Hi. It's Mr. Andersen and this is Crosscutting Concept 3. It's on scale,
proportion and quantity. And so it's really letting our kids understand the difference
between really big and really small. And that's important, this sense of scale because in
science it allows us to understand phenomena at different scales. And in engineering it's
really important. So a scale model for example or a sense of scale in a design is super important.
And so let me give you an example of this. This right here is a sea star. And you might
think of it as a starfish. And if you look at it when you're snorkeling or scuba diving,
it seems really boring. It's just sitting there. And the reason why is that they move
incredibly slow. And so if you're to film them with a time lapse camera, all of the
sudden life jumps into action. They're going to move around. They're going to fight. They're
going to eat. They're going to defend territory. And we' can't see that. They just look like
they're sitting there, kind of boring, because we don't have a sense of their time scale.
Or if we were to look at this laser beam right here. How fast light is, or even what a photon
is, it's hard for us to wrap our head around that because it's so fast. But other things
like a mountain seems permanent because we don't realize how slowly it moves or even
how big it is and the forces that move it are. And if we're talking about big we could
get no bigger than the universe itself. So this idea that the whole universe, that singularity
before the big bang, was less than the size of a period in a sentence is crazy. But we
really have to understand this sense of scale before we can really understand phenomena.
In other words for science to work. And so basically there are three continuums. We have
the continuum of size. Things can be incredibly big or incredibly small. We've got this idea
of time span. In other words it can be a really long period of time or incredibly short period
of time. And then we have huge amounts of energy or no amounts of energy. And so if
we're talking about a proton for example, it's going to be incredibly small. Have a
really tiny amount of energy. And it's going to exist or it's going to operate on a really
small time span. But something like continental drift is going to be massive in size, huge
amounts of energy and is going to take a long period of time for that to occur. And so to
summarize, we've basically got human scale, what we can see and deal with, you know just
with our hands and with our eyes. We have those things that are really small and really
fast and things that are too large or too slow for us to observe. And so to give you
an idea of the power of sense of scale, let's look at a snowflake. This is a snowflake that
we've taken a picture of it using an electron microscope. It looks gorgeous. But if we were
to just see that without a sense of scale, we wouldn't know anything. But now there's
a scale bar down here on the bottom and so it's saying that this, from here to here is
one millimeter. And that's basically how far you can hold your fingers apart without letting
them touch. And so that's really small. But as we zoom in with an electron microscope
we can see more detail and more detail, but if I didn't have a sense of scale, if I didn't
know that this now is .05 millimeters or as we move closer and closer and closer, now
we're getting to micrometers, then I really wouldn't know what I was looking at. And so
it's important in science that we have a sense of scale. Because when we get into this level,
at this really small level it's important that we really know what we're looking at.
And that scale is going to be important. In other words we're going to have meaningful
concepts at different levels of scale. And so if you were to touch a piece of wood or
a nail or to hammer a nail into wood, you would say these are solid. In other words,
wood is solid. If I knock on wood it sure seems solid. But if we were to move our scale
down to the very small, if we were to get down to the level of electrons and electron
clouds of probability, being a solid really doesn't mean anything. In fact when I put
my hands on this table or put my hands together, they're not really touching. It's not solids
in contact. It's the electrons kind of hovering and interacting on top of each other. And
so as we get into this really zoomed in scale, it's important that we know what are the meaningful
concepts at each level. And so a powerful tool that we can use in science is the idea
of proportion. It allows us to wrap our head around these differences in scale. And so
you can think of proportion as a ratio. In other words a ratio of quantity A to quantity
B. In other words it's a fraction. And when I say the word fraction you tend to think
of something like this. Parts of a whole. In other words this piece of the pie is 7%
of the pie. And that's really important that we understand a ratio as that. But ratios
are way more powerful than that because a ration could also allow us to move between
different units. In other words, velocity is going to be change in position over a change
in time and that's a proportion but it's also allowing us to move between different scales.
Or density as well is a proportion. And so it's important that we understand that a scale
doesn't have to be distance over distance or unit over unit. It can be different units
as well. So this quantity and the understanding the units is super important as well. So what's
the goal? We want our students to be able to sense scale and understand scale. And so
we want them to understand relative scales. We then want them to understand quantities
and we'll use units of measure to get to that. But finally we want to understand this idea
of proportion and ratio. And so as we move from middle school into high school the power
of estimation is important and then mathematical modeling is important as well. So what's the
progression? In other words how do you start doing this in kindergarten and then progress
through high school. In other words, how do you start throwing darts and the dart board
from the beginning but get better and better and closer to the bull's eye over time? Well
how do you do this in an early elementary class? You could do it as simply as this.
And so we've got these four pictures of organisms right here. Could you have your students classify
them according to speed? Which is going to be the slowest and what's going to be the
fastest? Well slowest I would say is probably the sunflower. Then maybe the snail. Then
the whale. And then probably the falcon. Could you classify them according to size scale?
Which one is going to be the smallest? Which one is going to be the biggest? Or what about
lifespan? Could you put it in life span from the smallest lifespan to the greatest? The
students should be able to figure out or take a stab at it. I learned this, that the sunflower,
I knew the sunflowers are obviously only going to live one year, but snails will live like
five to seven years. And so I would put them next. Then the bird and then the whale. And
so have them sensing scale from the beginning. But then we want to move into units of measure.
And when you're teaching scale, the one that you want to begin with is length. So you want
to have a really good understanding as we move through elementary of length. But once
we have length and the units of length we always try to use the meter system if we can,
or the metric system if we can. Then we move towards weight, time and then temperature.
And so we want to be using units so we're measuring what the quantity is but we also
want to have what is that quantity measuring? Is it a distance? Is it time? And it's really
important when you're doing science that you have a unit of measure that goes along with
that quantity that we actually measured. As we move forward, estimation becomes important.
So how many kernels of corn are in here? I don't really know the right answer, but we
could us estimation to figure it out. In other words if it's uniform throughout we could
figure out how many are in there. And so estimation is important and then understanding the powers
of 10 is important. So what is the powers of 10? Well basically if this little dot right
here represents 1 or 10 to the 0, then this right here is 10 to the 9. Or this is one
billion of those little dots. And so this gives you a sense of scale of the powers of
10. And you want to give them that power. You want to have students estimating and then
understanding the power of 10 and why we use a base 10 system. And then as you move up
grades we really want to do mathematical modeling of observed phenomena. So this is something
I used to do in my class. Basically when I was getting at units of measure and power
of graphing what I would say is, Choose 10 objects in the room. They all have to be a
circle. And I want you to measure what their circumference is. And I want to measure what
their diameter is. And so just gather some data. But be as precise as you can. And then
when you're done I want you to graph the data. So we have circumference on the y and then
we have the diameter on the x. And what you'll find is if we graph circumference over diameter
were going to get a linear relationship. But now we're going to get a line and if you ask
them to calculate the line of that you're going to find that that's around three. In
other words it's around 3.14. So the slope is important. And so basically what I'm showing
them is that we can have different senses of scale. We can gather data. But we can make
predictions from that data. In other words we could extend this out and figure out other
things. Also we want to get into the importance of linear versus exponential growth. And they
will have seen these things in their math class. But this is an interesting picture.
What we've got here is basically a linear relationship. That's going to be in red. We've
got a cubed relationship and then we've got this exponential relationship right here where
we're actually putting x up here in the exponent. And what we'll find is that exponential growth
is going to out pace the other two. And exponential growth and the importance of that is super
important in biology because it shows how bacteria grow. They're going to grow exponentially.
One makes two, makes four, and so we're going to have a huge amount of growth. And that
gives us fast growth. Small things growing really really quickly. Another sense of scale.
And so scale is important. We use proportions as a tool and units of measure to get at that
and I hope this was helpful.