle graphs are appropriate when children have an understanding
of fractions; they provide children with a means of displaying the
relationship of parts to whole.
86 Grade 5 Classroom Strategies
23. Children may create circle graphs informally before they are able to Notes and textbook
measure angles and figure proportions. For example, counters representing references
the total units are evenly spaced around the circle. When the divisions
occur, a radius is drawn to divide the circle into appropriate parts. A
second informal method is to mark units on a strip and then loop to form a
circle, drawing radii as appropriate.
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Grade 5 Classroom Strategies 87
24. Notes and textbook
references
88 Grade 5 Classroom Strategies