Another thing we can do with students is
we can provide them with a yardstick or
a meter stick, and that will serve as a
number line, and a piece of yarn or
string. And I oftentimes give the
scenario of this is a road, an ant road.
So it's kind of small and short, and that
kind of helps them with the scenario. So
almost like it's a log that gets shifted.
It's kind of how we think about it. So
here you can see, on the number line that
the ending point is four, for the
starting point is that one, and what is
the difference or the distance between
one and four? So we can go ahead and see that it's one, two, three. So the
difference between those two points is
three. So here you can see that the log
or the ant road has shifted so we can
see that the ending point is that five.
The starting point is at two. What is the difference or the distance
between the starting and ending points?
One, two, three, and one more example. Four
and seven. So here we have seven at the
ending point. Four is the starting point,
and the distance or difference between
those two points is still three. Now
what's really powerful here is, you will
see an additional resource that we've
provided that would help your student,
students engage in this activity in
small groups or partners, in which they
are physically moving the string and
recording the points. And then the real
power is when you have the conversation,
and help them see the pattern, and the
structure of the difference between
those points. So what's really
interesting is students will start to
notice, because you've asked them, is
you know, take a look at the relationship
between the red equation and the green
equation. What's happening? What do you
notice? What's that relationship? Oh, we've actually increased the ending
point by three, and the starting point by
three. Oh, so that that road has shifted.
So if the starting point shifts forward
three places, then the back of that road
is going to shift forward three places
as well. But, once again, you could talk
them to death. But unless they physically
can see, and record, and start to discuss
those patterns, and why it's happening,
that's where the real power will be.
Otherwise, they will begin to wonder, when do I add one? When do I subtract one? So
it's critical that they're reasoning and
making sense of it.
