Back to Primaria (pre-K/K) this week. The teachers asked me to
explain how lenses work, because the kids had been making toy
eyeglasses out of pipecleaners and were curious about it. I had long
wanted to do some demos with light anyway. It takes a lot of trouble
to make a room really dark (so that the light relevant to the
demonstration is more visible) during school hours, so I figured I
would go to that trouble and combine topics. Linus (my son in
Primaria) had asked just a week or so before about the Moon. He
thought the phases of the Moon were due to Earth's shadow falling on
the Moon. I pointed out that the crescent Moon appears not too far
from the Sun, so the Earth's shadow cannot be falling on it. He came
up with some crazy stuff about light bouncing back and forth, back and
forth between Earth, Sun, and Moon "like an air hockey puck." So I
had a motivation to do phases of the Moon with the kids, but first I
had to build on basic concepts of light, like the difference between
emission and reflection (the Sun emits light and is the source of
light in our solar system; the Moon reflects some fraction of the
light it receives, but not enough to illuminate the other bodies in
the solar system).
So I set up in the kids' bathroom, which is the only room with no
windows. I still had to spend a lot of time taping up the open
doorway with black plastic to prevent a lot of light coming in. In
groups of 5-6, the kids came in and we started by talking about how we
couldn't see anything without a source of light. I then turned on an
unexpected source of light: a laser pointer. We discussed how they
couldn't see the source of light directly, but they could see the
light when it reflected off the ceiling. Next, a flashlight. I
pointed it directly at them, then pointed it at the ceiling. So a
given light source can be seen directly or indirectly (reflected)
depending on your relationship to it.
Now I turned on the "Sun": a naked light bulb. Unlike a flashlight or
laser pointer, it emits in all directions. But can we always see the
Sun? We discussed various reasons for not seeing the Sun, such as
clouds. But when is it really dark? At night. And what is night?
"Clouds" were again offered as a reason, so we discussed what happens
just before night: "the Sun goes down behind the mountains." So then
we each pretended we were the Earth, and slowly turned around so that
the Sun came into and out of our field of view. [The next day, my
wife Vera offered a really good suggestion: have them extend their
arms to make a "horizon" which turns with them.] To be honest, a lot
of kids spun way too rapidly and weren't really getting it. I
repeated the whole thing with a globe. We agreed on the location of
California and looked at how California varied between bright and dark
as the Earth turned. A problem with this is that light reflecting off
the walls provides a non-negligible amount of illumination for the
back side of the Earth, and the effect is not nearly as dramatic as
you would thing. Vera suggests decoupling the day/night concept from
the light demo, just pasting up a picture of the Sun in a regular
classroom and doing the horizon thing. I think she's right about
that! Another possibility is to build a little model. If the Sun were
a Christmas-tree bulb and the Earth a nearby marble, relatively little
light would bounce off the walls of the room!
Next, we tackled phases of the Moon. I had one child volunteer to be
Earth while I took a volleyball Moon and moved it around Earth,
showing how the Earth-person sees a fully-illuminated Moon when it is
opposite the Sun, and sees (rather, does not see) an un-illuminated
Moon when it is more or less between Earth and Sun. However, this did
not work well for several reasons. Each group had a bunch of other
kids who were not the Earth and saw the whole thing from a variety of
vantage points. It was very difficult to steer the kids into seeing
what they were "supposed" to see. One girl said "now I'm the Earth"
when the Moon happened to come close to her. In one group, the
Earth-volunteer gave the wrong answer when I asked him whether the
side of the Moon he was seeing was bright or dark; I think he just
didn't know what to compare to, so I need to be more careful about
exactly how I word my questions.
Finally, the lens. The key to a good visualization is to avoid using
all three dimensions. I put a flashlight on a table so they can see
how the light spreads out by looking at the light and dark patterns on
the table. I put a comb in front of the light to give a visual
impression of light rays spreading out on the table. Then I set a
special lens on the table, which is like a slice of a lens so that it
can sit flat on the table. This shows that the light rays which go
through the lens are bent so that they converge back together rather
than continue diverging. It's quite striking if set up right. I had
a card which I pretended was a movie screen, and projected the focused
image there. We talked about movie theaters and where they would sit,
did they ever look behind them and see the bright light coming out of
the lens, and what would happen if there was no screen. For the
groups which had a bit of time left at the end, I moved the lens
around to show that if it's too close to the light, it's not powerful
enough to converge the light. It might be powerful enough to stop
further spreading of the light, though, and I showed how a second lens
could then converge that light. The idea was to show that there are
many combinations and possibilities.
I felt that the kids were more disengaged than usual, and I felt that
it was directly attributable to the "demo" rather than "hands-on"
nature of the activity. I made the "demo" decision because I felt it
would be chaos to have 4- and 5-year-olds handling flashlights and
lenses in teams of two or three. That may have been correct, but I
should have found some way to prevent the whole 20 minutes from being
all demo. One possible structure is the sandwich: an initial demo
followed by hands-on activities with a more complicated demo or
summary discussion at the end. But this didn't fit with the list of
topics I wanted to cover. I realize now that I was too much in
"professor" mode: practicing inquiry is more important than covering a
list of topics! The kids brought up (indirectly) one thing I had
thought about last year but forgotten: setting up a light so that they
can make shadows themselves. They love doing this, and if I set it up
right they can actually explore different aspects of light. For
example, I could set up two lights of different colors and they could
see how to control the color of the shadow. Or they could explore how
a given object can have differently shaped shadows depending on its
orientation to the light. I can even imagine setting up a "light
studio" which they could play with during the week before or after my
visit.
Saturday, December 10, 2011
Friday, December 2, 2011
Turn! Turn! Turn!
At the elementary school, we continued our theme of learning more
about how things move, in preparation for designing the playground at
the new school site. Tomorrow, we have an optional field trip to the
Berkeley Adventure Playground to see what other kids have designed and
built. Today, we focused on spinning things.
We started with a spinnable chair. A volunteer sits in it and holds
two weights close to his/her chest while I spin up the chair. Then I
ask the volunteer to extend his/her arms as far as possible. The
chair then spins much more slowly. Arms in: the chair speeds up
again. Arms out: slows down again.
I ask the kids what else they have seen which is like this.
Surprisingly, no one said figure skating. I had to nudge them a bit
to realize it is just like the figure skater who brings her arms in to
spin rapidly. A lot of them did refer to playground equipment,
though. There is a public playground near the school (to which they
sometimes walk for lunch/PE) which has something like that, and I
think now they will have a new appreciation for it. But why does
pulling in your arms speed you up?
We had talked four weeks ago about how more massive things are more
difficult to accelerate. And to decelerate. In short, they have more
inertia. Rotational motion has an added complication. Rotational
inertia involves not only how much mass there is, but how far it is
from the center of rotation: the further from the center, the greater
the inertia. So it is much easier to spin up something whose mass is
concentrated near the center, compared to something of equal mass
whose mass is far-flung. The property of being spun up, which
physicists call angular momentum, is conserved so that a slowly
spinning far-flung object can easily be transformed into a rapidly
spinning concentrated object. Here's an analogy: I can have a certain
volume of water, but it results in a taller water level if it is put
in a skinny glass than if it is put in a wide glass. Here the volume
of water is analogous to the angular momentum (both are conserved),
and the height of the water level is analogous to the rate of
rotation.
Next, I gave them a chance to apply this new principle. I had a set
of two rods of the same size and mass, one of which secretly had most
of its mass concentrated near the middle, and the other of which
secretly had most of its mass concentrated near the ends. You grasp
the center of each rod in either hand, and rotate them back and forth.
There is a startling difference in the resistance to rotation! Once
each child had a chance to feel it, I asked them to come up with
hypotheses as to why one is easier to rotate. Surprisingly, the
connection was not instant. (I wonder how often words are a dead
giveaway. I used the word "rotation" here, but in class I just said,
"go like this." I bet if I had said "rotate the rods" something would
have clicked. But this something would not have been understanding of
physics! Asking questions with familiar terminology leads students to
"solve" problems they don't really understand, and make both teachers
and students overconfident in how much understanding has been gained.)
Many students insisted that the rods did not weigh the same, despite
my assurances. Next time, I should bring a scale to prove it!
Some students were able to guess that it had something to do with how
the weight was distributed (at least that's how I rephrased what they
said), or that something inside the hard-to-turn rod moved (which it
didn't, but I think they were on the right track in thinking that a
similar effect would be produced by some of the weight moving from the
middle toward the ends). I had to give quite a few hints, in one case
sitting on the demo chair and stretching my arms back and forth. We
finally established that we could explain the behavior by supposing
that one rod had most of its mass on the end and the other had most in
the middle. I pointed out that we had just used what we could see to
figure out something about what we couldn't see directly. That's
pretty cool, and that's what science is about.
Next, we took a bicycle wheel and I passed it around. Each student
felt that it is easy to change the orientation of the wheel (in other
words, change where its axis pointed) when the wheel is not spinning,
but quite difficult to do the same thing when the wheel is spinning.
This is another manifestation of conservation of angular momentum.
The rotating wheel seems to fight back; you have to do a lot of work
to change its direction. I asked in what real-life situations they
might have noticed the same thing. "Bicycle wheel" was a very popular
answer, but they couldn't pin down what about a bicycle wheel was
relevant. I had to hint a bit before they realized that this is why
it's easier to stay up on a bike when you're moving faster. When
you're not moving, the wheels can just fall over. When you're moving
fast, changing the axis of the wheels is not so easy, so you find it
easier to balance.
The same bicycle wheel can be used for a really neat demo. Sit on the
spinnable chair, hold the bicycle wheel so it's vertical, and have
someone spin the wheel. Now, when you turn the wheel so it is
sideways, the change in angular momentum gets transferred to the
chair, which begins to spin. Now flip the wheel over, and the chair
begins to spin the other way! This is the rotational equivalent of
two ice skaters pushing off each other and sliding off in opposite
directions.
Finally, I showed them a model of a merry-go-round, to the center of
which I had attached a spring with a small mass on the end. They
predicted that upon spinning the turntable, the mass would go toward
the outside (which it did), but they were not able to articulate
precisely why. I reminded them of the donutapult experiment four
weeks earlier: objects travel in straight lines unless acted upon by a
force. If an object is on a merry-go-round and does not hold on,
travel on a straight line means sliding off the merry-go-round. The
spring was there to prevent losing the mass, and when the turntable
slowed, the spring pulled the mass back toward the center, as the kids
predicted.
We talked about how to apply these ideas in designing a
playground. Some of the ideas were far-fetched, but that's ok! I
didn't want to discourage creativity. We also talked about space and
astronauts. Muscle and bone become very weak after extended periods
in space, and one way to provide artificial gravity to counteract this
is to spin a space station. Because everything inside "wants" to
stick to the rim of a spinning space station, the people inside will
feel like the outside edge of the station is "down", and that there is
gravity pulling things that way. And one child remarked that if you
still need some zero-g environment in the space station, you can put
it inside the axis of the spinning part. One child also asked about
stars, and I explained how some stars which are much more compact than
the Sun (neutron stars) rotate much more rapidly, as often as 30 times
per second! We know that because we can see a hot spot for a brief
period during each revolution.
about how things move, in preparation for designing the playground at
the new school site. Tomorrow, we have an optional field trip to the
Berkeley Adventure Playground to see what other kids have designed and
built. Today, we focused on spinning things.
We started with a spinnable chair. A volunteer sits in it and holds
two weights close to his/her chest while I spin up the chair. Then I
ask the volunteer to extend his/her arms as far as possible. The
chair then spins much more slowly. Arms in: the chair speeds up
again. Arms out: slows down again.
I ask the kids what else they have seen which is like this.
Surprisingly, no one said figure skating. I had to nudge them a bit
to realize it is just like the figure skater who brings her arms in to
spin rapidly. A lot of them did refer to playground equipment,
though. There is a public playground near the school (to which they
sometimes walk for lunch/PE) which has something like that, and I
think now they will have a new appreciation for it. But why does
pulling in your arms speed you up?
We had talked four weeks ago about how more massive things are more
difficult to accelerate. And to decelerate. In short, they have more
inertia. Rotational motion has an added complication. Rotational
inertia involves not only how much mass there is, but how far it is
from the center of rotation: the further from the center, the greater
the inertia. So it is much easier to spin up something whose mass is
concentrated near the center, compared to something of equal mass
whose mass is far-flung. The property of being spun up, which
physicists call angular momentum, is conserved so that a slowly
spinning far-flung object can easily be transformed into a rapidly
spinning concentrated object. Here's an analogy: I can have a certain
volume of water, but it results in a taller water level if it is put
in a skinny glass than if it is put in a wide glass. Here the volume
of water is analogous to the angular momentum (both are conserved),
and the height of the water level is analogous to the rate of
rotation.
Next, I gave them a chance to apply this new principle. I had a set
of two rods of the same size and mass, one of which secretly had most
of its mass concentrated near the middle, and the other of which
secretly had most of its mass concentrated near the ends. You grasp
the center of each rod in either hand, and rotate them back and forth.
There is a startling difference in the resistance to rotation! Once
each child had a chance to feel it, I asked them to come up with
hypotheses as to why one is easier to rotate. Surprisingly, the
connection was not instant. (I wonder how often words are a dead
giveaway. I used the word "rotation" here, but in class I just said,
"go like this." I bet if I had said "rotate the rods" something would
have clicked. But this something would not have been understanding of
physics! Asking questions with familiar terminology leads students to
"solve" problems they don't really understand, and make both teachers
and students overconfident in how much understanding has been gained.)
Many students insisted that the rods did not weigh the same, despite
my assurances. Next time, I should bring a scale to prove it!
Some students were able to guess that it had something to do with how
the weight was distributed (at least that's how I rephrased what they
said), or that something inside the hard-to-turn rod moved (which it
didn't, but I think they were on the right track in thinking that a
similar effect would be produced by some of the weight moving from the
middle toward the ends). I had to give quite a few hints, in one case
sitting on the demo chair and stretching my arms back and forth. We
finally established that we could explain the behavior by supposing
that one rod had most of its mass on the end and the other had most in
the middle. I pointed out that we had just used what we could see to
figure out something about what we couldn't see directly. That's
pretty cool, and that's what science is about.
Next, we took a bicycle wheel and I passed it around. Each student
felt that it is easy to change the orientation of the wheel (in other
words, change where its axis pointed) when the wheel is not spinning,
but quite difficult to do the same thing when the wheel is spinning.
This is another manifestation of conservation of angular momentum.
The rotating wheel seems to fight back; you have to do a lot of work
to change its direction. I asked in what real-life situations they
might have noticed the same thing. "Bicycle wheel" was a very popular
answer, but they couldn't pin down what about a bicycle wheel was
relevant. I had to hint a bit before they realized that this is why
it's easier to stay up on a bike when you're moving faster. When
you're not moving, the wheels can just fall over. When you're moving
fast, changing the axis of the wheels is not so easy, so you find it
easier to balance.
The same bicycle wheel can be used for a really neat demo. Sit on the
spinnable chair, hold the bicycle wheel so it's vertical, and have
someone spin the wheel. Now, when you turn the wheel so it is
sideways, the change in angular momentum gets transferred to the
chair, which begins to spin. Now flip the wheel over, and the chair
begins to spin the other way! This is the rotational equivalent of
two ice skaters pushing off each other and sliding off in opposite
directions.
Finally, I showed them a model of a merry-go-round, to the center of
which I had attached a spring with a small mass on the end. They
predicted that upon spinning the turntable, the mass would go toward
the outside (which it did), but they were not able to articulate
precisely why. I reminded them of the donutapult experiment four
weeks earlier: objects travel in straight lines unless acted upon by a
force. If an object is on a merry-go-round and does not hold on,
travel on a straight line means sliding off the merry-go-round. The
spring was there to prevent losing the mass, and when the turntable
slowed, the spring pulled the mass back toward the center, as the kids
predicted.
We talked about how to apply these ideas in designing a
playground. Some of the ideas were far-fetched, but that's ok! I
didn't want to discourage creativity. We also talked about space and
astronauts. Muscle and bone become very weak after extended periods
in space, and one way to provide artificial gravity to counteract this
is to spin a space station. Because everything inside "wants" to
stick to the rim of a spinning space station, the people inside will
feel like the outside edge of the station is "down", and that there is
gravity pulling things that way. And one child remarked that if you
still need some zero-g environment in the space station, you can put
it inside the axis of the spinning part. One child also asked about
stars, and I explained how some stars which are much more compact than
the Sun (neutron stars) rotate much more rapidly, as often as 30 times
per second! We know that because we can see a hot spot for a brief
period during each revolution.
Friday, November 18, 2011
Playground Design 101
The motivation for the next few visits to the elementary school is
that the kids are going to help design the playground for their new
school site, so I'm going to show them a bit about how things work, ie
classical mechanics. One thing I love about this school is that the
teachers frame things this way. Instead of just hearing that "today
we're going to be learning Newton's laws of motion" students have this
wonderful backdrop to keep them motivated and (perhaps more important)
foster creativity. The laws of mechanics will be a springboard to
creating something wonderful, not a straitjacket of rules we have to
memorize.
We set the foundation last time with
Newton's laws of motion exemplified in the simplest possible situations,
to make them as clear as possible. This time, we added complications to
show how interesting it can be when forces interact. I concocted three
different examples of interacting forces and set up three
stations. Each group of 6-8 kids split into 3 groups of 2-3 and spent
5 minutes at each station, with 5 minutes left at the end for group
discussion.
Station 1: I repeated the pulley activity from last week at Primaria.
I rigged up different pulley arrangements to lift identical 20-pound
weights. One arrangement was just a single pulley at the top as you
might expect, reversing the direction of the rope so that the kids
could stand on the ground and pull down on the rope to make the block
go up. The second arrangement had the end of the rope tied at the
top, running down to an "upside down" pulley attached to the block,
and then back up to a pulley at the top which acted much like the
single pulley, just reversing the direction of the rope. The kids
tried both setups and compared the difficulty of lifting the block.
The second arrangement is much easier, but why? I challenged the kids
to go beyond simple explanations like "two pulleys are better than
one" and "there are two ropes pulling up the weight so it's twice as
strong." The latter statement starts to get to the answer, but is by
no means a complete answer. If I have to drag something with a rope,
tying two ropes to it doesn't make it any easier.
The trick is to observe closely what happens when you pull. The
moving pulley makes it so that if I pull my end of the rope one foot,
the weight moves up half a foot. This means that you only need half
the muscle that you need with the fixed pulley. (This is called
"mechanical advantage" but I did not use that term.) This was not too
easy for the elementary kids; in fact I think last week the pre-K/K
kids did better, possibly because the three-station setup this week
was very distracting. They were able to extrapolate how to make it
even easier to lift (add more pulleys) but we didn't have time to
discuss how we would connect those extra pulleys, which would really
probe understanding. This could be a good home activity for
interested parents and kids: set up a 4-pulley system so that it's 4
times easier to lift a given weight. How do you set it up, and how
much rope will you have to pull to lift the weight 1 foot? (Advice:
don't try to connect 4 separate pulleys, because the ropes will easily
get twisted and tangled. Buy two "double parallel pulleys" so that
everything stays more or less aligned.)
Also note that in each case, one pulley exists only to reverse the
direction of the pull. You could simplify the comparison by thinking
about standing on a deck and pulling a weight straight up (no pulleys)
vs. tying one end of the rope to the deck, running it around a pulley
attached to the weight, and then pulling up on the other end. Here it
is clear that to get the weight up to the deck, you will need to pull
a length of rope which is twice the height of the deck. But the
benefit is that you need only half the strength to pull the rope.
Station 2: an overhead pulley with an adjustable amount of weight
attached to the rope on each side. This can be used to emphasize a
few different concepts. First, balance: when the weight on each side
is the same, neither side moves. This might seem boring, but it is
actually an easy way to move weight up and down. In balance, it takes
only a tiny amount of strength to move one side up or down, because
you are not moving any net weight up or down. This is how elevators
work: there is a counterweight so the motor doesn't have to work so
hard. This also provides safety in case the motor breaks: the
counterweight is always there and needs no power to function.
Wouldn't it be fun to have some kind of human-powered elevator on the
playground?
Second, this station can serve to reinforce ideas about force and
acceleration (Newton's laws of motion). When there is only slightly
more weight on one side, the net force due to gravity is small, and
that side accelerates downward quite slowly. But with a relatively
small counterweight, the the net force due to gravity is large, and
the heavy side accelerates downward quite rapidly. It's kind of like
a seesaw with rope, which makes it relevant to the playground.
See the Wikipedia article on the Atwood machine for a nice diagram,
and this video demonstrating the small acceleration when the weight is nearly the same on each side.
Third station: this was very much like a small seesaw, with a meter
stick balanced on a pivot at the center. The kids could hang weights
of various sizes at various distances from the center. They were
supposed to figure out that a small weight placed far from the center
could balance a much heavier weight placed close to the center.
However, five minutes was not enough time to absorb this. In many
cases it took them just a few minutes to figure out that if one side
of the balance beam is down, piling more weight on that side doesn't
help balance it! And others were not cognizant that the weights came
in different amounts, from 5 to 50 grams, and just counted the number
of weights rather than the total amount of weight. (OK, I know the
gram is not technically a unit of weight, but we have to keep things
simple!) So in the future I would structure the balance beam as a
complete activity in itself, and define a series of goals starting
from a very basic level. This time, I can forgive myself because I
only had one setup, which wouldn't have worked for 6-8 kids. Anyway,
with the balance beam station I also brought the discussion back to
the playground. What fun things could they design which might involve
balancing big things on one side and small things on the other? Maybe
a balance beam for kids to hang from and balance each other?
After the stations, we had a 5-minute wrapup for each group of 6-8
kids, discussing some of the nuances I wrote about above, which were
missed in the quick 5-minute rotations. This is the first time I
tried having small groups work on different things, and I have to say
it was hectic. Thank goodness the school is well staffed! I had at
least one teacher or or aide or intern rotate in with each group,
which saved the whole thing from being a complete organizational
disaster.
After all the groups rotated through, the kids reassembled in one big
group for circle time, and I asked for 5-10 minutes to do a few demos. I
did these in the big group because (1) there was no time to do it
during the rotations; and (2) the kids would have fought over these
things if it had been a hands-on activity. First, I showed a rod with
a heavy ball on one end and a light ball on the other end, and I asked
how I should place the rod so that it balances on my finger. Not
everyone answered near the heavy ball! So it was worth demonstrating.
But the really cool part is that if something is well balanced, it
will rotate nicely. So I showed how it spins about its balance
point very smoothly and for a long time, whereas it clearly would not
spin nicely about the center of the rod. Here's a video: (apologies for
the appalling quality of the video. I figured it was more important
to help parents see what their kids saw than to worry about looking
good.)
Second, I demonstrated Newton's cradle. This again relates to forces,
and a large version would make a really cool addition to a playground.
(Note: if your kids have studied pendulums, Newton's cradle may be best
understood as a kind of pendulum.)
To wrap up, I asked for their ideas on the playground. After taking a
few, we ran out of time, and we agreed that kids would draw their
concepts during free-choice time. In two weeks, I'll return to the
elementary for some activities involving rotation, and the next day
we'll take an optional family field trip to the Berkeley Adventure
Playground which has "many unusual kid designed and built forts,
boats, and towers." Then we'll get to work more seriously on
designing our own playground!
that the kids are going to help design the playground for their new
school site, so I'm going to show them a bit about how things work, ie
classical mechanics. One thing I love about this school is that the
teachers frame things this way. Instead of just hearing that "today
we're going to be learning Newton's laws of motion" students have this
wonderful backdrop to keep them motivated and (perhaps more important)
foster creativity. The laws of mechanics will be a springboard to
creating something wonderful, not a straitjacket of rules we have to
memorize.
We set the foundation last time with
Newton's laws of motion exemplified in the simplest possible situations,
to make them as clear as possible. This time, we added complications to
show how interesting it can be when forces interact. I concocted three
different examples of interacting forces and set up three
stations. Each group of 6-8 kids split into 3 groups of 2-3 and spent
5 minutes at each station, with 5 minutes left at the end for group
discussion.
Station 1: I repeated the pulley activity from last week at Primaria.
I rigged up different pulley arrangements to lift identical 20-pound
weights. One arrangement was just a single pulley at the top as you
might expect, reversing the direction of the rope so that the kids
could stand on the ground and pull down on the rope to make the block
go up. The second arrangement had the end of the rope tied at the
top, running down to an "upside down" pulley attached to the block,
and then back up to a pulley at the top which acted much like the
single pulley, just reversing the direction of the rope. The kids
tried both setups and compared the difficulty of lifting the block.
The second arrangement is much easier, but why? I challenged the kids
to go beyond simple explanations like "two pulleys are better than
one" and "there are two ropes pulling up the weight so it's twice as
strong." The latter statement starts to get to the answer, but is by
no means a complete answer. If I have to drag something with a rope,
tying two ropes to it doesn't make it any easier.
The trick is to observe closely what happens when you pull. The
moving pulley makes it so that if I pull my end of the rope one foot,
the weight moves up half a foot. This means that you only need half
the muscle that you need with the fixed pulley. (This is called
"mechanical advantage" but I did not use that term.) This was not too
easy for the elementary kids; in fact I think last week the pre-K/K
kids did better, possibly because the three-station setup this week
was very distracting. They were able to extrapolate how to make it
even easier to lift (add more pulleys) but we didn't have time to
discuss how we would connect those extra pulleys, which would really
probe understanding. This could be a good home activity for
interested parents and kids: set up a 4-pulley system so that it's 4
times easier to lift a given weight. How do you set it up, and how
much rope will you have to pull to lift the weight 1 foot? (Advice:
don't try to connect 4 separate pulleys, because the ropes will easily
get twisted and tangled. Buy two "double parallel pulleys" so that
everything stays more or less aligned.)
Also note that in each case, one pulley exists only to reverse the
direction of the pull. You could simplify the comparison by thinking
about standing on a deck and pulling a weight straight up (no pulleys)
vs. tying one end of the rope to the deck, running it around a pulley
attached to the weight, and then pulling up on the other end. Here it
is clear that to get the weight up to the deck, you will need to pull
a length of rope which is twice the height of the deck. But the
benefit is that you need only half the strength to pull the rope.
Station 2: an overhead pulley with an adjustable amount of weight
attached to the rope on each side. This can be used to emphasize a
few different concepts. First, balance: when the weight on each side
is the same, neither side moves. This might seem boring, but it is
actually an easy way to move weight up and down. In balance, it takes
only a tiny amount of strength to move one side up or down, because
you are not moving any net weight up or down. This is how elevators
work: there is a counterweight so the motor doesn't have to work so
hard. This also provides safety in case the motor breaks: the
counterweight is always there and needs no power to function.
Wouldn't it be fun to have some kind of human-powered elevator on the
playground?
Second, this station can serve to reinforce ideas about force and
acceleration (Newton's laws of motion). When there is only slightly
more weight on one side, the net force due to gravity is small, and
that side accelerates downward quite slowly. But with a relatively
small counterweight, the the net force due to gravity is large, and
the heavy side accelerates downward quite rapidly. It's kind of like
a seesaw with rope, which makes it relevant to the playground.
See the Wikipedia article on the Atwood machine for a nice diagram,
and this video demonstrating the small acceleration when the weight is nearly the same on each side.
Third station: this was very much like a small seesaw, with a meter
stick balanced on a pivot at the center. The kids could hang weights
of various sizes at various distances from the center. They were
supposed to figure out that a small weight placed far from the center
could balance a much heavier weight placed close to the center.
However, five minutes was not enough time to absorb this. In many
cases it took them just a few minutes to figure out that if one side
of the balance beam is down, piling more weight on that side doesn't
help balance it! And others were not cognizant that the weights came
in different amounts, from 5 to 50 grams, and just counted the number
of weights rather than the total amount of weight. (OK, I know the
gram is not technically a unit of weight, but we have to keep things
simple!) So in the future I would structure the balance beam as a
complete activity in itself, and define a series of goals starting
from a very basic level. This time, I can forgive myself because I
only had one setup, which wouldn't have worked for 6-8 kids. Anyway,
with the balance beam station I also brought the discussion back to
the playground. What fun things could they design which might involve
balancing big things on one side and small things on the other? Maybe
a balance beam for kids to hang from and balance each other?
After the stations, we had a 5-minute wrapup for each group of 6-8
kids, discussing some of the nuances I wrote about above, which were
missed in the quick 5-minute rotations. This is the first time I
tried having small groups work on different things, and I have to say
it was hectic. Thank goodness the school is well staffed! I had at
least one teacher or or aide or intern rotate in with each group,
which saved the whole thing from being a complete organizational
disaster.
After all the groups rotated through, the kids reassembled in one big
group for circle time, and I asked for 5-10 minutes to do a few demos. I
did these in the big group because (1) there was no time to do it
during the rotations; and (2) the kids would have fought over these
things if it had been a hands-on activity. First, I showed a rod with
a heavy ball on one end and a light ball on the other end, and I asked
how I should place the rod so that it balances on my finger. Not
everyone answered near the heavy ball! So it was worth demonstrating.
But the really cool part is that if something is well balanced, it
will rotate nicely. So I showed how it spins about its balance
point very smoothly and for a long time, whereas it clearly would not
spin nicely about the center of the rod. Here's a video: (apologies for
the appalling quality of the video. I figured it was more important
to help parents see what their kids saw than to worry about looking
good.)
Second, I demonstrated Newton's cradle. This again relates to forces,
and a large version would make a really cool addition to a playground.
(Note: if your kids have studied pendulums, Newton's cradle may be best
understood as a kind of pendulum.)
To wrap up, I asked for their ideas on the playground. After taking a
few, we ran out of time, and we agreed that kids would draw their
concepts during free-choice time. In two weeks, I'll return to the
elementary for some activities involving rotation, and the next day
we'll take an optional family field trip to the Berkeley Adventure
Playground which has "many unusual kid designed and built forts,
boats, and towers." Then we'll get to work more seriously on
designing our own playground!
Saturday, November 12, 2011
Gearheads
The Primaria kids continue to be fascinated by contraptions,
factories, and the like. Thursday, the day before my visit, they
built contraptions using empty cardboard boxes, egg cartons, steel
cans, etc, plus a lot of imagination. So I explored pulleys and gears
with them on Friday.
In my previous visit we built an elevator; that was more about the
principle of balance than about pulleys, but it did give them a basic
intro to pulleys. This time, I rigged up different pulley arrangements
to lift identical concrete blocks, using the monkey bars to hang the
pulleys. One arrangement was just a single pulley at the top as you
might expect. The second arrangement had the end of the rope tied at
the top, running down to an "upside down" pulley attached to the
block, and then back up to a pulley at the top which acted much like
the single pulley, just reversing the direction of the rope so that
the kids could stand on the ground and pull down on the rope to make
the block go up. The kids tried both setups and compared the
difficulty of lifting the block.
The second arrangement is much easier. I didn't expect the kids to
figure out why, but I did expect them to see that it had two pulleys
instead of one, or that it had a moving pulley rather than just a
fixed one. Two of the four groups did not see this and required some
coaxing. But I made a kind of game out of it, telling them that in
science we have to be very observant, asking them to watch carefully
as I pull each one slowly, etc. I was happy to be able to frame it
such that they could gradually work toward the answer rather than just
have me give them the answer.
So why does the moving-pulley system make it easier? I took lots of
very entertaining guesses on this one before having them observe the
motion again. The moving pulley makes it so that if I pull my end of
the rope one foot, the weight moves up half a foot. This means that
you only need half the muscle that you need with the fixed pulley.
(This is called "mechanical advantage" but I did not use that term.)
Then I asked how they could imagine making it even easier to pull.
Some of the groups digressed at first ("add a motor", "get a lighter
block") but we generally concluded that even more pulleys would be
better. Kids love big numbers, and instead of suggesting four pulleys
some went straight to "a thousand pulleys!" I had tried setting up
four pulleys, but the ropes got too twisted. If you want to go to
four pulleys, I recommend buying sets of two pulleys already bolted
together side-by-side to avoid this twisting (parallel pulleys). I
can't imagine how twisted the ropes would get with a thousand pulleys!
Next, we did gears. They had already played a lot with
Gears!Gears!Gears! sets, but those are limited in terms of gear
concepts. I ordered some bags of gears of very different sizes and
had hoped to mount them in some way which allowed for exploration, but
I ran out of time drilling holes at 8:45 Friday morning. So this was
more of a demonstration than a hands-on activity, but that was ok
because it allowed me to use something I had only one copy of: the
book Get in Gear by Sholly Fisch, which is a really nice book. Each
page describes a new gear concept and gives you the framework for
assembling it and seeing it work for yourself.
Before going to the book, I wanted to make sure they understood gear
ratios (although I didn't use that term). I showed a little gear
turning a big gear in one of my homemade setups, and we counted how
many times we had to turn the little gear all the way around before
the big gear went around once. In this case, it was about 3, because
the big gear had about 3 times as many teeth. Conversely, turning the
big gear once makes the little gear go around about 3 times. So if
you need to build a high-speed machine, hook a motor up to a big gear
which turns a little gear, and the little gear will go crazy fast.
And if you need to build a low-speed machine, hook your motor up to
the little gear, and the big gear will trun slowly. We talked about
why people might need to build a low-speed machine. This connects
back to the pulleys: when moving a heavy weight, low-speed is
better. (I left it at that without talking about forces; I think the
low-speed motion of the concrete block in the easy-to-pull setup was
the most effective and appropriate "proof" for this age group.)
On to the book. I had noticed that the kids are paying attention to
clocks and starting to learn about time, so I started with the clock.
This was a natural segue from the gear ratio demo. We want to make
the hour hand go slowly, so how do we do that with gears? Attach the
hand to a big gear which is driven by a small gear! And we want to
make the minute hand go fast, so how do we do that with gears? Attach
it to a small gear which is driven by a big gear! I was pleased that
the kids were able to guess these answers most of the time. So here's
the clock in action:
Next, I showed them that gears are not limited to circular motion. Here is a rack gear in action:
Rack gears are used for turning circular motion into linear motion. In addition to all kinds of machines, rack gears are used in steep mountain railways, where the track contains the rack gear and the engine carries and pushes on the circular gear. (It's also used for rack-and-pinion steering; the pinion is the circular gear which meshes with the rack.) We talked about what kinds of machines might need to do this kind of motion. Maybe squeezing grapes for grape juice, or printing presses.
And we can also set up gears to do a sweeping motion, by attaching something off-center:
The last thing we had time for was planetary gears, so called because little gears go around a bigger gear like the planets around the sun:
This is cool and could just be a work of art, but there are applications. Note that around the outside is what is basically a really big inside-out gear (difficult to see in the video because it's made of clear plastic). I went back to the homemade big+small gear setup and asked why it would be useful to put the small gear inside the big gear. Answer: to save space, if you need to make a small machine, like a pencil sharpener, a kitchen mixer, maybe an electric toothbrush.
Finally, we didn't get time to build the piece de resistance, but here is a machine which combs your hair and brushes your teeth at the same time:
The whole activity worked well. I learned something about organizing kids, too. Because there weren't enough pulley setups, kids had to wait, but there wasn't really a line because it was just a few kids waiting. This led to a lot of confusion until Teacher Jessica brought "waiting chairs." When the kids have to sit in chairs to wait, it is 100% clear who is next!
If you want to see more, I recommend the video Gear Basics.
factories, and the like. Thursday, the day before my visit, they
built contraptions using empty cardboard boxes, egg cartons, steel
cans, etc, plus a lot of imagination. So I explored pulleys and gears
with them on Friday.
In my previous visit we built an elevator; that was more about the
principle of balance than about pulleys, but it did give them a basic
intro to pulleys. This time, I rigged up different pulley arrangements
to lift identical concrete blocks, using the monkey bars to hang the
pulleys. One arrangement was just a single pulley at the top as you
might expect. The second arrangement had the end of the rope tied at
the top, running down to an "upside down" pulley attached to the
block, and then back up to a pulley at the top which acted much like
the single pulley, just reversing the direction of the rope so that
the kids could stand on the ground and pull down on the rope to make
the block go up. The kids tried both setups and compared the
difficulty of lifting the block.
The second arrangement is much easier. I didn't expect the kids to
figure out why, but I did expect them to see that it had two pulleys
instead of one, or that it had a moving pulley rather than just a
fixed one. Two of the four groups did not see this and required some
coaxing. But I made a kind of game out of it, telling them that in
science we have to be very observant, asking them to watch carefully
as I pull each one slowly, etc. I was happy to be able to frame it
such that they could gradually work toward the answer rather than just
have me give them the answer.
So why does the moving-pulley system make it easier? I took lots of
very entertaining guesses on this one before having them observe the
motion again. The moving pulley makes it so that if I pull my end of
the rope one foot, the weight moves up half a foot. This means that
you only need half the muscle that you need with the fixed pulley.
(This is called "mechanical advantage" but I did not use that term.)
Then I asked how they could imagine making it even easier to pull.
Some of the groups digressed at first ("add a motor", "get a lighter
block") but we generally concluded that even more pulleys would be
better. Kids love big numbers, and instead of suggesting four pulleys
some went straight to "a thousand pulleys!" I had tried setting up
four pulleys, but the ropes got too twisted. If you want to go to
four pulleys, I recommend buying sets of two pulleys already bolted
together side-by-side to avoid this twisting (parallel pulleys). I
can't imagine how twisted the ropes would get with a thousand pulleys!
Next, we did gears. They had already played a lot with
Gears!Gears!Gears! sets, but those are limited in terms of gear
concepts. I ordered some bags of gears of very different sizes and
had hoped to mount them in some way which allowed for exploration, but
I ran out of time drilling holes at 8:45 Friday morning. So this was
more of a demonstration than a hands-on activity, but that was ok
because it allowed me to use something I had only one copy of: the
book Get in Gear by Sholly Fisch, which is a really nice book. Each
page describes a new gear concept and gives you the framework for
assembling it and seeing it work for yourself.
Before going to the book, I wanted to make sure they understood gear
ratios (although I didn't use that term). I showed a little gear
turning a big gear in one of my homemade setups, and we counted how
many times we had to turn the little gear all the way around before
the big gear went around once. In this case, it was about 3, because
the big gear had about 3 times as many teeth. Conversely, turning the
big gear once makes the little gear go around about 3 times. So if
you need to build a high-speed machine, hook a motor up to a big gear
which turns a little gear, and the little gear will go crazy fast.
And if you need to build a low-speed machine, hook your motor up to
the little gear, and the big gear will trun slowly. We talked about
why people might need to build a low-speed machine. This connects
back to the pulleys: when moving a heavy weight, low-speed is
better. (I left it at that without talking about forces; I think the
low-speed motion of the concrete block in the easy-to-pull setup was
the most effective and appropriate "proof" for this age group.)
On to the book. I had noticed that the kids are paying attention to
clocks and starting to learn about time, so I started with the clock.
This was a natural segue from the gear ratio demo. We want to make
the hour hand go slowly, so how do we do that with gears? Attach the
hand to a big gear which is driven by a small gear! And we want to
make the minute hand go fast, so how do we do that with gears? Attach
it to a small gear which is driven by a big gear! I was pleased that
the kids were able to guess these answers most of the time. So here's
the clock in action:
Next, I showed them that gears are not limited to circular motion. Here is a rack gear in action:
Rack gears are used for turning circular motion into linear motion. In addition to all kinds of machines, rack gears are used in steep mountain railways, where the track contains the rack gear and the engine carries and pushes on the circular gear. (It's also used for rack-and-pinion steering; the pinion is the circular gear which meshes with the rack.) We talked about what kinds of machines might need to do this kind of motion. Maybe squeezing grapes for grape juice, or printing presses.
And we can also set up gears to do a sweeping motion, by attaching something off-center:
The last thing we had time for was planetary gears, so called because little gears go around a bigger gear like the planets around the sun:
This is cool and could just be a work of art, but there are applications. Note that around the outside is what is basically a really big inside-out gear (difficult to see in the video because it's made of clear plastic). I went back to the homemade big+small gear setup and asked why it would be useful to put the small gear inside the big gear. Answer: to save space, if you need to make a small machine, like a pencil sharpener, a kitchen mixer, maybe an electric toothbrush.
Finally, we didn't get time to build the piece de resistance, but here is a machine which combs your hair and brushes your teeth at the same time:
The whole activity worked well. I learned something about organizing kids, too. Because there weren't enough pulley setups, kids had to wait, but there wasn't really a line because it was just a few kids waiting. This led to a lot of confusion until Teacher Jessica brought "waiting chairs." When the kids have to sit in chairs to wait, it is 100% clear who is next!
If you want to see more, I recommend the video Gear Basics.
Saturday, November 5, 2011
An object in motion...
So it's time for the elementary kids to learn Newton's laws of motion.
The key for good demos and hands-on activities is getting rid of
friction, so we can see how objects behave in the absence of forces.
I usually use hover pucks, devices that look like very big hockey
pucks but have a fan inside so they float on a cushion of air, like
air hockey without the table. (They are also sold under the brand
name Kick Dis.) But I decided we would have more fun and soap up a
table so that we could slide anything without friction. The night
before, I started soaping tables to see how frictionless I could get
them. The result was a lot of frustration. I could never really get
them frictionless, not close enough to make convincing demos. I even
tried soaping a large sheet of glass (one of the mirrored sliding
doors on my closet) and that was better, but still not good enough.
It seems that no table or mirror is quite flat enough; objects will
glide along a bit, but then hit a high point and stop. So I ended up
going to bed late and frustrated, with some mess still to clean up in
the morning. Such is the life of an educator.
So Friday morning quick I went to work and picked up a bunch of
hoverpucks. (I also bought some donuts for the donutapult; see
below.) I had already picked up some carts which looked like very
large skateboards. On a smooth floor or sidewalk, these are
reasonably frictionless and safe to kneel on.
After scouting the school to find the smooth surfaces, I set up a
three-stage plan for each group. We started at the long, smooth table
with the hoverpucks. I asked the kids what they knew about friction,
and then I asked them to rub their hands together to feel friction.
Then I slid a switched-off hoverpuck on the table (it went a very
short distance) to show that friction is why it's hard to slide
things, and I asked them for ideas to get rid of friction. After
entertaining various ideas, I asked them to make predictions for how
the hoverpuck would move after I switched it on and pushed it toward
the other end of the table. Then I did just that, and it went in a
perfectly smooth straight line. So this makes it clear that, in the
absence of forces, objects in motion continue their motion (in a
straight line at constant speed). This is Newton's first law of
motion, but I didn't ask them to remember that. We had too many cool
experiments to do, and I can count on the regular teachers to review
the terminology several times!
So I seamlessly continued with the hoverpuck. I asked a child seated
along the middle of the table to give the puck a sideways tap as it
passed her down the long axis of the table. First time with a small
tap, then with a larger one, and each time I asked the kids to predict
the subsequent motion. This sequence shows a few things. First, that
a bigger force (or tap, or push) causes a bigger acceleration (change
in motion, whether it be a change in speed or direction...mostly
direction in this case), which is part of Newton's second law.
Second, a force changes the motion only while the force is being
applied. The tap changes the direction of the puck, but only while
the tap is applied. After the tap, the puck follows its new direction
in a straight line. A one-time tap cannot make it keep curving
around. This reinforces the first law: while there are no forces, it
goes in a straight line at constant speed.
To wrap up the hoverpuck activity (which was only the first of the
three stages I had planned), I gave each child a hoverpuck and asked
them to figure out how to make it travel in a circle (which is
distinct from spinning). They needed this bit of playing to relieve
the wiggles, because to this point it had been mostly demo, with some
assistance from 1-2 kids. After several minutes, we discussed how the
only way to make the puck go in a circle is to keep your hand on it
and move your hand in a circle. In other words, circular motion
requires a continuously changing direction of motion, and therefore a
continuous force. This bit isn't strictly necessary if we just wanted
to do Newton's laws, but it connects to the next stage and some other
interesting ideas in the next paragraph.
Second stage: we went outside and I made a bagel-on-a-string go around
in circles over my head. I asked them to imagine what would happen if
the string broke. If they really got Newton's first law, they would
answer that it would fly off in a straight line, but of course most
people don't grasp it that well after just the first demo. So some
said it would fall straight down, a few said it would fly off in a
circular motion, etc. So now comes the really fun part. It's not
practical to cut the string, so instead I tie a donut to a string, and
the string cuts its own way through the soft donut as I whip it around
over my head. I ask them to observe well, because once the donut
comes free there's only a split second before it hits the fence, or a
tree, or a person! Of course it flies off in a straight line:
Newton's first law strikes again. Then I ask them to think of
anything else that moves in a circle. Sometimes I have to hint "in
space", but they can guess Earth around the Sun, or the Moon around
the Earth. So that's the proof that there is a force keeping the Moon
around the Earth: if there were not, the Moon would fly off in a
straight line. (This comes as a revelation to many adults and college
students...they were never helped to make the connection between real
life and Newton's abstract laws of motion.) Then I ask them what the
name of that force is, and in each group at least one child knew it
was called gravity.
Third stage: we went to the sidewalk for the cart activity. First,
each child gave a push to an unloaded cart, and then the same size
push to a cart loaded with 40 pounds of weights. The heavier cart
accelerated much less. This is the other facet of Newton's second
law: acceleration is proportional to force, but inversely proportional
to the mass of the object being accelerated. The phrase "same size
push" is an attempt to make "same force" sound less technical. Some
kids initially seemed to interpret it as "make the cart accelerate the
same amount" so I made sure to counter this by continually repeating
phrases like "use all the same muscles" or "push just as hard as last
time." In cases where they still didn't quite get it, I asked if they
ever got so mad at their brother (or sister, or friend) that they
wanted to push them. Yes, you can admit it! Pretend the cart is your
brother, you are mad, and you push him. Now, for the other cart,
you're still just as mad, so push just the same!
Also, a common misconception is to look at how far the cart travels as
a measure of the effect of the push. We must not do this, because how
far it travels is a complicated function of how much friction there
is, whether it had to roll over a small stone or a crack, fight a gust
of wind, etc. No, we must observe how fast the cart was moving
immediately after the push.
Finally, we get to Newton's third law. I need two volunteers, one to
kneel on each cart. Alone, each child can't get his or her cart to
start moving. But they can if they push against each other, and this
results in equal and opposite accelerations if I wisely chose
volunteers of the similar mass. This shows that forces come in equal
and opposite pairs, which is Newton's third law. (The usual
formulation, "Every action has an equal and opposite reaction," is
very misleading because it gives the impression that the net result is
zero.)
After giving each child a turn at this, we had a minute or two left in
some of the groups, so we did a more advanced third-law demo. I got
on a cart and held a bathroom scale, while I gave the child on the
other cart a bathroom scale. We pushed off each other's scales, and
her cart accelerated a lot while mine accelerated only a little. I
had asked them to predict the accelerations, and they invariably get
that right. But then I asked them what they thought the forces (the
readings on the scales as we pushed) were: more on my scale, more on
hers, or the same? They invariably think more on mine, because I'm
bigger and so they think I must exert more force. But the scale
readings are the same, which is just Newton's third law! The effect
of the force (the acceleration) is different because she has little
mass and I have a lot, but the amount of force is the same.
Similarly, in a car collision, where the massive vehicle decelerates
relatively little while the light vehicle decelerates a lot; this can
only happen if the forces are the same!
The kids seemed to really like these activities. In fact, Becca told
her mom so, and Becca is hard to impress. The only thing I would do
differently is not buy such cheap bathroom scales. They constantly
had to be re-zeroed, and were not very reliable or accurate. But stay
away from the digital ones too, which you have to step on, step off,
step on again, etc. These would be frustrating for kids in a pushing
experiment.
The key for good demos and hands-on activities is getting rid of
friction, so we can see how objects behave in the absence of forces.
I usually use hover pucks, devices that look like very big hockey
pucks but have a fan inside so they float on a cushion of air, like
air hockey without the table. (They are also sold under the brand
name Kick Dis.) But I decided we would have more fun and soap up a
table so that we could slide anything without friction. The night
before, I started soaping tables to see how frictionless I could get
them. The result was a lot of frustration. I could never really get
them frictionless, not close enough to make convincing demos. I even
tried soaping a large sheet of glass (one of the mirrored sliding
doors on my closet) and that was better, but still not good enough.
It seems that no table or mirror is quite flat enough; objects will
glide along a bit, but then hit a high point and stop. So I ended up
going to bed late and frustrated, with some mess still to clean up in
the morning. Such is the life of an educator.
So Friday morning quick I went to work and picked up a bunch of
hoverpucks. (I also bought some donuts for the donutapult; see
below.) I had already picked up some carts which looked like very
large skateboards. On a smooth floor or sidewalk, these are
reasonably frictionless and safe to kneel on.
After scouting the school to find the smooth surfaces, I set up a
three-stage plan for each group. We started at the long, smooth table
with the hoverpucks. I asked the kids what they knew about friction,
and then I asked them to rub their hands together to feel friction.
Then I slid a switched-off hoverpuck on the table (it went a very
short distance) to show that friction is why it's hard to slide
things, and I asked them for ideas to get rid of friction. After
entertaining various ideas, I asked them to make predictions for how
the hoverpuck would move after I switched it on and pushed it toward
the other end of the table. Then I did just that, and it went in a
perfectly smooth straight line. So this makes it clear that, in the
absence of forces, objects in motion continue their motion (in a
straight line at constant speed). This is Newton's first law of
motion, but I didn't ask them to remember that. We had too many cool
experiments to do, and I can count on the regular teachers to review
the terminology several times!
So I seamlessly continued with the hoverpuck. I asked a child seated
along the middle of the table to give the puck a sideways tap as it
passed her down the long axis of the table. First time with a small
tap, then with a larger one, and each time I asked the kids to predict
the subsequent motion. This sequence shows a few things. First, that
a bigger force (or tap, or push) causes a bigger acceleration (change
in motion, whether it be a change in speed or direction...mostly
direction in this case), which is part of Newton's second law.
Second, a force changes the motion only while the force is being
applied. The tap changes the direction of the puck, but only while
the tap is applied. After the tap, the puck follows its new direction
in a straight line. A one-time tap cannot make it keep curving
around. This reinforces the first law: while there are no forces, it
goes in a straight line at constant speed.
To wrap up the hoverpuck activity (which was only the first of the
three stages I had planned), I gave each child a hoverpuck and asked
them to figure out how to make it travel in a circle (which is
distinct from spinning). They needed this bit of playing to relieve
the wiggles, because to this point it had been mostly demo, with some
assistance from 1-2 kids. After several minutes, we discussed how the
only way to make the puck go in a circle is to keep your hand on it
and move your hand in a circle. In other words, circular motion
requires a continuously changing direction of motion, and therefore a
continuous force. This bit isn't strictly necessary if we just wanted
to do Newton's laws, but it connects to the next stage and some other
interesting ideas in the next paragraph.
Second stage: we went outside and I made a bagel-on-a-string go around
in circles over my head. I asked them to imagine what would happen if
the string broke. If they really got Newton's first law, they would
answer that it would fly off in a straight line, but of course most
people don't grasp it that well after just the first demo. So some
said it would fall straight down, a few said it would fly off in a
circular motion, etc. So now comes the really fun part. It's not
practical to cut the string, so instead I tie a donut to a string, and
the string cuts its own way through the soft donut as I whip it around
over my head. I ask them to observe well, because once the donut
comes free there's only a split second before it hits the fence, or a
tree, or a person! Of course it flies off in a straight line:
Newton's first law strikes again. Then I ask them to think of
anything else that moves in a circle. Sometimes I have to hint "in
space", but they can guess Earth around the Sun, or the Moon around
the Earth. So that's the proof that there is a force keeping the Moon
around the Earth: if there were not, the Moon would fly off in a
straight line. (This comes as a revelation to many adults and college
students...they were never helped to make the connection between real
life and Newton's abstract laws of motion.) Then I ask them what the
name of that force is, and in each group at least one child knew it
was called gravity.
Third stage: we went to the sidewalk for the cart activity. First,
each child gave a push to an unloaded cart, and then the same size
push to a cart loaded with 40 pounds of weights. The heavier cart
accelerated much less. This is the other facet of Newton's second
law: acceleration is proportional to force, but inversely proportional
to the mass of the object being accelerated. The phrase "same size
push" is an attempt to make "same force" sound less technical. Some
kids initially seemed to interpret it as "make the cart accelerate the
same amount" so I made sure to counter this by continually repeating
phrases like "use all the same muscles" or "push just as hard as last
time." In cases where they still didn't quite get it, I asked if they
ever got so mad at their brother (or sister, or friend) that they
wanted to push them. Yes, you can admit it! Pretend the cart is your
brother, you are mad, and you push him. Now, for the other cart,
you're still just as mad, so push just the same!
Also, a common misconception is to look at how far the cart travels as
a measure of the effect of the push. We must not do this, because how
far it travels is a complicated function of how much friction there
is, whether it had to roll over a small stone or a crack, fight a gust
of wind, etc. No, we must observe how fast the cart was moving
immediately after the push.
Finally, we get to Newton's third law. I need two volunteers, one to
kneel on each cart. Alone, each child can't get his or her cart to
start moving. But they can if they push against each other, and this
results in equal and opposite accelerations if I wisely chose
volunteers of the similar mass. This shows that forces come in equal
and opposite pairs, which is Newton's third law. (The usual
formulation, "Every action has an equal and opposite reaction," is
very misleading because it gives the impression that the net result is
zero.)
After giving each child a turn at this, we had a minute or two left in
some of the groups, so we did a more advanced third-law demo. I got
on a cart and held a bathroom scale, while I gave the child on the
other cart a bathroom scale. We pushed off each other's scales, and
her cart accelerated a lot while mine accelerated only a little. I
had asked them to predict the accelerations, and they invariably get
that right. But then I asked them what they thought the forces (the
readings on the scales as we pushed) were: more on my scale, more on
hers, or the same? They invariably think more on mine, because I'm
bigger and so they think I must exert more force. But the scale
readings are the same, which is just Newton's third law! The effect
of the force (the acceleration) is different because she has little
mass and I have a lot, but the amount of force is the same.
Similarly, in a car collision, where the massive vehicle decelerates
relatively little while the light vehicle decelerates a lot; this can
only happen if the forces are the same!
The kids seemed to really like these activities. In fact, Becca told
her mom so, and Becca is hard to impress. The only thing I would do
differently is not buy such cheap bathroom scales. They constantly
had to be re-zeroed, and were not very reliable or accurate. But stay
away from the digital ones too, which you have to step on, step off,
step on again, etc. These would be frustrating for kids in a pushing
experiment.
Saturday, October 29, 2011
Going up?
The pre-K/K kids have been really interested in machines for a few
weeks now. When I first heard about that interest, I (with Linus's
permission) brought our set of Gears!Gears!Gears! to the room for a
long-term loan. Since then, I have seen kids playing with the gears
every morning I drop Linus off. When we saw a slightly more advanced
set of Gears!Gears!Gears! in Costco one Sunday (with different size
gears and a loop gear, plus some non-gear bells and whistles), it was
a no-brainer to buy that and bring that for a long-term loan as well.
The kids seem to really be into it.
So I thought of building on that interest by doing something with
pulleys, and I settled on building a simple elevator as an activity
which seemed doable, but still challenging enough to be interesting.
I borrowed a big old pulley from the physics department, brought some
of my own ropes and weights, and counted on the school having some big
dairy cartons and a decent place to hang the pulley.
After some looking around and testing, I settled on a certain tree
branch as a good place to hang the pulley, and I found a dairy carton
big enough for a kid to climb into. With the first group, I started
from scratch, asking them what they thought would be necessary to
build an elevator, and they suggested a basket (they even found one)
and rope (which I supplied). They needed a bit of prodding to suggest
a pulley, but they got that too after I suggested looking above my
head. Most of them didn't really know what a pulley was, so we
discussed that. I strung a rope through it and we each verified that
pulling down on one end of the rope made the other end go up. The kid
were really excited at this point! It was difficult for some of them
not to grab the rope, jump up and down, etc. I pointed out that one
advantage of the pulley is that the puller (the kids in this case, a
motor in real life) need not be on the roof to make the elevator work.
Then I attached the large milk carton and put some heavy object in it
for a first test. The more excited kids volunteered to pull on the
other end of the rope. They were able to lift the elevator, but it
was quite difficult; they had to recruit help and I think it was
successful only with four boys pulling at once. I warned them that if
they let go suddenly, the elevator would crash to the ground and hurt
the (imaginary) people in the elevator.
So I asked them to think about what could make the pulling and the
letting down easier and safer. They thought of all kinds of crazy
ideas before they spotted my weights. So I attached the
counterweights (in a small basket so we would adjust the amount of
counterweight) and we saw that the elevator was much easier to lift
and also easier and safer to let down. So then we were ready to give
rides.
The problem was that the dairy carton tilted too easily when lifted
off the ground, threatening to dump the passenger out. I tried to
stabilize it with additional ropes and by telling the passenger to balance,
but it never really worked. So starting with the second group, I
forbade rides. Instead, we used three containers full of sand to
represent three people. This was actually nice for the lesson because
I was able to put in just enough sand to balance the particular
counterweight I had; with a human passenger, the counterweight was a
help, but never really made it super easy to ascend and descend. With the fake
passengers matched to the counterweight, ascents and descents were very easy,
and I could tell the "motor" to let go, simulating a broken motor. The elevator
did not crash to the ground because it was attached to the just-right
counterweight.
So, once we got it going smoothly, I repeated these steps for each
kid: remove the counterweight; ask them to lift the passengers to the
top floor and have them discover how difficult that is; have them feel
how tricky the descent (from whatever point they reached) is; after
finishing the descent, add the counterweight and ask them to lift the
passengers to the top floor and see how easy it is this time; ask them
to let the passengers descend safely and feel how easy that is; ask the
motor to "break" and see how the passengers do not crash to the ground
because of the counterweight; finish the descent and start over with
another kid. I repeated this whole cycle about a million times
because many kids wanted to do it over and over! I was exhausted by
the end.
This was a pretty simple activity and the kids had a lot of fun. This
is a good lesson for me because I'm often tempted to think that a
potential activity is too simple and that I have to add a lot to it.
Simple can be good! If I ever try rides again, I need to experiment
beforehand how to make the elevator "car" tip-proof. But I think the
rides may have been a distraction. Each child was quite happy in the
"motor" role, so much that they wanted turns over and over, and of
course the motor role is the instructive one.
A small improvement would be to use two pulleys, to give some
horizontal space between the elevator car and the counterweight. One
thing which would take this to the next level would be to crank the
whole thing with some gears attached to a drum which winds up the
rope. I'll keep my eye out for surplus equipment which might be used
for this. And for a toy gear set with these kinds of pieces, which I
will then have to buy and put on long-term loan!
weeks now. When I first heard about that interest, I (with Linus's
permission) brought our set of Gears!Gears!Gears! to the room for a
long-term loan. Since then, I have seen kids playing with the gears
every morning I drop Linus off. When we saw a slightly more advanced
set of Gears!Gears!Gears! in Costco one Sunday (with different size
gears and a loop gear, plus some non-gear bells and whistles), it was
a no-brainer to buy that and bring that for a long-term loan as well.
The kids seem to really be into it.
So I thought of building on that interest by doing something with
pulleys, and I settled on building a simple elevator as an activity
which seemed doable, but still challenging enough to be interesting.
I borrowed a big old pulley from the physics department, brought some
of my own ropes and weights, and counted on the school having some big
dairy cartons and a decent place to hang the pulley.
After some looking around and testing, I settled on a certain tree
branch as a good place to hang the pulley, and I found a dairy carton
big enough for a kid to climb into. With the first group, I started
from scratch, asking them what they thought would be necessary to
build an elevator, and they suggested a basket (they even found one)
and rope (which I supplied). They needed a bit of prodding to suggest
a pulley, but they got that too after I suggested looking above my
head. Most of them didn't really know what a pulley was, so we
discussed that. I strung a rope through it and we each verified that
pulling down on one end of the rope made the other end go up. The kid
were really excited at this point! It was difficult for some of them
not to grab the rope, jump up and down, etc. I pointed out that one
advantage of the pulley is that the puller (the kids in this case, a
motor in real life) need not be on the roof to make the elevator work.
Then I attached the large milk carton and put some heavy object in it
for a first test. The more excited kids volunteered to pull on the
other end of the rope. They were able to lift the elevator, but it
was quite difficult; they had to recruit help and I think it was
successful only with four boys pulling at once. I warned them that if
they let go suddenly, the elevator would crash to the ground and hurt
the (imaginary) people in the elevator.
So I asked them to think about what could make the pulling and the
letting down easier and safer. They thought of all kinds of crazy
ideas before they spotted my weights. So I attached the
counterweights (in a small basket so we would adjust the amount of
counterweight) and we saw that the elevator was much easier to lift
and also easier and safer to let down. So then we were ready to give
rides.
The problem was that the dairy carton tilted too easily when lifted
off the ground, threatening to dump the passenger out. I tried to
stabilize it with additional ropes and by telling the passenger to balance,
but it never really worked. So starting with the second group, I
forbade rides. Instead, we used three containers full of sand to
represent three people. This was actually nice for the lesson because
I was able to put in just enough sand to balance the particular
counterweight I had; with a human passenger, the counterweight was a
help, but never really made it super easy to ascend and descend. With the fake
passengers matched to the counterweight, ascents and descents were very easy,
and I could tell the "motor" to let go, simulating a broken motor. The elevator
did not crash to the ground because it was attached to the just-right
counterweight.
So, once we got it going smoothly, I repeated these steps for each
kid: remove the counterweight; ask them to lift the passengers to the
top floor and have them discover how difficult that is; have them feel
how tricky the descent (from whatever point they reached) is; after
finishing the descent, add the counterweight and ask them to lift the
passengers to the top floor and see how easy it is this time; ask them
to let the passengers descend safely and feel how easy that is; ask the
motor to "break" and see how the passengers do not crash to the ground
because of the counterweight; finish the descent and start over with
another kid. I repeated this whole cycle about a million times
because many kids wanted to do it over and over! I was exhausted by
the end.
This was a pretty simple activity and the kids had a lot of fun. This
is a good lesson for me because I'm often tempted to think that a
potential activity is too simple and that I have to add a lot to it.
Simple can be good! If I ever try rides again, I need to experiment
beforehand how to make the elevator "car" tip-proof. But I think the
rides may have been a distraction. Each child was quite happy in the
"motor" role, so much that they wanted turns over and over, and of
course the motor role is the instructive one.
A small improvement would be to use two pulleys, to give some
horizontal space between the elevator car and the counterweight. One
thing which would take this to the next level would be to crank the
whole thing with some gears attached to a drum which winds up the
rope. I'll keep my eye out for surplus equipment which might be used
for this. And for a toy gear set with these kinds of pieces, which I
will then have to buy and put on long-term loan!
Monday, October 24, 2011
We all learn with a little submarine
Friday I did the submarine activity at the elementary. This was at a
somewhat higher level because the kids here had been studying weight
and volume and how to measure them. Because I had told Lorie I would
be doing this activity, she sneaked in a lesson on density before my
visit. So I was able to discuss how density related to the
experiment. (What they remembered about density is that it's "weight
and volume together", but they were not able to articulate just how,
so this served as a good reinforcement.)
A few notes to myself on implementation: (1) the little rocks at
Lorie's house are great for shoveling in the bottles easily; (2) the
right kind of water container (low and flat) is really important,
because high walls and/or deep water is a big inconvenience; and (3)
don't let any kids fill their bottle with sand!
Overall, I'd say it worked just as well with the elementary as it did
with Primaria. That's not to say it was the same; it was definitely
different, but it's amazing how the same thing can be viewed through
different lenses and be valuable in different ways for different age
groups.
somewhat higher level because the kids here had been studying weight
and volume and how to measure them. Because I had told Lorie I would
be doing this activity, she sneaked in a lesson on density before my
visit. So I was able to discuss how density related to the
experiment. (What they remembered about density is that it's "weight
and volume together", but they were not able to articulate just how,
so this served as a good reinforcement.)
A few notes to myself on implementation: (1) the little rocks at
Lorie's house are great for shoveling in the bottles easily; (2) the
right kind of water container (low and flat) is really important,
because high walls and/or deep water is a big inconvenience; and (3)
don't let any kids fill their bottle with sand!
Overall, I'd say it worked just as well with the elementary as it did
with Primaria. That's not to say it was the same; it was definitely
different, but it's amazing how the same thing can be viewed through
different lenses and be valuable in different ways for different age
groups.
Sunday, October 16, 2011
A boat which sinks on purpose
This builds very well on the previous pre-K/K activity, in which we
investigated what floats and what sinks. By the end of that
activity, the kids had figured out that sinking a plastic soda bottle
takes quite a bit of effort. They need to put in some heavy things
like rocks (small ones which fit through the neck), but that is not
enough; they also had to get rid of most of the air by replacing it with
water. We started by reviewing what we had learned last time (by me
asking them questions, not by me lecturing).
After reviewing the basics, I showed them a bottle with some rocks in
it and the cap on and asked them if it would float or sink. Many of
them had forgotten how easily it floats unless it's really full of
rocks. We talked about boats, how they float because they have lots
of air inside (we had made aluminum-foil boats last time), and how a
submarine is special because it has to sink when desired but then has
to float again when desired. Most kids are under the misconception
that submarines dive just by having their engines push them down, but
if so then subs would have to have engines roaring just to stay still
underwater. Instead, they really do sink. We talked about how the
rocks inside represent heavy stuff that has to be on the submarine,
like engines and other equipment, people, etc, and also how there
still has to be some air on the submarine for people to walk around
and breathe.
So I challenged them to make a bottle almost sink with heavy stuff,
and then I would help them with the next step. I brought a box of
small rocks, and one bottle per child. They consistently
underestimate how many rocks it takes to sink the bottle with the cap
on. It needs to be about 2/3 full (although a fair fraction of this
2/3 is still air pockets between the rocks). When a child was ready
test, I put on the cap for them and tested it even when I knew it
wouldn't sink. Eventually they got close enough, but next time I
might consider marbles or something similar which would roll into the
mouth of the bottle more easily than irregularly shaped rocks, some of
which were too big anyway. The kids got a lot of practice making
predictions that it would sink, testing those predictions, and
modifying their hypotheses.
Before class, I had drilled two small holes in each bottle so water
could enter and exit if desired. These were drilled along one side,
which is considered the bottom of the sub when the bottle is floating
lengthwise, somewhat resembling the actual shape of a sub:
With enough ballast to get it close to sinking, I gave the kids new
caps which had had holes drilled and straws inserted through the holes
in a (nearly) watertight manner. It worked well that each kid got the
ballast done at different times, so that I could do some one-on-one
with each at the critical moment. I pointed out how the darn thing
still wouldn't sink, and why do they think it wants to float so much?
We would eventually hit on the idea of getting rid of the air using
the straw. Many of the kids were not old enough to know the difference
between blowing and sucking! They were supposed to suck the air out,
thus pulling water in through the holes on the bottom. Many blew to
begin with, but figured it out.
When they finally got it to sink, it was cause for high-fives. I made sure to
point out that there was still air in the sunken sub, so the crew would still be
able to breathe. I then challenged them to get it to float again, which involves
blowing on the straw, thus forcing water out through the bottom holes.
From that point on, it was just fun time as kids experimented with
their creations.
I think we took about 20 minutes per group of five students. I would
recommend using a shallow container of water such as a water table,
not an aquarium! Water deeper than say 6 inches is just unnecessary
and a pain....straws are only so long, and high aquarium walls make it
difficult to reach.
This activity was pretty successful in terms of student interest. The
first group was the most difficult, because they had to put in all the
ballast, which was a lot of work. After that, I took out just some of
the ballast between groups so that each group went through the process
without it being quite so arduous. As I wrote above, in the future I
should check out types of ballast which will go in more easily.
investigated what floats and what sinks. By the end of that
activity, the kids had figured out that sinking a plastic soda bottle
takes quite a bit of effort. They need to put in some heavy things
like rocks (small ones which fit through the neck), but that is not
enough; they also had to get rid of most of the air by replacing it with
water. We started by reviewing what we had learned last time (by me
asking them questions, not by me lecturing).
After reviewing the basics, I showed them a bottle with some rocks in
it and the cap on and asked them if it would float or sink. Many of
them had forgotten how easily it floats unless it's really full of
rocks. We talked about boats, how they float because they have lots
of air inside (we had made aluminum-foil boats last time), and how a
submarine is special because it has to sink when desired but then has
to float again when desired. Most kids are under the misconception
that submarines dive just by having their engines push them down, but
if so then subs would have to have engines roaring just to stay still
underwater. Instead, they really do sink. We talked about how the
rocks inside represent heavy stuff that has to be on the submarine,
like engines and other equipment, people, etc, and also how there
still has to be some air on the submarine for people to walk around
and breathe.
So I challenged them to make a bottle almost sink with heavy stuff,
and then I would help them with the next step. I brought a box of
small rocks, and one bottle per child. They consistently
underestimate how many rocks it takes to sink the bottle with the cap
on. It needs to be about 2/3 full (although a fair fraction of this
2/3 is still air pockets between the rocks). When a child was ready
test, I put on the cap for them and tested it even when I knew it
wouldn't sink. Eventually they got close enough, but next time I
might consider marbles or something similar which would roll into the
mouth of the bottle more easily than irregularly shaped rocks, some of
which were too big anyway. The kids got a lot of practice making
predictions that it would sink, testing those predictions, and
modifying their hypotheses.
Before class, I had drilled two small holes in each bottle so water
could enter and exit if desired. These were drilled along one side,
which is considered the bottom of the sub when the bottle is floating
lengthwise, somewhat resembling the actual shape of a sub:
With enough ballast to get it close to sinking, I gave the kids new
caps which had had holes drilled and straws inserted through the holes
in a (nearly) watertight manner. It worked well that each kid got the
ballast done at different times, so that I could do some one-on-one
with each at the critical moment. I pointed out how the darn thing
still wouldn't sink, and why do they think it wants to float so much?
We would eventually hit on the idea of getting rid of the air using
the straw. Many of the kids were not old enough to know the difference
between blowing and sucking! They were supposed to suck the air out,
thus pulling water in through the holes on the bottom. Many blew to
begin with, but figured it out.
When they finally got it to sink, it was cause for high-fives. I made sure to
point out that there was still air in the sunken sub, so the crew would still be
able to breathe. I then challenged them to get it to float again, which involves
blowing on the straw, thus forcing water out through the bottom holes.
From that point on, it was just fun time as kids experimented with
their creations.
I think we took about 20 minutes per group of five students. I would
recommend using a shallow container of water such as a water table,
not an aquarium! Water deeper than say 6 inches is just unnecessary
and a pain....straws are only so long, and high aquarium walls make it
difficult to reach.
This activity was pretty successful in terms of student interest. The
first group was the most difficult, because they had to put in all the
ballast, which was a lot of work. After that, I took out just some of
the ballast between groups so that each group went through the process
without it being quite so arduous. As I wrote above, in the future I
should check out types of ballast which will go in more easily.
Sunday, October 2, 2011
Floating and Sinking
Most kids love playing with water, and in hot weather water is a good thing to do science outdoors with. (Not to mention that the ocean is the theme in Primaria this year!) Discovering what sinks and what floats is a natural entry point for science because it is so simple that the youngest kids can appreciate it, yet it can lead to quite sophisticated concepts for the older ones who are ready to handle those. Furthermore, I designed this activity to lead naturally up to a submarine-building activity I want to do next time.
I started with just a simple glass of water visible. I asked each
child if they thought a wood chip would float or sink. For me, this
next step is really important. If the vote is not unanimous, I ask if
we can settle the issue just by counting the votes. Science is not a
democracy! We have to do the experiment and pay attention to the
results if we want to make any progress! And if the vote is unanimous, I
ask them if maybe we don't need to do the experiment. We agree
(sometimes with some nudging from me) that even if we all think it's
going to float, we should still do the experiment because sometimes we
could all be wrong in our predictions. I really want to emphasize
these aspects of the scientific method as early as possible, and this
activity is a good place to do it.
Then I repeat with several objects, such as a stone, a marble, a piece
of plastic, a bolt, a paper clip, etc. The kids have some idea that
lighter things are more likely to float, so the paper clip gives some
pause. I try not to use the word "density" because this means nothing
to the pre-K/K kids, but I do try to summarize that floating/sinking
is expected for something that is light/heavy for its size, not just
light/heavy in some absolute sense.
Then we get to the more interesting demo. (Some of them desperately
want to play with this stuff already, but I promise they can play if
they pay attention for just a bit longer.) I pull out a hard-boiled
egg and we see that it sinks. But if I add plenty of salt to the
water, the egg begins to float. This shows that the salt is mixing
with the water in a way which makes the water heavier. (By the way,
floating an egg is apparently how people used to determine they had
added enough salt to their pickling solution when making pickles.)
Then we repeat the whole thing with sand. Try as we might, the egg
does not float and the sand just collects at the bottom rather than
dissolving in the water. Here we have the observational basis for
some chemistry: salt in water forms a solution, but sand in water does
not. (I didn't state it this technically, but we did talk about how
ocean water behaves at the beach...the salt is an integral part of it,
as we can tell by its taste, but the sand is not.) We also have the
idea of different kinds of mixtures, which ties in nicely with the
previous pre-K/K science activity.
Finally we get to the play time. But this is serious play. I bring
out one tub of water in which I place some aluminum-foil boats.
Although they are metal, they do not sink. I challenge them to figure
out how to sink the boats. In parallel, a second tub contains empty
8-oz plastic soda bottles which I also challenge the children to sink.
The challenge aspect is really important. They come up with the ideas
and try them out. It seems like play time, but it has a purpose. This
particular challenge has the extra purpose that it builds up to the
future submarine activity.
With the foil, I have extra challenges ready for those who quickly
figure out how to sink the boats with stones. I challenge them to sink
the foil just by crumpling it up into a ball. It is surprisingly
difficult to do this; small air bubbles trapped in the foil are
surprisingly effective at floating it even after squeezing as hard as
possible. Some of them easily recognize that air bubbles must be the
problem, while others need some hints. The persistent ones finally
succeed in hammering out the air bubbles using anything vaguely
hammer-like. Meanwhile, others have gone in a slightly different
direction, crumpling the foil around a stone so that it forms a ball
with high average density.
With the plastic bottles, students take one of two initial strategies:
filling the bottles with water, or with stones/sand. Those who try
water see that water is not heavier than water, so that a waterlogged
plastic bottle still does not sink. Then they tend to start over with
stones/sand. However, the stone/sand strategy is surprisingly
ineffective. You can fill a bottle 1/4 full or even 1/2 or even 2/3 full of
stones/sand and it still doesn't sink. There's just too much air in
the bottle. However, few students have the patience (or the time left
in the activity) to fill the small-necked bottle completely with stones/sand.
They figure out (possibly with some hints) that they can
replace the bothersome air with water and finally get it to sink.
This is really good background for the submarine activity!
I think we spent 20 minutes with each group of about 5 kids, and that
was the perfect amount of time and the perfect size group. Larger groups could be
accommodated with more tubs of water; more than 3 kids per tub would not be good.
I started with just a simple glass of water visible. I asked each
child if they thought a wood chip would float or sink. For me, this
next step is really important. If the vote is not unanimous, I ask if
we can settle the issue just by counting the votes. Science is not a
democracy! We have to do the experiment and pay attention to the
results if we want to make any progress! And if the vote is unanimous, I
ask them if maybe we don't need to do the experiment. We agree
(sometimes with some nudging from me) that even if we all think it's
going to float, we should still do the experiment because sometimes we
could all be wrong in our predictions. I really want to emphasize
these aspects of the scientific method as early as possible, and this
activity is a good place to do it.
Then I repeat with several objects, such as a stone, a marble, a piece
of plastic, a bolt, a paper clip, etc. The kids have some idea that
lighter things are more likely to float, so the paper clip gives some
pause. I try not to use the word "density" because this means nothing
to the pre-K/K kids, but I do try to summarize that floating/sinking
is expected for something that is light/heavy for its size, not just
light/heavy in some absolute sense.
Then we get to the more interesting demo. (Some of them desperately
want to play with this stuff already, but I promise they can play if
they pay attention for just a bit longer.) I pull out a hard-boiled
egg and we see that it sinks. But if I add plenty of salt to the
water, the egg begins to float. This shows that the salt is mixing
with the water in a way which makes the water heavier. (By the way,
floating an egg is apparently how people used to determine they had
added enough salt to their pickling solution when making pickles.)
Then we repeat the whole thing with sand. Try as we might, the egg
does not float and the sand just collects at the bottom rather than
dissolving in the water. Here we have the observational basis for
some chemistry: salt in water forms a solution, but sand in water does
not. (I didn't state it this technically, but we did talk about how
ocean water behaves at the beach...the salt is an integral part of it,
as we can tell by its taste, but the sand is not.) We also have the
idea of different kinds of mixtures, which ties in nicely with the
previous pre-K/K science activity.
Finally we get to the play time. But this is serious play. I bring
out one tub of water in which I place some aluminum-foil boats.
Although they are metal, they do not sink. I challenge them to figure
out how to sink the boats. In parallel, a second tub contains empty
8-oz plastic soda bottles which I also challenge the children to sink.
The challenge aspect is really important. They come up with the ideas
and try them out. It seems like play time, but it has a purpose. This
particular challenge has the extra purpose that it builds up to the
future submarine activity.
With the foil, I have extra challenges ready for those who quickly
figure out how to sink the boats with stones. I challenge them to sink
the foil just by crumpling it up into a ball. It is surprisingly
difficult to do this; small air bubbles trapped in the foil are
surprisingly effective at floating it even after squeezing as hard as
possible. Some of them easily recognize that air bubbles must be the
problem, while others need some hints. The persistent ones finally
succeed in hammering out the air bubbles using anything vaguely
hammer-like. Meanwhile, others have gone in a slightly different
direction, crumpling the foil around a stone so that it forms a ball
with high average density.
With the plastic bottles, students take one of two initial strategies:
filling the bottles with water, or with stones/sand. Those who try
water see that water is not heavier than water, so that a waterlogged
plastic bottle still does not sink. Then they tend to start over with
stones/sand. However, the stone/sand strategy is surprisingly
ineffective. You can fill a bottle 1/4 full or even 1/2 or even 2/3 full of
stones/sand and it still doesn't sink. There's just too much air in
the bottle. However, few students have the patience (or the time left
in the activity) to fill the small-necked bottle completely with stones/sand.
They figure out (possibly with some hints) that they can
replace the bothersome air with water and finally get it to sink.
This is really good background for the submarine activity!
I think we spent 20 minutes with each group of about 5 kids, and that
was the perfect amount of time and the perfect size group. Larger groups could be
accommodated with more tubs of water; more than 3 kids per tub would not be good.
Friday, September 23, 2011
Length, Area, Volume, Dinosaurs and Giant Insects
One of the strengths of Peregrine School is that learning is
integrated. Instead of offering isolated concepts and facts, we try
to design activities which build on and reinforce each other. The
past week or two, the elementary students have been reviewing how to
measure. They have measured their bedrooms and mapped their rooms on
pieces of graph paper, for example. So I thought I would follow that
up by specifically relating length with area and volume and leading
into one of the most underappreciated aspects of science: scaling
relations.
(By the way, I didn't get time to talk about a lot of these ideas with
each group, so this post may be a good resource for parents who would
like to follow up the activity and investigate more.)
Beforehand, I printed out some graph paper with 3/4" squares to match
the unifix cubes we had on hand. This way, when we shifted from
measuring area (counting squares of graph paper) to measuring volume
(counting cubes), the kids would not be distracted by a change in the
size of the measuring unit. To people who understand area and volume,
a change in grid size might be an irrelevant detail, but to those who
don't, it could be the start of a long and unnecessary detour.
First, I asked them to draw a map of a room which was 1x1, and measure
the area by counting the squares inside (1, obviously). This should
be really boring and easy, but it took a surprisingly long time to get
everybody clear on what I was asking. Maybe next time, to speed
things up, I would start by drawing the 1x1 square so they would
instantly see my intention rather than having to parse my words.
Next, I asked them to draw a 2x2 square, predict the area, and then
measure it. Over the course of 3 groups, I learned to be stricter
about making the prediction. Once kids understand what the task is,
they are quite happy to do bigger and bigger squares and get answers
without making any predictions. But they don't learn anything this
way; only if they see that their prediction was wrong will they take
the trouble to figure out what's really going on. (In principle, the
discomfort of realizing that reality conflicts with his/her beliefs
("cognitive dissonance") will spur the student to make the effort to
really understand. In practice, it doesn't always work that
way...perhaps the subject of another post. But the fact that some
students won't care when their predictions are wrong should not stop
us from trying; they are even less likely to care if they never commit
to a prediction. And if we get even a bare majority of the class
modifying their beliefs based on evidence, we are doing a great
thing!)
So, in the spirit of being strict about making predictions, I ask you
to make a prediction. If you were to double the length and the width
of the 1x1 square, what would happen to the area? What if you were to
triple the length and width? Quadruple? Make your predictions before
reading on!
With the kids telling me the results of their experiments, I compiled
the following chart:
length area
---------------
1 1
2 4
3 9
4 16
5 25
Note that very few of them made correct predictions of these results!
I also made a graph of this, to show them the pattern in different
ways. The graph shows a very rapidly rising curve. The area
increases much faster than the length!
Why should we care? None of them knew. And I think this is a weakness
with traditional math education. These concepts are taught in a
vacuum and never made relevant. (A recent op-ed in the New York Times
agrees with me on this.) So I gave two examples:
(1) if you wanted a room twice as long and twice as wide, how many
times more carpet would you need to cover the floor? Amazingly, no
one got this right even after I pointed to the chart, with numerous
hints! The most popular answer was double. They were not able to
transfer the idea from the chart to a new situation, so they had not
really learned. Good thing I asked them instead of just moving on!
So we discussed this a bit before moving on.
(2) Suppose you have a small room full of people, like at a party.
There's a door in each wall so if there's a fire, they can easily
escape. But now imagine a room 3x longer and 3x wider. It can fit 9x
the people, so now there will be long lines at the doors when the fire
alarm goes off. People could die if architects didn't think about
these things! We'll need a lot more doors for rooms which, if we
thought only about length, might not seem so much bigger. Or you
could think about evacuating a city. A city 10x the size in each
direction has 100x the people, but nowhere near 100x the number of
escape routes, so it may be simply impossible to evacuate in a short
amount of time.
(3) I didn't have time to show that surface area behaves the same way
as area, but it does. That is, if we wanted to carpet ALL the
surfaces of a room, a room twice as big in each dimension would still
take only 4x the carpet of the smaller room. (In either case, the
total surface area is 6x the area of the floor.) Furthermore, the
same is still true of an irregular surface such as the surface of your
body. A dog twice as large in each dimension will have quadruple the
surface area you need to brush!
Ok, now we moved on to volume. I asked them to model a 1x1x1 room
with cubes and tell me the volume, then predict the volume of a 2x2x2
room. Again, no one got it right! We quickly built up a new column
in our chart:
length area volume
---------------------------
1 1 1
2 4 8
3 9 27
4 16 64
5 25 125
(actually, I filled in the 64 and 125 due to lack of time). Again,
why do we care? Well, the volume increases much faster than even
the area does, so if you wanted a swimming pool twice as long,
twice as wide, and twice as deep, it would have quadruple the surface area but
you should plan to pay for eight times the water to fill it up!
And here's where I finally got to the applications I thought would
interest the kids. If you have a dog twice as long, twice as tall,
and twice as wide as another dog, it will have 8x the volume and thus
8x the weight. You will have to feed that dog 8x the amount of energy
if it's going to have the same activity level as the smaller dog (thus
explaining why larger dogs generally do NOT have the same activity
level as larger dogs). If you have a dinosaur four times the size of
a rhino in each dimension, it will weigh as much as 64 rhinos!
This actually explains why there is a limit to the size of animals.
If you double the size of an animal in each dimension, it has eight
times the weight to support. But the strength of its bones grows only
as their cross-sectional area (4x in this example). So the bones will
not be able to support the weight. To make that bigger animal, we
will need to change the plan and not just scale everything up. This
explains why we don't see mice the size of elephants. To go from
mouse-size to elephant size requires a drastic redesign and
proportionally much thicker bones. And there's a limit to how thick
you can make the bones, so there's a limit to the redesign strategy.
So why are the largest whales so much bigger than elephants? Because
whales don't really support their weight; the ocean does.
And why were the largest dinosaurs so much bigger than elephants? I'm
guessing that it's due to a more subtle limit on the elephant. If you
double each dimension of an elephant so it has 8x the weight, then it
also produces 8x the heat because it is warm-blooded. But this heat
can only escape through the surface area, which is 4x the original surface area. So the 2x-scale elephant would overheat! Dinosaurs (at least the biggest
ones, as far as we know) were cold-blooded, so they didn't have this
issue. (It was also thought at one time that the largest dinosaurs
were swamp-dwellers so that water supported some of their weight, but
this seems to be unsupported by evidence.)
(Why don't blue whales overheat? I'm guessing it's because
water conducts heat away much better, and because they are very long
and skinny, thus maximizing their surface area; they are NOT 2x-scale
copies of smaller whales.)
This heat consideration explains a couple of other things. Larger
mammals have slower metabolisms than smaller mammals, to avoid
overheating. (Slower metabolisms, by the way, enable longer life
spans. Ever notice how the life span of a mammal correlates roughly
with its size?) And elephants have enormous ears to help them get rid
of heat.
Finally, let's think about insects. Insects get oxygen by absorbing
it through their "skin", so if we make a 2x-scale insect, we can get
oxygen in at 4x the rate, but we have 8x the amount of flesh which
needs oxygen. That's not gonna work. So we have a limit on the size
of insects. But why were there 2.5-foot dragonflies hundreds of
millions of years ago? Turns out that there was much more oxygen in
the atmosphere at that time, so each bit of surface area could take in
oxygen more effectively, and the area/volume tradeoff could be pushed
further towards more volume.
Now, I didn't get time to talk about many of these ideas, at least in
any detail. We will expand my science slot to 30 minutes with each
group. But here are some resources for parents to follow up:
Wikipedia article on the square-cube law: this repeats much of what I said about volume vs area, but has links to related articles in more depth. In particular, if you like to think about animals, you might want to check out....
Wikipedia article on allometry: allometry is the fact that most larger animals are NOT scaled-up smaller animals, but have changes in body plan.
Wikipedia article on Meganeura: this is the 2.5-foot dragonfly. It has a link to the 1999 Nature article linking insect gigantism to oxygen supply.
integrated. Instead of offering isolated concepts and facts, we try
to design activities which build on and reinforce each other. The
past week or two, the elementary students have been reviewing how to
measure. They have measured their bedrooms and mapped their rooms on
pieces of graph paper, for example. So I thought I would follow that
up by specifically relating length with area and volume and leading
into one of the most underappreciated aspects of science: scaling
relations.
(By the way, I didn't get time to talk about a lot of these ideas with
each group, so this post may be a good resource for parents who would
like to follow up the activity and investigate more.)
Beforehand, I printed out some graph paper with 3/4" squares to match
the unifix cubes we had on hand. This way, when we shifted from
measuring area (counting squares of graph paper) to measuring volume
(counting cubes), the kids would not be distracted by a change in the
size of the measuring unit. To people who understand area and volume,
a change in grid size might be an irrelevant detail, but to those who
don't, it could be the start of a long and unnecessary detour.
First, I asked them to draw a map of a room which was 1x1, and measure
the area by counting the squares inside (1, obviously). This should
be really boring and easy, but it took a surprisingly long time to get
everybody clear on what I was asking. Maybe next time, to speed
things up, I would start by drawing the 1x1 square so they would
instantly see my intention rather than having to parse my words.
Next, I asked them to draw a 2x2 square, predict the area, and then
measure it. Over the course of 3 groups, I learned to be stricter
about making the prediction. Once kids understand what the task is,
they are quite happy to do bigger and bigger squares and get answers
without making any predictions. But they don't learn anything this
way; only if they see that their prediction was wrong will they take
the trouble to figure out what's really going on. (In principle, the
discomfort of realizing that reality conflicts with his/her beliefs
("cognitive dissonance") will spur the student to make the effort to
really understand. In practice, it doesn't always work that
way...perhaps the subject of another post. But the fact that some
students won't care when their predictions are wrong should not stop
us from trying; they are even less likely to care if they never commit
to a prediction. And if we get even a bare majority of the class
modifying their beliefs based on evidence, we are doing a great
thing!)
So, in the spirit of being strict about making predictions, I ask you
to make a prediction. If you were to double the length and the width
of the 1x1 square, what would happen to the area? What if you were to
triple the length and width? Quadruple? Make your predictions before
reading on!
With the kids telling me the results of their experiments, I compiled
the following chart:
length area
---------------
1 1
2 4
3 9
4 16
5 25
Note that very few of them made correct predictions of these results!
I also made a graph of this, to show them the pattern in different
ways. The graph shows a very rapidly rising curve. The area
increases much faster than the length!
Why should we care? None of them knew. And I think this is a weakness
with traditional math education. These concepts are taught in a
vacuum and never made relevant. (A recent op-ed in the New York Times
agrees with me on this.) So I gave two examples:
(1) if you wanted a room twice as long and twice as wide, how many
times more carpet would you need to cover the floor? Amazingly, no
one got this right even after I pointed to the chart, with numerous
hints! The most popular answer was double. They were not able to
transfer the idea from the chart to a new situation, so they had not
really learned. Good thing I asked them instead of just moving on!
So we discussed this a bit before moving on.
(2) Suppose you have a small room full of people, like at a party.
There's a door in each wall so if there's a fire, they can easily
escape. But now imagine a room 3x longer and 3x wider. It can fit 9x
the people, so now there will be long lines at the doors when the fire
alarm goes off. People could die if architects didn't think about
these things! We'll need a lot more doors for rooms which, if we
thought only about length, might not seem so much bigger. Or you
could think about evacuating a city. A city 10x the size in each
direction has 100x the people, but nowhere near 100x the number of
escape routes, so it may be simply impossible to evacuate in a short
amount of time.
(3) I didn't have time to show that surface area behaves the same way
as area, but it does. That is, if we wanted to carpet ALL the
surfaces of a room, a room twice as big in each dimension would still
take only 4x the carpet of the smaller room. (In either case, the
total surface area is 6x the area of the floor.) Furthermore, the
same is still true of an irregular surface such as the surface of your
body. A dog twice as large in each dimension will have quadruple the
surface area you need to brush!
Ok, now we moved on to volume. I asked them to model a 1x1x1 room
with cubes and tell me the volume, then predict the volume of a 2x2x2
room. Again, no one got it right! We quickly built up a new column
in our chart:
length area volume
---------------------------
1 1 1
2 4 8
3 9 27
4 16 64
5 25 125
(actually, I filled in the 64 and 125 due to lack of time). Again,
why do we care? Well, the volume increases much faster than even
the area does, so if you wanted a swimming pool twice as long,
twice as wide, and twice as deep, it would have quadruple the surface area but
you should plan to pay for eight times the water to fill it up!
And here's where I finally got to the applications I thought would
interest the kids. If you have a dog twice as long, twice as tall,
and twice as wide as another dog, it will have 8x the volume and thus
8x the weight. You will have to feed that dog 8x the amount of energy
if it's going to have the same activity level as the smaller dog (thus
explaining why larger dogs generally do NOT have the same activity
level as larger dogs). If you have a dinosaur four times the size of
a rhino in each dimension, it will weigh as much as 64 rhinos!
This actually explains why there is a limit to the size of animals.
If you double the size of an animal in each dimension, it has eight
times the weight to support. But the strength of its bones grows only
as their cross-sectional area (4x in this example). So the bones will
not be able to support the weight. To make that bigger animal, we
will need to change the plan and not just scale everything up. This
explains why we don't see mice the size of elephants. To go from
mouse-size to elephant size requires a drastic redesign and
proportionally much thicker bones. And there's a limit to how thick
you can make the bones, so there's a limit to the redesign strategy.
So why are the largest whales so much bigger than elephants? Because
whales don't really support their weight; the ocean does.
And why were the largest dinosaurs so much bigger than elephants? I'm
guessing that it's due to a more subtle limit on the elephant. If you
double each dimension of an elephant so it has 8x the weight, then it
also produces 8x the heat because it is warm-blooded. But this heat
can only escape through the surface area, which is 4x the original surface area. So the 2x-scale elephant would overheat! Dinosaurs (at least the biggest
ones, as far as we know) were cold-blooded, so they didn't have this
issue. (It was also thought at one time that the largest dinosaurs
were swamp-dwellers so that water supported some of their weight, but
this seems to be unsupported by evidence.)
(Why don't blue whales overheat? I'm guessing it's because
water conducts heat away much better, and because they are very long
and skinny, thus maximizing their surface area; they are NOT 2x-scale
copies of smaller whales.)
This heat consideration explains a couple of other things. Larger
mammals have slower metabolisms than smaller mammals, to avoid
overheating. (Slower metabolisms, by the way, enable longer life
spans. Ever notice how the life span of a mammal correlates roughly
with its size?) And elephants have enormous ears to help them get rid
of heat.
Finally, let's think about insects. Insects get oxygen by absorbing
it through their "skin", so if we make a 2x-scale insect, we can get
oxygen in at 4x the rate, but we have 8x the amount of flesh which
needs oxygen. That's not gonna work. So we have a limit on the size
of insects. But why were there 2.5-foot dragonflies hundreds of
millions of years ago? Turns out that there was much more oxygen in
the atmosphere at that time, so each bit of surface area could take in
oxygen more effectively, and the area/volume tradeoff could be pushed
further towards more volume.
Now, I didn't get time to talk about many of these ideas, at least in
any detail. We will expand my science slot to 30 minutes with each
group. But here are some resources for parents to follow up:
Wikipedia article on the square-cube law: this repeats much of what I said about volume vs area, but has links to related articles in more depth. In particular, if you like to think about animals, you might want to check out....
Wikipedia article on allometry: allometry is the fact that most larger animals are NOT scaled-up smaller animals, but have changes in body plan.
Wikipedia article on Meganeura: this is the 2.5-foot dragonfly. It has a link to the 1999 Nature article linking insect gigantism to oxygen supply.
Friday, September 16, 2011
The Sift Hits the Sand
Today was my first day with the 4-6 year olds. I generally try to
think of an activity which builds on or is related to what the kids
are doing the rest of the week, so that my visits are not put in a
pigeonhole marked "Science" which has nothing to do with the rest of
their lives or studies. (A big point I want to get across is that
Everything is Connected. At the university level this might mean
emphasizing the unity of knowledge---students tend to see different
chapters of a textbook or different lectures as unrelated pigeonholes,
and must be prodded to think about the connections, which are actually
the important part! But for these kids, it's enough to make
connections between science and their everyday lives.)
But this being the start of the school year, the emphasis so far has
been on community-building, and there wasn't an obvious hook into
physical science. Teacher Jessica said that the kids had been
fascinated with some aspects of sand, so I thought of a way to build
on that. I had them separate big, medium, and small particles from
the sandpile, and used that to discuss solids, liquids, and molecules,
as well as engineering.
Before class, I built seven sets (seven is the maximum number of kids
per group) of coarse and fine sifters at low cost as follows. I took
a 4" diameter PVC pipe and sliced it into short segments to form the
frames of the sifters. For the mesh, I bought screen material. I
wanted a variety of mesh sizes, but this was difficult at the hardware
store. I ended up using what is basically window screen material. I
also had on hand a much coarser wire mesh designed to form a skeleton
for papier mache constructions. So I had two sizes, although I would
have liked even more and I will keep my eye out for different
materials in the future. (A baker's sifter has a finer mesh, but mine
had no walls so it was too easy to spill the sane rather than sift the
sand.) I cut the meshes into circles and duct-taped them onto the PVC
frames. I also brought some small cardboard boxes, some paper coffee
filters, and 21 (3 for each child) 44-oz plastic cups, which happen to
have mouths which fit well with the 4" PVC pipe. I wanted to bring
tweezers as well, but I forgot it.
I showed each group that I had been able (before class) to obtain one
cup of big stones and woodchips, one of medium stones, and one of fine
sand, and I gave them 10 minutes or so to experiment with any and all
of these tools to see if they could do it. They all pretty much got
it, usually with some guidance (as much to keep them focused as to
show them how to do it), and no one found it so easy as to be boring.
One of the girls found an advanced way to do it: stack the coarse
filter on top of the fine filter on top of a cup, load the top with
sand, and shake the whole thing to do it all at once. Like an oil
refinery, but with the heavy stuff staying on top! This is why I
mentioned engineering: although I often emphasize the cognitive value
in being able to understand or accomplish something in more than one
way, there is often great practical value in finding the most
efficient way!
We then talked about alternative ways to do the separation. Some had
wanted tweezers to separate the particles one by one; I forgot to
bring tweezers, but that's a valid---even if very
time-consuming!---way to do it. No one thought of using the box, but
when I asked how they would use the box about one kid in each group
guessed that if I just shake a box full of this mixture, the bigger
pieces come to the top. I even brought a cereal box to make the
connection to every kid's experience of the small pieces of cereal
always being on the bottom. This is because only the small particles
are able to fall into the small gaps which open up when the box is
shaken, very much like a sifter.
Next, I asked them if we could figure out a way to separate the fine
sand into even finer particles. We tried a coffee filter, but the
holes in the coffee filter were too small to let any sand through.
Here I made the connection to the atomic theory of matter: water does
go through the holes in the coffee filter, and so must be made up of
very small particles, too small to see. The same with air; air is able to push things because it is made up of small particles, even though we can't see them.
Finally, we talked about solids vs liquids. I can pour sand from a
cup, so is it a liquid? Most didn't want to say it's a liquid but
couldn't say why. Again, it's useful to point out the progression of
sizes. The bigger stones could be poured out of a cup but look
nothing like the flow of a liquid. The finest sand flows more like a
liquid, but not quite. The liquid has invisibly small particles, so
flows perfectly smoothly as far as we can see. You can pour sand and
make a pile, but you cannot pour water and make a pile of water!
At the start of each group, I promised them that we would experiment
with quicksand if they made good choices during the main experiment.
The night before, I whipped up a batch of water-soaked sand, which,
with some imagination, could be quicksand. (Quicksand is water-soaked
sand, but apparently not quite the kind of sand we have in our
sandbox!) This mixture of a liquid plus small solid particles has
interesting properties which are between those of a solid and those of
a liquid. They had fun with this, but I plan to someday make better
quicksand, perhaps with corn starch.
All in all, I think this 20-minute activity worked very well for the
4-6 year-olds, and I think it will be something they will continue to
experiment with even after my visit. I limited it to 20 minutes
because we had to get four groups through, but a longer time would be
fine too because many kids wanted to do more sifting.
think of an activity which builds on or is related to what the kids
are doing the rest of the week, so that my visits are not put in a
pigeonhole marked "Science" which has nothing to do with the rest of
their lives or studies. (A big point I want to get across is that
Everything is Connected. At the university level this might mean
emphasizing the unity of knowledge---students tend to see different
chapters of a textbook or different lectures as unrelated pigeonholes,
and must be prodded to think about the connections, which are actually
the important part! But for these kids, it's enough to make
connections between science and their everyday lives.)
But this being the start of the school year, the emphasis so far has
been on community-building, and there wasn't an obvious hook into
physical science. Teacher Jessica said that the kids had been
fascinated with some aspects of sand, so I thought of a way to build
on that. I had them separate big, medium, and small particles from
the sandpile, and used that to discuss solids, liquids, and molecules,
as well as engineering.
 |
| Simple materials. |
Before class, I built seven sets (seven is the maximum number of kids
per group) of coarse and fine sifters at low cost as follows. I took
a 4" diameter PVC pipe and sliced it into short segments to form the
frames of the sifters. For the mesh, I bought screen material. I
wanted a variety of mesh sizes, but this was difficult at the hardware
store. I ended up using what is basically window screen material. I
also had on hand a much coarser wire mesh designed to form a skeleton
for papier mache constructions. So I had two sizes, although I would
have liked even more and I will keep my eye out for different
materials in the future. (A baker's sifter has a finer mesh, but mine
had no walls so it was too easy to spill the sane rather than sift the
sand.) I cut the meshes into circles and duct-taped them onto the PVC
frames. I also brought some small cardboard boxes, some paper coffee
filters, and 21 (3 for each child) 44-oz plastic cups, which happen to
have mouths which fit well with the 4" PVC pipe. I wanted to bring
tweezers as well, but I forgot it.
I showed each group that I had been able (before class) to obtain one
cup of big stones and woodchips, one of medium stones, and one of fine
sand, and I gave them 10 minutes or so to experiment with any and all
of these tools to see if they could do it. They all pretty much got
it, usually with some guidance (as much to keep them focused as to
show them how to do it), and no one found it so easy as to be boring.
One of the girls found an advanced way to do it: stack the coarse
filter on top of the fine filter on top of a cup, load the top with
sand, and shake the whole thing to do it all at once. Like an oil
refinery, but with the heavy stuff staying on top! This is why I
mentioned engineering: although I often emphasize the cognitive value
in being able to understand or accomplish something in more than one
way, there is often great practical value in finding the most
efficient way!
 |
| The oil-refinery configuration with the finer mesh in the middle. If we had more types of mesh, we could separate into many different sizes all at once. Chaining together many separation devices to derive an ultrapure sample is a principle used in a variety of contexts I did not discuss with these kids, such as uranium enrichment. They might be able to see that a coin-sorting machine might be built this way, though. |
We then talked about alternative ways to do the separation. Some had
wanted tweezers to separate the particles one by one; I forgot to
bring tweezers, but that's a valid---even if very
time-consuming!---way to do it. No one thought of using the box, but
when I asked how they would use the box about one kid in each group
guessed that if I just shake a box full of this mixture, the bigger
pieces come to the top. I even brought a cereal box to make the
connection to every kid's experience of the small pieces of cereal
always being on the bottom. This is because only the small particles
are able to fall into the small gaps which open up when the box is
shaken, very much like a sifter.
 |
| Pub mix after a light shake: the trend from small things at the bottom to big things at the top is pretty clear. |
sand into even finer particles. We tried a coffee filter, but the
holes in the coffee filter were too small to let any sand through.
Here I made the connection to the atomic theory of matter: water does
go through the holes in the coffee filter, and so must be made up of
very small particles, too small to see. The same with air; air is able to push things because it is made up of small particles, even though we can't see them.
Finally, we talked about solids vs liquids. I can pour sand from a
cup, so is it a liquid? Most didn't want to say it's a liquid but
couldn't say why. Again, it's useful to point out the progression of
sizes. The bigger stones could be poured out of a cup but look
nothing like the flow of a liquid. The finest sand flows more like a
liquid, but not quite. The liquid has invisibly small particles, so
flows perfectly smoothly as far as we can see. You can pour sand and
make a pile, but you cannot pour water and make a pile of water!
At the start of each group, I promised them that we would experiment
with quicksand if they made good choices during the main experiment.
The night before, I whipped up a batch of water-soaked sand, which,
with some imagination, could be quicksand. (Quicksand is water-soaked
sand, but apparently not quite the kind of sand we have in our
sandbox!) This mixture of a liquid plus small solid particles has
interesting properties which are between those of a solid and those of
a liquid. They had fun with this, but I plan to someday make better
quicksand, perhaps with corn starch.
All in all, I think this 20-minute activity worked very well for the
4-6 year-olds, and I think it will be something they will continue to
experiment with even after my visit. I limited it to 20 minutes
because we had to get four groups through, but a longer time would be
fine too because many kids wanted to do more sifting.
Friday, September 9, 2011
Icebreaking Activity: Mystery Tubes
Today was my first day with the elementary kids. This is a brand-new school with about 22 students total in grades 1-6, and there is flexibility to work with age-segregated or mixed-age groups. I did the mystery tube activity (with extension #1) because it's a good icebreaker, and it naturally comes first because it addresses the nature of science. (By the way, I discovered this activity when the folks from http://undsci.berkeley.edu/ came to UC Davis and conducted a workshop on science outreach. Their website is worth a look, especially the diagram showing the real process of science, which is the exact opposite of the cookbook 5-step procedure you see in most textbooks. But maybe that's another post.)
I chose mixed-age groups because I was afraid the younger kids would struggle with it, and could use assistance from the older ones (the activity is recommended for grades 6-16, but I was pretty confident that grades 4-6 could handle it well). There was a fair amount of awkwardness because everybody was new to the school, and there was no established pattern of working in groups; some students still didn't know some other students' names! Considering that, it seemed to go fairly well. While some younger kids did struggle, a few other younger kids just nailed it. So while I still wouldn't recommend it for a group younger than 4th grade, it was eye-opening to see some really good results from individual 2nd-graders. At the same time, I have to admit that there wasn't much discussion of concepts like "Test results sometimes cause scientists to revise their hypotheses." We were doing those concepts, but it was hard to discuss them in these mixed-age groups. In the future, if I have mixed-age activities I might think about how to "debrief" the older kids separately afterward, to discuss how they can take what they learned in the activity and generalize it to make it useful in other parts of their studies and their lives.
A few tips for those wishing to do this:
Most discussions of the process of science focus on the mechanics of it. Students pose a question ("How does this thing work?"), suggest hypotheses (saying "I think there's a knot inside" and drawing a diagram of where and what kind of knot), and then test their hypotheses ("If I pull here it should..."). This is all great, but teachers usually present it in a context where the correct answer is already known, or revealed at the end. If the answer is already known ("today we will measure the density of water"), the activity turns into a dry, dull exercise. If the answer is revealed at the end, the whole idea of science as an ongoing process of inquiry is subverted.
I chose mixed-age groups because I was afraid the younger kids would struggle with it, and could use assistance from the older ones (the activity is recommended for grades 6-16, but I was pretty confident that grades 4-6 could handle it well). There was a fair amount of awkwardness because everybody was new to the school, and there was no established pattern of working in groups; some students still didn't know some other students' names! Considering that, it seemed to go fairly well. While some younger kids did struggle, a few other younger kids just nailed it. So while I still wouldn't recommend it for a group younger than 4th grade, it was eye-opening to see some really good results from individual 2nd-graders. At the same time, I have to admit that there wasn't much discussion of concepts like "Test results sometimes cause scientists to revise their hypotheses." We were doing those concepts, but it was hard to discuss them in these mixed-age groups. In the future, if I have mixed-age activities I might think about how to "debrief" the older kids separately afterward, to discuss how they can take what they learned in the activity and generalize it to make it useful in other parts of their studies and their lives.
A few tips for those wishing to do this:
- have a bucket of threadable beads ready. These are handy for tying onto the strings in the models so they don't slip through the holes in the toilet paper tubes, as well as for connecting the strings in the interior (in any way they wish; I don't hint in any way that they should use the beads to connect the strings, but they get used because they're handy).
- I made tubes with different types of connections in the interior, because often when two groups of scientists think they're doing the same experiment, they're not really, due to some confounding variable. So I think having all tubes identical subverts the process-of-science aspect of the lesson, and this came in really handy when students begged me for the answer (I honestly didn't know the answer for each individual tube) or thought they figured out the answer and tried to tell everyone else rather than let the others experiment more.
- If you suspect groups might not function well as a group, it's ok to forget about "sharing findings" and the like. I wish I had more toilet paper tubes because many students wanted to make their own model, and I think that would have been better than forcing students to build models in groups. It's hard to wait for your turn at improving the model!
- We did it in 3 rotations of 20-25 minutes each. I think it needs a bit more time than that, like 30 minutes.
Most discussions of the process of science focus on the mechanics of it. Students pose a question ("How does this thing work?"), suggest hypotheses (saying "I think there's a knot inside" and drawing a diagram of where and what kind of knot), and then test their hypotheses ("If I pull here it should..."). This is all great, but teachers usually present it in a context where the correct answer is already known, or revealed at the end. If the answer is already known ("today we will measure the density of water"), the activity turns into a dry, dull exercise. If the answer is revealed at the end, the whole idea of science as an ongoing process of inquiry is subverted.
The World in a Grain of Sand: Science Through Beginners' Eyes
To see a world in a grain of sand,--William Blake
And a heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.
This blog will be about my adventure in bringing science to preschool and elementary-school children over the coming year. Although Blake is known as a mystic rather than a scientist, this quote captures how I feel about bringing science to kids: too many people have never seen that curiosity and a sense of wonder are a big part of science. Everyday objects like grains of sand and flowers, if looked at with a genuine sense of curiosity, lead us to think about bigger and bigger ideas, until we practically hold infinity in the palms of our minds.
The main purpose of this blog is to record something about my activity each week: what I did with the kids, how well it worked, how it could be made to work better, etc. This is for my own benefit so that I have a journal to refer back to if I do this again next year. If others happen to look at this blog and use it to help bring science to kids, that would be fantastic.
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