A River of Sand

Today was my last day with the 5-7 graders.  We spent most of the time learning about beaches: how sand gets there and how sand moves once it's there (California grade 6 standard 2c).  It's a lot more interesting than you might think, and it's explained well in this video.  Normally I show just short clips of videos, 30 seconds or a minute here and there to support whatever I want to talk about; a lot of "educational" videos have a lot of fluff surrounding the critical part(s).  But I found this video to be packed full of good visualizations of what's going on with beaches, far better than I could set up myself, and very little fluff.  So we watched all 20 minutes (ok, I skipped the fluffy first 80 seconds), and I highly recommend it for parents too.  Aside: It's from the 1960's, and told in the "voice of God" style strongly reminiscent of the films I was shown when I was in elementary school.  Science videos today are quite different, typically with a friendly host just like us who wants to take part in experiments just like we do.  That's probably an improvement on average, but I experienced some nostalgia for the "voice of God" style as I watched it. 

After the video, I set the kids to work on the "Rollin' Down the Sand Highway" activity from this packet (the last activity in the packet).  I didn't provide maps, but just looked them up online as needed.  Some kids had never seen a topo map before, so I explained that in context.  But for most of the time most of the kids were stuck on the math, which surprised me because the math is pretty simple.  I guess it's a question of applying math outside of math class!  It's always easier to apply a concept when you've just learned it and you know that the problem you've been given can be solved using that concept.

More specifically, the students did not have a clear idea of how to go about converting cubic yards of sand per year to dump trucks per minute.  I led them through  the easy step of converting cubic yards per year to dump trucks per year, and I thought this would give them the boost they needed to complete it on their own, but I was wrong.  As I circulated around the room helping students, it came out that we would need to know how many minutes per year, and the students were able to come up with that number (although they may have Googled it on a mobile device behind my back): 525,600.  But there was a huge amount of confusion regarding whether they multiply or divide by this number, and whether the result would be dump trucks per minute or minutes per dump truck.  I walked them through how I think about it, and they stared at me totally lost; I stared back wondering how they could not have seen this before.  So I backed up and (much wailing and gnashing of teeth omitted here) found a way to get it across. 

Here's what worked: let's say that you are asked to compute 3 times 4, divided by 7 times 3:

3x4
----  = ?
7x3

The kids universally said the following: multiply across the top and also across the bottom:

3x4     12
----  = ---
7x3     21

This surprised me because it's not what I would do, but once I figured out that one kid was thinking like this, I repeated it for all the kids.  Although the answer surprised me, it's not wrong, so let's continue along these lines and see what happens.  The natural next step is to simplify the fraction 12/21: is this its simplest form?  The typical answer from a student was: ...um...well, I don't see any common factors.  And of course it's hard to see the common factors when you're staring at 12/21.  But if instead you look at

3x4    
----  =?
7x3    
the common factor of 3 is jumping up and down screaming "I'm a common factor!"  So cancel the 3's and you immediately get 4/7.  This is not only much less work than writing 12/21 and then trying to simplify; it avoids the potential for a lot of mistakes.  Although this kind of thing is second nature to me, it was not natural for the kids, who were intent on following the specific rules they had learned about multiplying fractions.

I had to go through all this just to get to the main idea: we can do the same kind of thing with items like dump trucks and minutes instead of specific numbers.  We are given dump trucks per year and we want to get dump trucks per minute, so we can represent the problem like this:

dump trucks      ?         dump trucks
--------------- x   --   =   ---------------
year                     ?           minute


We have to get rid of years and introduce minutes, so if we put years per minute in the question marks, we get:

dump trucks      year           dump trucks
--------------- x   -----     =   ---------------
year                   minute           minute

The years on the left cancel each other, leaving dump trucks in the numerator and minutes in the denominator.  If we had instead tried:

dump trucks      minute           dump trucks
--------------- x   ---------    =   ---------------
year                      year                 minute

this equation is manifestly false; the right hand side should contain dump truck minutes on the top and years squared on the bottom. This kind of thinking seemed to be new to the 6th graders, and I'm glad I did it because it's really important.  It provides a system for making sure you do the right thing.  Don't know whether to multiply by 525,600 or divide by 525,600?  One system popular among the students was to just try one approach, and then if the teacher says it's wrong, just do the other!  But here's a system which makes clear that we have to multiply by years/minute, or 1/525600. And not sure if the resulting number represents dump trucks per minute or minutes per dump truck? Again, the system makes clear that the result is dump trucks per minute.

Another thing the kids need to internalize much better is sanity checking.  If you multiply 722,222 cubic yards by the $5 per cubic yard it costs to remove, you should get a number bigger than 722,222, not less than 722,222.  The kids didn't apply this kind of sanity checking to any of their results, and therefore didn't catch any of their mistakes before showing their answers to me.  This was the first math-based activity I had really done with the upper-graders, and I was probably naive to expect that they could apply math outside the context of a math class.  I should have given a little primer on how to estimate before calculating, how to check that your answer is right after calculating, etc.  This is not really math; it's metacognition in a math context, and I'm now kicking myself for not emphasizing metacognition throughout this trimester with the upper graders.

In any case, we spent a lot of time on this activity: 1 hour, including the movie, before break; then maybe another 20 minutes after break.  It was worth it to work through these issues, but then I did have to cut down on my planned post-break activity.  I'll dedicate the next blog post to the humidity-related activities we did in the last 30 minutes of the morning.

Dinosaur layer cake

Some of the boys in Primaria are really into dinosaurs and have been
asking for a dinosaur-related experiment.  By talking to them on
previous visits, I got a sense of what would be useful.  They knew
that dinosaurs did not live at the same time as cavemen, but they
didn't know how we know that.  Understanding this brings together a
lot of key ideas in geology and in scientific reasoning, so I thought
it would make a great activity.  But it turned out to be more of a
demo than a small-group activity, so it fit the schedule well on a day
when there was less time for science due to the Easter egg hunt.

I brought a large, clear plastic box and set it on a table in the
outdoor area.  As part of the setup I also filled some buckets with
different materials in the yard: sand, wood chips, and black dirt from
the planter boxes.  I started, as usual, by asking them what they know
about the topic, and I tried to steer the resulting conversation
toward how they know what they know. (Aside: this is one of the few
times I had a conversation with the entire class of 20+ kids at once,
and it was surprisingly not chaotic.  It really helped to have them
seated before the start, with everyone able to see because I was on a
platform.)  One boy was able to give an answer like "men hadn't
evolved yet" but no one know how we know that.  So that provided the
motivation for the following demo.

As part of the preparation, I had also printed out skeletons of
different dinosaurs as well as Lucy and a modern human, and glued
these to pieces of cardboard.  I pulled out the stegosaurus and asked,
"Who knows what this is?"  Then we imagined stegosaurus caught in a
mudslide.  I had a volunteer help me pour the bucket of sand over the
stegosaurus (in the large clear plastic box).  Then, some time later,
here comes a...does anyone know what this is? Triceratops.
Triceratops dies and gets buried in a layer of wood chips, symbolizing
a different type of soil in that area at that time, which ultimately
forms a different layer of rock.  We repeated with a T. Rex and
another layer of sand.

Then we imagined that the area was underwater for a time.  We talked
about how an area could be underwater at times and above water at
other times.  We reviewed what they had learned about rivers and the
water cycle, and decided that layers of sediment can build up on the
lake's bottom or the sea floor.  We also related it to what they had
learned about the deep ocean, that things (like whale bones and
smaller bits of nutrients) rain down from above.  We simulated this by
having a few volunteers rain down black dirt, while I dropped an
elasmosaurus skeleton in.

Next, I did a special, thin, brightly colored layer using a bottle of
paprika.  They guessed it represented lava but I said we would come
back to discuss it later.

Then I brought out Lucy and discussed her, buried her in another layer
of wood chips and then brought out the modern human skeleton and
buried him in a final layer of sand.  The final product was
impressive, clearly showing seven different layers of "rock" through
the clear plastic.  (The box was about 2.5 feet long by 1.5 wide by
1.5 feet deep, and was about 2/3 filled by the end.)  We discussed how
the oldest rock layers are on the bottom and the newest are on the
top, so that the fossils we find on the bottom layers are of creatures
who lived long ago, and the fossils we find on the top layers are of
creatures who lived recently.  (This is true even if an earthquake
comes later and tilts the layers.  I tilted the box and asked who had
been to the Grand Canyon and seen the tilted layers there; a
substantial minority had seen it.)  Do we ever find cavemen (Lucy) on
the bottom layers? No.  Do we ever find dinosaurs on the top layers?
No.  We can even tell which dinosaurs lived earlier, and which lived
later.

Next, I had them exercise their hypothetico-deductive reasoning
skills.  If Lucy had lived as early as the dinosaurs, what would we
find?  If the dinosaurs had lived as late as Lucy, what would we find?

Finally, I returned to the thin paprika band. All over the world, we
find an easily identifiable band called the K-T boundary, and we find
dinosaur fossils only below that band, indicating that dinosaurs died
out around the time the band was formed.  And the band has been found
to contain an element, iridium, in much higher concentrations than
normally found on Earth, but consistent with a certain type of
asteroid.  The conclusion is that an asteroid impact and its aftermath
killed the dinosaurs.

I'm aware that this model is not universally accepted; some scientists
think volcanism played a role in the demise of the dinosaurs, and some
think the dinosaurs were dying out before the asteroid impact, which
perhaps only delivered the coup de grace. But there's only so much
detail you can go into with five-year-olds.  The best thing I can do
to help them deal with nuance as they grow more sophisticated is to
give them practice reasoning with evidence, just as I did.

I left the whole layer cake for the kids to excavate in their free time after lunch.
I had originally envisioned doing something which would make the layers set more
like stone so they would really have to chip away at it, but after finding out that
plaster of paris is toxic, decided not to go there.  I suppose a weak concrete might work,
and I may return to this idea in future years.  If I had done plaster or concrete, I would
have found something to color the layers slightly so they would show a bit of contrast.
As it happened, the sand/woodchips/black dirt made a beautiful set of layers.

I highly recommend reading this story of how Walter Alvarez and collaborators figured out the K-T boundary.  It really shows how
science works; it involves far more creativity and discovery than most
students are led to believe by being forced to do contrived lab
exercises in school.  Unfortunately, many K12 teachers have
experienced science only in that contrived, uninteresting context, and
themselves do not believe science requires creativity, and therefore
create a vicious cycle when they pass that attitude on to their
students.  I'll sign off with this link to a list of misconceptions about science.

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.

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.

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.

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.