Hands-on Activity: Growth and Graph
Standard : K (K-2)
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Brief
Students visit second- and fourth-grade
classes to measure the heights of older students using large building blocks
as a non-standard unit of
measure. They also measure adults in the school community. Results are
displayed in age-appropriate bar graphs
(paper cut-outs of miniature
building blocks glued on paper to form bar graphs) enabling a comparison of
the heights of different age groups. The activities that comprise this
activity help students develop the concepts and vocabulary to describe, in a
non-ambiguous way, how heights
change as children age. This
introduction to graphing provides an important foundation for creating and interpreting
graphs in future years.
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Real World Connection
Measuring and graphing are important skills
used in all engineering disciplines . When engineers design houses or cars or
bicycles, they need to know the likely shapes and sizes of the people who
will be using those structures, vehicles or products . Making graphs enables
engineers to look at lots of data at once, in order to see averages, trends
and patterns.
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Project Objectives
After this activity, students should be able to:
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Measure heights in a non-standard, age-appropriate way, such as by
using building blocks instead of rulers.
·
Display data in the form of pictorial bar graphs.
·
Interpret bar graphs.
·
Describe how the heights of
children change as they age.
Required
Resources
·
long building blocks , about 10 inches long; one for every two students
in the class
·
medium building blocks , half as long as the long blocks above; one for
every two students
·
15-30 sheets of construction
paper (preferably all the same color)
·
glue, for student use
·
poster board, several sheets, either all one color, or four different
colors, one for each age group
·
markers and pencil
·
paper cutter or scissors
·
ruler
Introduction
(Gather the class together and remind them of
the discussion that was held after they measured each other using building
blocks. Point out the list of student heights that was obtained during that
discussion.)
I know a way to show all that information in a
special type of picture called a graph. Who has heard of a graph? (Listen to
student responses.) Where have you seen a graph? How was it used? What did it
tell you?
Graphs are very useful because they let people
share or learn about a lot of information in a quick and easy way. Today, you
will help me make a large graph of your heights.
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Have a Glance
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Time Required : 180 minutes
Group Size : 2
Activity Dependency : How Tall Are We?
Subject Areas : Life Science
Measurement
Number and Operations
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Procedure
Before the Activity
Create and make copies
of a data sheet
for each student
to use when visiting the other grade classrooms to record the names
and heights of a second grader
and a fourth grader, and provide
space to make tally marks as they measure the older students.
•
Prepare about 500 construction paper rectangles, all sized -1 x 3--inches, for students to use, with
glue, to make bar graphs. It helps to use a paper cutter to make this easier. The exact
size does not matter but make them similar
in proportion to the building blocks
being used and an easy size
for students to handle. Since construction paper measures 9 x 12-inches, 1 x 3-inche
rectangles are easy to mark off and cut (1½ x 4-inch rectangles are also easy,
but require more construction paper). The exact number of rectangles needed
depends on the class size.
Use a meter stick and pencil to lightly draw vertical
lines about every three to four inches across the sheets of poster board. Draw
one vertical line for each student in the class, and write a different
student's name al the bottom of
each of line. The vertical
lines make ii easier for students lo glue the rectangles neatly
onto the poster
board into bar graphs.
Use the wider spacing if your rectangles are the larger size. This way, when
students glue down the rectangles, they can line up the pieces along the
vertical lines to keep the graphs from leaning
or becoming too crooked.
A week or two in advance, recruit a dozen or so adults to
visit your class and be measured by your students. These might be parents,
administrators, librarians, janitors or counselors-anyone who can spare a few
minutes. Try to get both men and women, and include yourself. It is best if all
the recruited adults visit the class at the same time, but if not, schedule
over several different days and times.
• A few days in advance, arrange
times when your class can visit a second-grade
class and a fourth-grade class.
It works best if you determine
in advance which pair of kindergartners will measure the
heights of which two older
students in each class.
OVERVIEW:
During the course of several days, students will:
•
As a class activity, create a bar graph that shows all the
heights of the students in the class. This is accomplished by students gluing
pre-cul rectangles, resembling the measuring
blocks students used, onto lined
prepared chart paper.
• Visit second-grade and fourth-grade classes lo measure
the heights of those (older)
students.
• Measure the heights of several adults
recruited from the school community.
• As a group activity,
create bar graphs
that compare the heights of second-graders, fourth-graders and adults.
Part 1: Making a Class Graph
1) Show the class
the already-prepared poster board and rectangles. Place the poster paper on the floor or a table so that
ii is flat. Then, using the
actual data for one student, show
how you can line up the rectangles on end, one above the other, to represent
that student's height. Do not glue those rectangles down. Also point out how to use
the vertical lines drawn on the poster paper lo keep the line of rectangles straight,
and that you placed the rectangles on the line marked with the name of the student
whose data you chose.
2) Explain that each
person's task is lo glue rectangles on the poster board to show his or her height, using the vertical line above his or her name.
Then, remove the rectangles you
used for demonstration and let
students begin creating and gluing down
their own graphs. To avoid
congestion, do this as a center activity in which groups of three rotate through.
Part 2: Measuring Second and Fourth Graders
1) Explain to students that ii would be fun to
visit some other classes and see
how tall some older students are. Explain that you have arranged
visits to a second-grade and a fourth grade class. Ask students: How do
you think the heights of these older students will compare lo your heights?
When students say they think the older students will be taller, ask them how much taller.
Students may use their arms to demonstrate, but ask them how many blocks
taller they think each group will be. Record their
predictions on chart
paper or the classroom board.
2) Next, explain
that this lime, students will work in pairs to measure two second-graders and two fourth-graders. This way, one kindergartner can work as the tally marker while the
other does the block measurement. Suggest that they trade jobs
each lime they measure a new student.
3) When you return to your own
classroom, ask the class how their measurements
compared to the predictions recorded earlier.
Part 3: Measuring Adults
1) On the appointed
day (or just before the first of the adult visits), ask the class how many
blocks tall they think adults are, compared to their heights. As before, record
their predictions.
2) As the adult recruits
visit the class to be measured,
record their names and heights
on the large data sheet
prepared in advance.
3) As the data comes in, compare
the actual adult
heights lo the student-predicted heights.
Part 4: Graphing Older Students and Adults
1) Using the poster
boards prepared in advance, have students glue on rectangles to represent
the measured second-grader
and fourth-grader heights. These should be made in the same manner
as the
graphs of their own heights. Again, do this as
a center activity.
2) Likewise, assign individual students to glue bars
representing the adults onto the poster board prepared earlier for the adult height graph.
Part 5: Discussion and Investigating Questions
1) Display all four
completed graphs in a row, ordered from the youngest to the oldest age groups.
Ask students to comment on what they observe about the graphs. Expect their
first response to be: as people get older, they get taller. Then
ask questions lo focus
their observations, such as:
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Do you see a big difference between the heights of kindergartners and the heights of second graders?
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Do you see a big difference between the heights of kindergartners and the heights of fourth graders?
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What about the difference between
second and fourth graders?
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What about the difference between
kindergartners and adults?
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Are all kindergartners the same height? What about all second and fourth
graders?
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Do you see a difference between the heights of boys and girls in each
class? (Expect not much height difference between genders, or possibly giris
may be slightly taller on average.)
·
Do you see a difference between the heights of men and women in the
adults?
2) Real-World Engineering Connection: Explain that the way students just spent some time carefully
examining all the measurements and graphs they made is similar to how engineers
look al the data they collect and the graphs they make, looking for
comparisons, averages, trends and patterns. II is how engineers figure out what
sizes to make everything from
skyscrapers to doorways,
car seats, bicycles, phones and shoes.
3) Next, explain
that there is a more exact way to talk about the differences between the
heights of the four age groups. Starting with the kindergartner poster, ask
who is the shortest person in the
class. At the bottom of the chart
paper, write down that
student's measurement. Then ask who is the next taller student. Write down that student's measurement directly above the first's. Continue putting the student heights
in order from shortest lo tallest.
4)
Then explain that you are going to start crossing off
heights two at a lime, by crossing off the shortest and tallest together. Then
cross off the second shortest and second tallest together, and continue
crossing off pairs of measurements until only one or two measurements in the
middle of the list remain. Explain lo the class that since you have crossed off
all the short and tall students, you now have the middle-sized kindergarten
height remaining. (In mathematical terms, you have determined the median
height, but avoid using this term with young children; "middle-sized"
is a term they can understand and serves just as well.)
5)
Repeat the same procedure for the second-grade class.
Point out that you can now easily compare the heights of middle-sized
kindergartners to middle-sized second graders. For example: A
middle-sized kindergartner is 4
blocks tall, and a middle-sized second
grader is 4½ blocks tall. So a second
grader is one-half a block
taller than a kindergartner."
6)
Do the same for the fourth grade class and the adults. By
having them compare the heights of the different age groups using numbers
(quantitatively), you are helping them develop both number sense and an
understanding that numbers can be used to help describe and compare things of
interest.
Safety Issues
•
Students may need to
stand on chairs or tables to measure adults, so be sure to monitor this
activity closely.
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Watch that students who
are easily angered or frustrated do not use the large building blocks to harm
others.
Troubleshooting Tips
Water hotter than 122° F
or 50°C may kill the yeast.
Notes to teacher.
·
Sample A involves
physical change of sugar dissolving.
·
Sample B (Alka-Seltzer)
contains a non-living chemical reaction.
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Sample C (yeast) contains
a living chemical reaction. This should be a long term reaction.
Assessment
Summary
Assessment: To assess whether
students are now able to independently use non-standard methods of measurement,
ask them to measure the heights of several objects in the classroom. This
time, have them use smaller
building blocks to
measure objects such as a book,
teddy bear or doll and paint brush.
See if they are able to show their results in the form of a bar graph by having them use
paper cut-cuts of the blocks (prepared
in advance, or else use existing toy blocks,
such as LEGO bricks) to create bar graphs that compare the
measurements of the various objects.
Activity Extensions
Conduct a similar
exercise with home-grown seedling plants by having students use stacking 1-inch
cubes (such as Unifix cubes) to measure the heights of growing plants over a
period of weeks. Have students plant bean or zinnia seeds according to package
directions, using 16-cunce plastic drinking cups with drainage holes made in
the bottoms. Use a good quality potting soil, and make several extra plantings
in case some seeds do not germinate. Keep the pots moist but not soggy, and
leave them in a sunny window.
Once the seedlings are
about two inches high, have students measure the heights with Unifix cubes
every three or four days. Provide data sheets for recording the height
measurements and the number of days since planting. Provide a large calendar
with the planting day prominently marked to help with this data collection
procedure.
After a few weeks, when
the plants reach full height, have students create bar graphs showing how their
own plants grew each time they were measured.
In a follow-up
discussion, be sure students realize that like humans, plants grow steadily at
first, and then their growth slows or even stops. Unlike humans, however, many
plants keep growing indefinitely, as long as they have enough nutrients and
water and remain disease-free. Trees are a familiar example.
