Heavens above!

Transcription

Heavens above!

Heavens above!
K-8 Astronomy and Physics course
3rd Module – Let’s observe more carefully
Following up more and more systematic and accurate observations, students will eventually
correlate two different quantities.
Users: Third Grade Students. Total amount of time: 20 hours. Teaching proposal and
educational material, cards for students.
Introduction
This Teaching Unit is addressed to third grade students. It is intense as far as both methodology
acquisition and concept learning.
As a matter of facts, students will definitely acquire the basis of the scientific method, i.e. observation of
phenomena, in this case, of celestial phenomena. Moreover, they will acquire or consolidate important
Astronomical concepts. For example, the Sun’s diurnal arch, the local midday… Others can be found in the
table, which summarizes the entire Module. Besides, they will learn how to get their bearings and they will
consolidate the concept of measure in Physics. Students will also acquire particularly important skills, such
us know how to compare quantities and measures, which are recorded at different times or by other
people.
In the second part of the module, since T.U.3.3, students will understand, that it is necessary to introduce
conventional straight lines, in order to get one’s bearings. This will come straight from observations
concerning the Sun. Observations of the Sun will lead students to a fundamental discovery, too. Day after
day, neither the Sun rises from the same point, nor it rises from the East point, as many schoolbooks
teach. Moreover, its diurnal arches are different from day to day. These are important and not so easy
steps for children. Therefore, it is important to keep students’ attention from wandering, and to try to
focus it on the main aims of the hands-on activities.
The expected time is around 20 hours. It has to be spread out over the full school year, because students
will observe long-period changes. This one, as well, is a hard point for students to deal with. In their
everyday life, as well as in their school life, they are used to short-time results and quick answers. This
experience is therefore focused on “knowing how to look and what to look for and waiting for the answer”.
If it is carried out properly along the year, it represents an important “conquest” for students, from a
formative point of view.
Since it is spread out over the full year, it is a long module. We therefore suggest the teacher, to carry
out more learning evaluation tests and concept consolidation games. This is meant for keeping students
from loosing information and concepts.
Another way for catching students’ attention and interest is through instrument building, such as easy
sundials. These moments are useful both for consolidation and catching-up. There are other ways for
catching students’ interest, like visiting a meridian line, which is particularly interesting from a historicaltown planning point of view, or direct observation of the Sun, through a modest telescope.
Posters, collection of drawings, images done by students are important to synthesize the hands-on
activities, which have been carried out, and to focus students’ attention on the concepts they learned.
Teachers are supposed to interfere as less as possible in children’s productions.
The “Night Under the Stars” starts teaching how to get one’s bearings by means of Polaris (in this
case, it is necessary to look for a dark area, in order to carry out better star observations). The
fundamental constellations, which are supposed to be observed, are the minimum set for getting one’s
bearings, for example the two Dippers and Cassiopeia.
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What some of the teachers, who tested this module, think about it
“I would like to point out children’s motivation and interest, for the hands-on activities, which were
always high. Keep in mind, that the hands-on activities required a kind of work (data recording), which
was often repetitive, and which could have lowered the motivation.
Moreover, with a certain satisfaction, I noticed, that, what children acquired lasted long, and in a precise
and effective way, because hands-on activities were involved (it is important to learn while doing).”
“It is important to start with the hands-on activities at the beginning of the school year, in order to have
enough time to carry it out carefully, and in order to exploit the potentialities of the module. I think that
at least the last T.U. can be carried out in the next grade; it could fit well the teaching program.”
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3rd Module Scheme, First part
3rd MODULE
Let’s observe more
carefully
TEACHING UNIT
3.0 Let’s observe
the Sun and the
shadows
Aims:
To teach students
methodic and
systematic observation
of celestial
phenomena, in order
to have a better
understanding of the
surrounding reality,
starting from simple
phenomena in
everyday life.
To acquire some
concepts, which are
fundamental from an
astronomical point of
view.
To correlate two
different physical
quantities.
CONTENTS
To know how to relate the position and
the length of the shadows over a day, to
the corresponding Sun’s position above Shadows over a day.
the horizon.
Sun’s position above
To learn how to formulate hypothesis, the horizon.
starting from examination of observed
phenomena.
To learn how to fill in tables.
3.1 How shadows
change over one
year
To know how to compare the position
Shadows on different
and the length of the shadows on
days.
different days.
To know how to choose, among different
objects, those which allow for sharper
shadows.
3.2 How the Sun’s
position above the
horizon changes at
the same time over
one year
Diffraction.
To know how to compare data about
Sun’s height above the horizon and
temperature, recorded on different days. Shadows on different
days.
To acquire the concept, that the Sun
Sun’s position above
does not rise always from the same
point.
the horizon.
To acquire the concept, that the Sun Different Sun’s diurnal
seems to draw different arches on arches.
different days.
To introduce the concept of scientific
hypothesis to students.
To consolidate the
concept of unit of
measure.
To rationalize some
astronomical and
geographic concepts.
OBJECTIVES
3.3 Local meridian
and local midday
determination
To learn how to get
one’s own bearings.
3.4 Conventionality
of midday
To define the fundamental points in
North-South direction.
To introduce the concept of local
meridian.
Local meridian.
Local midday.
Sun on the meridian.
Range of time.
Conventionality of
To acquire the concept that midday is a midday.
moment in time, which depends upon the
site, from where it is determined.
Comparison among
“middays” in other
To acquire the concept that the “day” is
towns.
that range of time, which elapses
between any two successive “shortest”
Range of time.
shadows.
To understand that the local meridian by
itself is not enough to determine the
position of a point on a surface.
3.5 North-South
East-West
East – West Axis and its
To acquire the idea that it is necessary to conventionality.
introduce another straight line, which is
conventional with respect to the first Geographic quadrants.
one.
To consolidate the relativity of the
positions among two or more bodies.
To determine univocally the position of a
point on a flat surface.
Cardinal points.
3.6 Let’s get our
bearings: the
cardinal points
To be able to build, and to know how to
use, a geographic grid for a flat
surface.
Geographic grid.
Methods for getting one’s
bearings.
To introduce the concept of geographic
grid on the Earth’s surface.
The Night Under
the Stars
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3rd Module Scheme, Second part
TEACHING UNIT
3.0 Let’s observe the Sun
and the shadows
EDUCATIONAL
MATERIAL
Sample card for carrying
out the activity.
MATERIAL FOR
STUDENTS
Sample card for data
recording.
EXPECTED TIME
3 hours
Sample card for learning
evaluation
3.1 How the shadows
change over one year
3.2 How the Sun’s position
above the horizon changes
at the same time over one
year
3.3 Local meridian and
local midday determination
3.4 Conventionality of
midday
out the activity.
out the activity.
evaluation.
out the activity.
Sample outline.
Sample card for data
recording.
4 hours
Sample outline.
Sample of a graph.
Sample outline.
2 hours
2 hours
evaluation.
out the activity.
Sample outline.
Instrument
construction card (the
nocturnel).
2 hours
out the activity.
3.6 North-South East-West
evaluation.
3 hours
Alternative sample card for
learning evaluation.
3.6 Let’s get our bearings:
the cardinal points
The Night Under the Stars
out the activity.
evaluation.
Plan for the night: “The
darkness gets our bearings”.
Instrument
construction card.
2 hours
2 hours
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Teaching Unit 3.0
“Let’s observe the Sun and the shadows”
The aim of this Teaching Unit is to provide students with, or to consolidate, some skills related to
temperature measurements. Moreover, it introduces students to Sun’s observation, starting from
shadows. With “shadow” we mean that particular phenomenon, which occurs when a beam of light hits
an object.
Contents
Shadows over a day, Sun’s position above the horizon.
Objectives
To know how to relate the position and the length of the shadows over a day, to the corresponding Sun’s
position above the horizon.
To learn how to formulate hypothesis, starting from examination of observed phenomena.
To learn how to fill in tables.
Glossary
Horizon, shade, penumbra, sharpness, orientation.
Required time
Two hours on the whole on the entire day, in order to collect four data.
One hour for the graph and the discussion.
Needed material
A sunny day.
A window, which allows for observing and recording the Sun’s position above the horizon, for at least 4
times during an entire day.
An object, of which you can study the shadow.
Some transparent glass vases, water, ink.
Thermometers.
Procedure
Part A: correlation between the Sun’s position above the horizon and the temperature.
1.
Start with an activity about how to use a thermometer, which allows for questions to be raised, too.
These questions will be answered further on. Every child has to fill in a transparent glass vase with a
liquid (we suggest to use liquids, having different colors: water, ink…). Have students measure the
temperature at the beginning of the activity.
2. Expose the vases to Sun’s light for a determined amount of time. Have students measure their
temperature again. It is good to do it again and again, exposing the vases for longer and longer times.
Every child has to choose how to collect data for his/her experience. Be careful at the way students
carry out their measurements. It is useful to have more than one thermometer, in order to collect
data. For this reason, before starting the hands-on activity, check that students measure the
temperature under the same conditions.
Picture 3.0.1 – The beginning of the hands-on activity: measurement of water temperature.
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3.
Choose the window, from which to observe the Sun. Then fix the position, form which observations
will be carried out.
Picture 3.0.2 – While observing from the window. Children’s eyes are protected by a welder’s helmet with a filter plate.
4.
Discussion about which conditions have to be met in order to compare data, which are collected in
different times (for example: the observer’s feet have to be always in the same position, the head
must not move, etc.). Draw a horizontal line on the window: it will be considered as the reference line
for all the measures. Record the Sun’s positions, by sticking little pieces of colored tape on the
window. At least four data have to be collected on the entire day.
Picture 3.0.3 – Data recorded on the window, are copied on a sheet of glossy paper, using the horizontal line as a
reference line. They will later be compared with other data.
Part B: Sun’s height above the horizon and length of the shadows
5.
Choose an object and observe its shadow. (We suggest that this object remain in the same position
inside the classroom. It can be, for example, a leg of a desk, a window jamb…). Have students
observe the features of the shadow and have them draw it. Their drawings have to be as close as
possible to the observation, which was done (sharp, blurred, slightly colored shadow…).
Picture 3.0.4 – Shadows cast by different objects.
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6.
At the same times, in which students observe the Sun’s position above the horizon, they have to
record the length and the features of the shadow (they can measure the length in number of tiles).
We suggest to use a table (recording card) to record the data.
Picture 3.0.5 – Sample of filled-in table.
7.
Plot the data in a XY graph: use time in the X-axis, and length of the shadow in the Y-axis
(Pic.3.0.6.a), b)).
a)
b)
Picture 3.0.6 – Different graphs for representing the same relation: the Sun’s height above the horizon and the length
of the shadow.
8.
Discussion about the graph. Students are supposed to answer to the following question: the higher
the Sun, the more …… the shadow.
Didactic-methodological suggestions
Remember that students’ eyes must be protected by a welder’s filter plate, shade 14.
The Teaching Unit, about the colored shadows (2nd module, “The colored shadows”), can be either
carried out at the beginning of this module, or it can be considered as a consolidation time. It allows for a
lot of concepts to be highlighted, just like the one of penumbra, which is usually hard to understand.
The time needed for the evaluation test is usually around 60 minutes.
a)
b)
Picture 3.0.7 – Because of difficulties students met, they have been asked to fill in the evaluation card twice. The
second evaluation card was given to students, after they carried out shadow observations more carefully. The same
student filled in both the evaluation cards above.
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Teaching Unit 3.0: “Let’s observe the Sun and the shadows”
Concept consolidation game
A lamp can replace of the Sun. By raising or lowering it, we can obtain shadows having different lengths.
Students are not supposed to see the lamp. A starting situation is set up, and by looking at the shadows,
students are asked if the lamp was raised or lowered, with respect to the starting position. It is a team
game. One team either raises or lowers the lamp, the other one guesses, if it was either raised or
lowered. If the guess is right, the team earns one point, and it is its turn to move the lamp.
Picture 3.0.8 – In this class, at the end of the consolidation game, conclusions have been written down.
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Recording card
(for students)
Observation date………………….
Sun’s distance
from the horizontal
line
Length of the
shadow
Characteristics of
the shadow
Drawing of the shadow
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Evaluation test
1.
Mark your answer (or answers) with a cross on the box on your left.
q
q
q
The higher the Sun above the horizon, the longer the shadows.
The lower the Sun above the horizon, the longer the shadows.
The length of a shadow does not depend upon Sun’s height above the horizon.
2. Draw the shadow of the house, taking into consideration the position of the Sun.
a)
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Evaluation test
Draw the shadow of the house, taking into consideration the position of the Sun.
b)
End of Teaching Unit 3.0
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Teaching Unit 3.1
“How shadows change over one year”
This Teaching Unit is an extensive work, because it takes place throughout the entire year. It is important
because, it is students’ first time to carry out observations, which last long. Students are supposed to
draw their conclusions only at the end of data collection.
Contents
Shadows on different days, diffraction.
Objectives
To know how to compare the position and the length of the shadows on different days.
To know how to choose, among different objects, those which allow for sharper shadows.
Glossary
Diffraction, shade, penumbra, graph.
Required time
Around four hours: one for each one of the three observations (we suggest to carry them out in the first
school months: October, November, December) and one for a graphic representation and a final
discussion.
Needed material
Different objects, which cast shadows, among which children themselves.
Sheets of wrapping paper.
Procedure
1.
Begin with shadow observation over one year. In order to do that, divide students into groups; each
group has to choose one object. If it is possible, objects have to be different as far as dimensions and
shapes. Among the objects, we suggest to use a child, too.
a)
b)
c)
Picture 3.1.1 – Three objects, which were chosen by a class: the globe, because students had just looked for a new
classmate’s origin state, the cube, as a geometric ruler, and the package, because at the beginning of the school year,
every child’s wishes were put inside it.
2.
3.
Discussion, about the way the hands-on activity should be carried out: students have to agree upon
the methodology: every group has to choose a position, which has to be the same for the entire
activity. Choose the observation days (we suggest to carry out three observations during the first
school months: October, November, December) and the observation times (three over one day: one
in the morning, as soon as students get to school, one at noon and the last one before leaving). They
have to be the same for all the groups. If it is not possible, observations can be carried out in the
morning. In this case it is important to start formulating hypothesis about what will happen in the
afternoon.
Every group makes a table for data recording (Recording card), on which it can write observations
about the different kinds of shadows, too.
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4.
The object, which each group chooses, has to be placed on a sheet of wrapping paper. Have students
draw the outline of the shadow, which is cast.
a)
b)
c)
Picture 3.1.2 – Different times of the work: a) students are drawing the shadows; b) the outcome of the three
observations over a day; c) comparison of the shadows, which were drawn at the same time, but on different days.
The shadows of a pen and of a child were drawn.
5.
Have students collect data and have them write them in a table (Recording card).
Picture 3.1.3 – Sample of filled-in table.
6.
7.
8.
Have students make a drawing, about the motion of the shadows (see picture 3.1.2.b).
Discussion about the data, which students collected. Since each group observes a different object, it
is important that the discussion is a joint discussion, and that the teacher collects data in one poster.
It has to contain the image of the objects used and the shadows they cast, too.
The discussion has to be focused on the differences among the shadows (sharpness, blurred outlines,
due to diffraction on the edges of the instrument). Determine under what conditions, the best
shadows are cast, for a better development of this activity.
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Teaching Unit 3.1: “How shadows change over one year”
While carrying out the activity, take into consideration the legal time, otherwise the length
of the shadows, time being equal, can no longer be compared.
As far as diffraction, do not try to explain it starting from light models, because it is a difficult concept.
What you are supposed to do, is to provide students with an operative definition. It can come out from a
discussion about the shadows, which students observed in the game (in place of the hole, diffraction
circles appear) or from other examples (for an in-depth study, see Hewitt, Conceptual Physics).
A lot of other activities, close to this one but often very complicated, can be carried out by using
angles and other measures. It is good to keep in mind children’s age: whatever activity, which involves a
major abstraction, can be useless if not counterproductive.
There is no evaluation test, just an outline card for the end of the year. It has to be used as a
summing-up and consolidation means about the entire activity. As a matter of fact, it helps students
highlight the most important concepts. It is students’ first time ever conceptualizing long time
experiences.
Picture 3.1.4 – Sample of filled-in outline card: it is used as a summing-up and consolidation means concerning the
entire activity.
Concept consolidation activity
Cut a circle out of the center of a piece of thick cardboard. The hole must be 0.5-1 cm in diameter.
Illuminate the hole by using a lamp, and discuss about the shadow, which is generated. What does it
appear on the other side of the hole?
Ask the following question: if it were Sunlight, which illuminates everything, how would we have to place
ourselves in order to cast shadows? How does this shadow look like, if compared to the ones of the
objects, which we used previously?
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Recording card
(for students)
Month
Time
Day
Characteristics of the shadows
Drawing
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Outline
Observe the table you have filled in and think about it:
What happened to the shadow? Did it move? In what direction? Did it become longer? Did it become
shorter?
Did it become more or less sharp?
Now fill in the lines below by writing your considerations:
On the same day, but at different times, the shadow of the object you chose is:
…………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………
On different days, but at the same time, the shadow of the object you chose is:
…………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………
Come to a conclusion: what do you think it will happen if you were to carry out the same observations
again in March?
…………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………
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Teaching Unit 3.2
“How the Sun’s position above the horizon changes
at the same time over one year”
This Teaching Unit provides students with a first understanding of correlation between two quantities, and
it goes on with the hands-on activity, which began in the former units. Its importance lies in the
acquisition of a correct methodology for carrying out works. It can be carried out together with the
previous T.U., if attention is paid to the fact that a lot of variables are involved.
Contents
Shadows on different days, Sun’s position above the horizon, different Sun’s diurnal arches.
Objectives
To know how to compare data about Sun’s height above the horizon and temperature, recorded on
different days.
To acquire the concept, that the Sun does not rise always from the same point.
To acquire the concept, that the Sun seems to draw different arches on different days.
To introduce the concept of scientific hypothesis to students.
Glossary
Hypothesis, data reduction, reference line.
Required time
Around one hour for three days, one more hour for the final data reduction.
Needed material
Colored tape.
Thermometers.
Procedure
1.
2.
3.
Repeat Part A in T.U. 3.0, more times over the school year, with one-month intervals, using the same
modalities. Students have to record the Sun’s position, and they have to measure the Sun’s height
with respect to the reference line, drawn on the sheet of paper. At the same time, they have to
measure the temperature on the observation windowsill, too. Data concerning the height and the
temperature can be organized into a table, which has to be brought up-to-date every month. It will
be used to build a graph, just like the one in picture 3.2.1.b.
Ask students what will happen on the next month: students are asked to formulate hypothesis, about
which every time a discussion is carried out.
Every datum is collected on the same sheet of paper (see picture 3.2.1)
a)
b)
Picture 3.2.1 – Sample of the work, which was carried out. a) Sun’s positions: different colors stay for different days.
b) On the right: a first graph.
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4.
5.
6.
7.
Every student is supposed to make a graph representation for each observation day: plot time on the
X-axis, and Sun’s height and temperature on the Y-axis. Sun’s height and temperature should have
different colors (see picture 3.2.2b).
Final discussion. From the data and from a comparison between the graphs, it comes out that, on
different days, the Sun seems to follow different paths. What we mean is that the Sun does not rise
always from the same point, and the higher the Sun above the horizon, the higher the temperature,
the shorter the shadows.
Have students make three XY-graphs on a sheet of glossy paper: they are supposed to put time on
the X-axis, and Sun’s positions and temperature on the Y-axis.
Final discussion. Have students overlap the three graphs and draw their conclusions… On different
days, the Sun seems to follow different paths. What we mean is that the Sun does not rise always
from the same point, and the higher the Sun above the horizon, the higher the temperature, the
shorter the shadows.
a)
b)
Picture 3.2.2 – Sample of the outcome of the final discussion. It points out a problem, which was not taken into
consideration at the beginning: the season change can cause problems! On the right, a graph representation of the
data collected.
Remember that children’s eyes must be protected by a welder’s filter plate, shade 14, when
looking directly at the Sun.
It is an important time for children, because they are asked to formulate hypothesis. They will later be
confirmed or rejected, depending upon the observation outcomes.
We suggest to carry out observations in October, November and December, and to observe three times
over a day: in the morning, as soon as students walk in, around eleven and before leaving from school.
It is better to give students an outline, in order to systematize fundamental concepts, and an
evaluation test.
This activity provides an enhancement of the fact that the higher the Sun above the horizon, the higher
the temperature, which we measure on Earth. In order to do that, we need a piece of thick cardboard,
with a hole in the center, a thermometer and a dark sheet of paper. The activity is supposed to be carried
out in three different times over a day, at two hours intervals.
Lay the dark sheet of paper on the ground. Hold the thick piece of cardboard with the hole, so that it is
parallel to the ground. Put the thermometer in the middle of the bright spot, which the Sun generates.
Measure the temperature.
Students are supposed to make a table with the data collected, and a graph. Final discussion about the
outcomes.
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Teaching Unit 3.2: “How the Sun’s position above the horizon changes at the same time over
one year”
Outline
(for students)
In order to sum up the notes you took during the lesson, fill in the lines below, by observing
your table and your graphs.
On the same day, but at different times, the Sun is (with respect to the horizon)
…………………………………………………………………………………………………………………………………………………………………………
and the value of temperature you measured is
…………………………………………………………………………………………………………………………………………………………………………
On different days, but at the same time, the Sun is (with respect to the horizon)
…………………………………………………………………………………………………………………………………………………………………………
and the value of temperature you measured is
…………………………………………………………………………………………………………………………………………………………………………
Come to a conclusion: what do you think it will happen, if you were to carry out the same observations
again in March?
…………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………………………………………
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one year”
Hint for the draft of the graph
Corresponds to 1 cm
-
Sun’s height with respect to the reference line
Corresponds to 1°C
-
Outside temperature
time
Month
time
time
time
Month
time
time
time
Month
time
time
20
one year”
Evaluation test
Mark your answer (or answers) with a cross on the boxes on your left
1. On different days, the Sun:
q seems to follow different paths in the Sky.
q seems to follow the same path in the Sky.
2. Can these two drawings represent two times on the same day?
Explain why.
……………………………………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………………………………
3. You carried out some observations in class. Make a drawing of the one, which struck you the
most.
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Teaching Unit 3.3
“Local meridian and local midday determination”
The length of the shadow cast by an object is the shortest at a certain time. This T.U. deals with the
determination, through observation, of that time of the day. Day after day, the shortest shadow cast by
an object lies always on the same line. This T.U. allows for confirming this phenomenon, too.
Contents
Local meridian, local midday, Sun on the meridian, range of time.
Objectives
To define the fundamental points in North-South orientation.
To introduce the concept of local meridian.
Glossary
Meridian, meridian line, local meridian, gnomon.
Required time
2 hours on the whole, in the entire scheduled time.
Needed material
Colored felt tip pens.
Blackboard rulers.
Procedure
1.
2.
Choose the position, from which observations will be carried out, and the observer’s position. Lay a
sheet of wrapping paper on the ground.
Choose one student, who will be the object (or you can choose a more sophisticated gnomon). Have
him/her stand on the sheet of paper and follow the shape of his/her shoes with a felt tip pen. This
allows him/her for taking the very same position on the next days.
a)
b)
Picture 3.3.1 – While choosing different gnomons for data collection.
3.
4.
Have students trace the outline of their schoolmate’s shadow at least four times over a day, and have
them write the hour by it, in which this datum is collected.
Carry out the activity on different days, every fifteen days, at least.
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Picture 3.3.2 – While working.
5.
6.
7.
8.
At the end of the hands-on activity, you will come up with a set of shadows, with the times, in which
data were collected, and with the outline of the gnomon’s base.
Discussion: focus students’ attention on the daily presence of the shortest shadow. Then, focus their
attention on the same line, on which the shortest shadows lay.
Trace this line, which connects the feet to the heads of the shortest shadows. Choose two names,
which allow for its identification (for example John and Jennifer, Romeo and Juliet). Insist upon the
conventionality of these two names. The words “North” and “South” will be introduced later on.
Introduce the scientifically correct word: the local meridian.
Discussion about the lack of precision involved in this measure, due to the gnomon.
a)
b)
Picture 3.3.3 – a) A drawing about the gnomon. b) A student’s report about the activity.
We suggest to carry out observations in January and in March (in order to avoid problems due to legal
time). Choose two days, on which you are supposed to record the shadow every hour.
Step 8 is particularly important, because it is students’ first time to meet the word “conventionality”.
The length of the shadow, cast by a vertical rod, changes over a day. It is the lowest, when the Sun is
the highest above the horizon, i.e. it is on the meridian. This time is the true local midday.
A question remains unanswered: why doesn’t the clock strikes midday when the shadow is the shortest?
Did we make something wrong in our activity? In order to answer to this question, have students carry
out the next hands-on activity (T.U. 3.4). It is supposed to be carried out together with another class or
with someone’s parent, who is travelling and available.
Day after day, the direction pointed by the shadow at that time is always the same one. On a horizontal
plane, it points out the meridian line. It follows that every point on Earth has its “local meridian”, which is
different from the one of nearby places.
23
•
The evaluation consists in a measuring activity, and it has to be carried out in groups. Each group has
to measure the length of the shadows on the poster, it has to make a summarizing table and it has to
draw a graph.
Picture 3.3.4 – While measuring on the poster for making a graph.
Picture 3.3.5 – Sample of evaluation card, with a final graph.
Concept consolidation
Ask students to carry out an easy research, about what instruments were used in ancient times, in order
to observe the Sun’s path (we remind you that in third grade, Italian students start studying history).
24
Teaching Unit 3.3: “Local meridian and local midday determination”
Outline
Gnomon data:
Object
height
________
_____________
Recording table:
Observation month
Observation time
Length of the shadow
February the 1st
March the 1st
April the 1st
10
11
12
14
10
11
12
14
10
11
12
14
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
cm
25
Teaching Unit 3.3: “Local meridian and local midday determination”
Evaluation activity
Plot the data you collected on the following grid.
10
o’clock
11
o’clock
12
o’clock
February the 1st
14
o’clock
10
o’clock
11
o’clock
12
o’clock
March the 1st
14
o’clock
10
o’clock
11
o’clock
12
o’clock
14
o’clock
April the 1st
Corresponds to 5 cm of the length of the shadows
26
Teaching Unit 3.4
”Conventionality of midday”
This Teaching Unit is particularly important, because it provides students with an understanding of a
basic concept. The time, at which an object cast its shortest shadow, and the time, at which a clock
strikes midday, are not the same. To this statement, we add the fact that the shortest shadow is not cast
at the same time in any two different towns (which have slightly different values of longitude). What
follows is the conventionality of hours and the Earth rotation, too.
Contents
Conventionality of midday, comparison among “middays” in other towns, range of time.
Objectives
To acquire the concept that midday is a moment in time, which depends upon the site, from where it is
determined.
To acquire the concept that the “day” is that range of time, which elapses between any two successive
“shortest” shadows.
Glossary
Gnomon, local meridian, meridian line.
Required time
Around two hours, one of which for an e-mail discussion.
Needed material
Computers with Internet connections.
Another class, in another town, for a comparison of the activity.
If you cannot find another class, look for someone’s parent, who is in a different town, who is willing to
carry out the same experience and who can talk on the phone with you.
A gnomon (i.e. a rod, which is perpendicular to the ground).
A sheet of wrapping paper.
Procedure
1.
2.
3.
4.
5.
6.
In the discussion at the end of the previous T.U., we defined “midday” as that moment in time, in
which the Sun is the highest above the horizon, and the shadow is the shortest over the day. Students
wonder straightforward: “When it is midday for us, is it midday for everybody?” or better: “When the
shadow is the shortest here by us, is it the shortest for children, who live in other towns, too?”. Get
ready for a comparison with another class, which has to carry out the same activity (T.U.3.3, which
we will go through again pretty fast).
Fix a gnomon on the ground and have students start drawing the shadows and writing the hours, in
which shadows are drawn. Begin at 10 in the morning, have students identify the shortest shadow and
record the time, struck by the clock.
Hand this information over to the other class and wait for its outcome.
E-mail discussion with the parallel class: why is not midday time, measured with the shadows, the
same for both classes? Why is not midday time, measured with the shadows, the same of the time
struck by the clock, even if it is the same time for both classes? (Think about the time signal).
Discussion (with your class) for highlighting the reasons, why there is an agreed time for midday.
Have students answer to the following question: “What does the range of time between two
successive middays represent?”
27
a)
b)
Picture 3.4.1 – Two classes’ contemporaneous work, one in Treviso and the other one in Bologna.
A “day” is that range of time, which elapses between two successive Sun’s transits over its highest point
in its path, i.e. two successive Sun’s transits over the meridian. This statement is important as far as the
introduction of the concept of range of time.
You can begin to build an instrument (the first one), which allows for time determination.
Since these concepts are very abstract, we suggest to fill in an outline, which allows for highlighting the
most important concepts, and which replaces the card for learning evaluation.
•
The evaluation test will take place at the end of the following T.U., meanwhile observing a
meridian line or visiting a sundial.
It is carried out by means of a simple instrument, which students are supposed to build. It is a simple
sundial, which allows for enhancement of the concept of conventionality (in this case, of the concept of
range of time, too).
Procedure: have students detect the shadows at two different times. Have them notice the angular
interval bounded by the two shadows. Have them divide the angle into as many “hours” as they want.
Guide a discussion, which lets students understand, when they can use this kind of “clock”.
a)
b)
FPicture.3.4.2 – All you need is a piece of cardboard, a drawing pin and a pencil for building a simple “clock”. You are
supposed to detect the position of two shadows of the pencil.
28
Teaching Unit 3.4: “Conventionality of midday”
Outline
In order to sum up the notes you took during the lesson,
1. describe the trend of the shadows
before midday:
…………………………………………………………………………………………………………………………………………………………………
after midday:
…………………………………………………………………………………………………………………………………………………………………
2. complete the following sentence:
with respect to the parallel class, your midday took place
…………………………………………………………………………………………………………………………………………………………………
3. ty to define the local meridian, taking into consideration what we said:
………………………………………………………………………………………………………………………………………………………………
29
Teaching Unit 3.5
"North-South; East-West"
This T.U. is meant for having students choose the methodology they need, in order to communicate the
position of a point. Obviously, everything is done in two dimensions. Nevertheless, it is fundamental,
because it allows for a further enhancement of the concept of conventionality.
Contents
East – West Axis and its conventionality, geographic quadrants.
Objectives
To understand that the local meridian by itself is not enough to determine the position of a point on a
surface.
To acquire the idea that it is necessary to introduce another straight line, which is conventional with
respect to the first one.
To consolidate the relativity of the positions among two or more bodies.
Glossary
Geographic quadrants, geographic coordinates.
Required time
Around three hours.
Needed material
Long rulers.
Materials, which were used in the previous T.U. (3.4)
Procedure
1.
2.
3.
Discussion: take the drawing about the meridian line, which was done in T.U.3.4. Ask students the
following question: let’s imagine we want to tell our position to another person, who cannot see us. Is
it enough to use the line, which we drew, as a reference system? Are the positions univocally
determined?
We have to introduce another straight line: how are we supposed to trace it? Open discussion,
whatever answer is provided has to be taken into consideration and tested.
Finally, trace a line, which is perpendicular to the previous one. This is a way to determine four
quadrants.
Picture 3.5.1 – Different positions of straight lines, which were suggested by students.
4.
Give a name to this straight line and to the four half-lines: all the names, which students suggest,
have to be taken into consideration and discussed about. Eventually, choose the ones, which are
universally shared: North, East, South, West.
30
a)
b)
c)
Picture 3.5.2 – Samples of works carried out by students; it is important to talk about conventionality.
5.
6.
Stress out how important it is, to have a reference system, which can be reproduced and agreed
upon by everybody.
Final discussion, in front of a drawing about two straight lines, which generate four quadrants.
Determine in what quadrant a student is, and determine where a student is with respect to another
one, too. This discussion closes the topic.
In this T.U., it is very important to let students try over and over to define the position of a body, with
respect to another one. The discussion is also as important.
In step 2, it is fundamental to test all the alternatives, which students suggest, for a better acquisition of
the concept of conventionality.
•
The evaluation test (concerning both T.U. 3.4 and 3.5) has to be done after a visit to a sundial
with a stem, which allows for a visual consolidation of all the concepts in this module, too.
•
If you cannot visit a sundial, we provide you with another evaluation test.
Team game: The team, which wins, is the one, which gets first to fifteen points. The class is divided into
two teams (A and B). Each team has to stay in a different room, so that it cannot see what the other one
is doing. Every team has a sheet of wrapping paper, pencils, a long ruler and some objects. Set the game
field: trace the axis and determine the quadrants. One of the teams has to place an object in one of the
quadrants, and to tell the other team its position. The other team has to place the object on its field. If
the quadrant is the right one, the team will earn one point and it will lead the game. Otherwise, it is the
first team, which will earn the point, and which will keep leading the game.
31
Teaching Unit 3.5: “North-South; East-West”
Evaluation test
Answer to the following questions, after you visited a sundial with gnomon:
1.
On the floor, where the sundial was built, there are a lot of different lines. What do they represent?
2.
Are there some symbols or particular images? What do they represent?
3.
If the lines represent the hours, how come there are not 24 of them?
4.
If you were asked to tell where the stars are, with respect to the sundial, where would you place
them?
5.
Think about the hands-on activity about the child, who stands still and whose shadow we have
studied. What difference is there between the child and this sundial?
6.
Think about the instrument, which we built using cardboard and a pencil: can we consider it to be a
sundial?
7.
Draw the sundial you saw.
32
Teaching Unit 3.5: “North-South; East-West”
Evaluation test
(alternative solution)
Have a pencil stand on a desk, so that the Sunlight illuminates it.
Draw the shadow cast by the pencil. Wait a little while, and then draw again the shadow cast
by the pencil. Answer to the following questions:
1.
By looking at the shift of the pencil shadow, do you think you can tell, where the Sun seems to move
towards?
2.
Define these two movements: which one of them looks like the one of the hands of the clock?
The one of the Sun?
The one of the shadow?
3.
Draw these two movements as you saw them.
4.
If you were asked to tell where the stars are, with respect to the Sun, where would you place them?
5.
Think about the hands-on activity about the child, who stands still and whose shadow we have
studied. What is the difference between that child and your pencil?
33
Teaching Unit 3.6
“Let’s get our bearings: the cardinal points”
T.U. 3.6 is meant to be a consolidating Teaching Unit. It allows for getting one’s bearings on a sphere and
therefore on Earth. Together with the previous one, it can be carried out in the next school year,
depending upon the teaching program or upon the knowledge and the skills, which students have
acquired in the current school year.
Contents
Cardinal points, geographic grid, methods for getting one’s bearings.
Objectives
To determine univocally the position of a point on a flat surface.
To be able to build, and to know how to use, a geographic grid for a flat surface.
To introduce the concept of geographic grid on the Earth’s surface.
Glossary
Cardinal points, get one’s bearings, grid.
Required time
Two hours on the whole, one for part A and one for part B.
Needed material
The drawings of T.U. 3.5.
Felt tip pens.
Little toy houses.
A foolscap sheet of paper with big squares.
Tape, scissors, glue.
Procedure
This T.U. is divided into two parts: part A, which deals with a grid on a flat surface, and part B, which deals
with spherical surfaces.
Part A: coordinates on a flat surface
1. Opening discussion, looking at the drawings of T.U. 3.5 (two orthogonal axis have to be traced
together with the cardinal points). Have students try to determine the position of a point. Have them
notice that it is not univocally determined, because we lack something.
2. The quadrant determines nothing but a wide area on a flat surface. If I want a position to be
unmistakably determined, I will have to introduce more subdivisions on each quadrant. Therefore, it is
necessary to draw other lines (remind students about conventionality). Have students agree, upon how
many lines they want to draw. At the end, we will obtain a grid.
Nort
hd
West
a)
Est
So
uth
b
)
Picture 3.6.1 – Two ways for grid construction. Solution b) was adopted by a class, which not long before had dealt
with the concept of angle. In this case, the consolidation game, i.e. the battleship, has to be modified (we will provide
an alternative team game).
34
3. Have students draw the straight lines, so that to come up with a grid. Define the conditions, under
which the position of a point is determined, i.e. to determine what quadrant and to measure the distance
from both axis. This means that we are determining the coordinates on a geographic grid on a flat surface.
4. Have students build an imaginary village. They can place the houses wherever they want, but they are
supposed to write by each of them their coordinates.
Picture 3.6.2 – The village, which was made out of different materials, at the end of its construction.
5. Sum-up the entire activity on notebooks, including the legend for future interpretations, too.
Part B: coordinates on a spherical surface
1.
2.
3.
Project a slide about the Earth as seen from above, in order to have students remember that we do
not live on a flat surface, but on a more or less spherical one. Therefore, in order to get our bearings
on the Earth, we have to turn our flat grid into something spherical.
With a previously-prepared grid (or with a sheet of paper with big squares), every student is supposed
to try to build “something which is the closest to the Earth”, so that the lines of the grid are as visible
as possible. They can cut, glue, tape…
Collection of all the Earths, which students built and final discussion, which allows for an introduction
of the concept of equator, meridians and parallels.
a)
b)
Picture 3.6.3 – Sample of Earth.
35
4.
5.
6.
Have students determine the position of a point on the Earth’s surface. What you need is, first of all,
the distance of the point from the equator. Then introduce a fix meridian, from which students are
supposed to determine the longitude (remind them about conventionality).
Practice with a globe, which allows for determining the coordinates of a point.
Widening, to encompass the Sky. It allows for determining the coordinates of a star (here, celestial
coordinates are given with respect to the equatorial plane)
Part A and part B are supposed to be carried out on different days, with around one week interval, in order
to allow for consolidating the different concepts.
Some steps look like games. For example, think about the building of the imaginary village, which was
introduced in order to acquire and consolidate the concept of geographic coordinates (on a flat surface). As
a matter of facts, it is a joint game, which puts together cognitive objectives (construction of a geographic
grid, determination of the coordinates,…) with behavioral objectives (be able to work in a group, be able to
discuss correctly,…).
In order to carry out step B2, give students 30 minutes at most, otherwise they will lose sight of the
importance of the model and of its characteristics. It is important to introduce students to the idea of
model here, because this idea represents the end of this T.U., as well as the beginning of soon-to-be
hands-on activities.
The evaluation test has to be completed in a short time, i.e. 30 minutes, because it deals with just one
concept, which students have to focus.
The consolidation game is very important. We wish to remind you, that children are used to play with
electronic toys. This is the reason why it is necessary to explain them all the rules of the game, which they
might not know.
1.
Geographic Battleship (i.e. every body is against the teacher).
If you use the usual grid with squares:
Determine the rules of the game: choose the position of the axis on the game field, the number
of ships, what positions are allowed and the total number of fires, before someone wins. On a
sheet of notebook with squares, both teacher and students draw two North – South, East – West
axis.
The teacher is the only one, who draws his/her ships on the sheet of paper. Students are
supposed to sink them, by calling one after the other the geographic coordinates, which identify
each ship (i.e. students are supposed to tell what quadrant, what distance from the North –
South axis and what distance from the East – West axis, in number of squares).
The goal of the game is to make the teacher’s ships sink, i.e. find out what squares correspond to
the positions of the ships. If students guess right, the teacher is supposed to say either “hit” or
“sunk”. Otherwise, he/she is supposed to say “water”. If some ships are not sunk, the teacher will
win.
2. Game on the grid.
If the grid is like the one in picture 3.6.1.b:
Divide students into groups, choose 10 objects to place on the grid, make a map and give each
group one copy of the map. Group 1 is supposed to draw the 10 objects on its map, hand it over
to group 2, which puts on the ground the 10 objects, following the instructions on the map. The
third group checks if the work was carried out properly. For each object, which was placed
correctly, the team earns one point. The game goes on, changing the roles. The team, which
wins, is the one, which gets more points.
36
Teaching Unit 3.6: “Let’s get our bearings: the cardinal points”
Evaluation test
In this card, the North has been drawn in different positions.
Determine the positions of the other cardinal points
North
North
North
North
Answer to the following question:
Why, on every geographic map, does the North point towards the top of the page?
37
Teaching Unit 3.6: “Let’s get our bearings: the cardinal points”
Instrument construction card: “The Nocturnel”
(to be used in the Night Under the Stars)
Goals
Have students start getting their bearings with the stars, and have them start getting used to a better
manual ability concerning also simple instruments, just as scissors.
Procedure-methodological suggestions
It has to be made out of quite thick cardboard. Not every child knows how to use a compass, therefore,
generally speaking, circumferences have to be drawn by the teacher.
Materials
1.
2.
3.
4.
Two squares: the first one measures 12 by 12 cm and it is made out of lightly stiff, white cardboard;
the second one measures 10 by 10 cm and it is made out of dark blue cardboard.
Compass.
A metallic pin, with two flat “wings”.
Phosphorescent pen.
Construction
1.
2.
Draw two circumferences on the two pieces of cardboard: the one on the white piece of cardboard is
supposed to be bigger in diameter, than the one on the blue piece of cardboard. Have students cut
out the circles.
Trace one of the radius of the white circle. This radius will be used as a reference line while
observing.
3.
On the blue circle, in their right positions, draw seven dots, which represent the Big Dipper, and
seven more, which represent the Little Dipper.
38
4. Mark the dots with a phosphorescent pen, so that they can be seen in the darkness, too.
5. Overlap the two circles and fasten them together, in their centers, by means of a pin, so that
they can rotate.
How to carry out the hands-on activity:
This instrument can be used during the observation night.
1. Find the Big Dipper in the Sky.
2. Put the nocturnel above your head, so that the Big Dipper on the nocturnel has the same position of
the real one.
3. On the nocturnel, find out the position, which the Polaris occupies (the center of the instrument) with
respect to the Little Dipper. If you trace in the Sky the same movement with your forefinger, you will
meet the real Polaris.
4. Trace an imaginary vertical line from the Polaris to the horizon, and determine the cardinal point
North in front of us. In this way, we can keep getting our bearings by finding out, where the other
cardinal points are.
39
3rd Module: “The Night Under the Stars”
The darkness gets our bearings
(plan for the Night Under the Stars)
We can start getting our bearings in the darkness by means of the Polaris. In this case, it is
necessary to find a place, which is quite dark. A dark place is necessary in order for students to see
the stars. The fundamental constellations, which students have to observe in the Sky, are the two
Dippers and Cassiopeia.
It would be better, to carry out observations close to where children live. In any case, you can
decide to go to a darker place, or to an Astronomical Institute. If you decide for the second option,
ask to carry out some fundamental experiences:
1.
to build a simple Sky map, which can be done using the ones, which are on the market.
It is supposed to have just the most important groups of stars, which we need for our
work. When building this map, take into consideration both the seeing of the
observation site and the period of the year, in which observations are carried out;
2.
to build a simplified nocturnel, which allows for identifying the main constellations, and
which will be used on the same night;
3.
to play “get one’s bearings” games, carried out by moving to and from different points
on the field, from where you are observing;
4.
to observe constellations, which you can see towards North, and to introduce the
zodiacal constellations, which can be seen that night.
Once the concept “get one’s bearings” is clear to children, you can set up activities and games,
which allow for identifying groups of stars, which can be seen when you look at the Sky. At the end
of this Night, have children look at a simple Sky map, which contains nothing but the most
important groups of stars, which were involved in this Night. If you want to find some very simple
Sky maps, or if you want to carry out further activities about constellations, have a look at the
“Libro delle Costellazioni” (“A Book about Constellations”, which can be found at the web site
www.lestelle.net). Also amateurish magazines usually have Sky maps, which month after month
tell you what you can see in the Sky. The teacher has to be ready to carry out some alternative
activities, even telling a short story, in case the weather is bad, in order not to waste the evening.
End of 3rd Module
40

Heavens above!

Transcription

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