Yesterday I was lucky to be a substitute at Salmon Creek School. I was taking over for
teachers who were being debriefed after observing a lecture to their students on a
writing program they have adopted. This program starts in 2nd grade and
goes through 8th grade. Each teacher uses the same terms and ideas to teach the
concepts they have always taught. The program has wonderful patterns and color
coding to help the students remember their writing skills.
I thought wouldn't this be great for Math. If all teachers defined words the same way.
If all phrases that take away from learning Math could be eliminated. If there were
problems that start in the 2nd grade and go to 8th grade. There are problems like this!
Now as students gain more knowledge in Math they can come closer to answering the
entire question, or answer deeper problems on the same question.
Example: The Tortoise and the Hare were having a race.
The race was 200', 100' forward and 100' back.
The Hare takes 2 steps of 3' in the same time that
the Tortoise takes 3 hops of 2'.
a) Who reached 100' first?
b) Who won the race?
c) How far back was the loser when
the winner crossed the finnish line?
d) If the loser was in the air when
the winner crossed the finnish line,
at what height was he?
We could start this problem in 2nd grade. Here we should only look
at part "a". But how do we do this? First of all, how far is 100'?
Our 2nd grade teacher can use the problem as an introduction to
measurement. Having measuring tapes of 25' they could find a
distance of 100' by simply adding 25', 4 times.
Next they could have one person be the Tortoise and one be the
Hare. They could then see how how each would move from the
start toward the 100' mark.
0_6'__12'__18'__24'___________________________96'_____100'
Both the Hare and the Tortoise arrive at 96' together!
What happens next?
How does the way they move effect what happens?
Are they both on the ground at 100'?
The tortoise in his next two hops lands on top of the 100' mark,
but the Hare's first step takes him to 99' and he would be in the
air going past the 100' mark as the Tortoise lands on the
100' mark.
They both get to 100' at the some time.
As our students are introduced to measurement and they find out about
feet and inches. They may also ask about the marks between the inch
marks.
It is up to our 3rd to 5th grades to discuss the "b" of the problem.
They must decide who wins the race and why. While they are doing
that they can work on the understanding of ½, ¼, or ¾ of an inch.
In the 2nd grade the use of the physical measuring tape will help students
to see how being at 2¾ then adding ¾ gets you to 3½. In the following
years they will see how 2 and 6/4 creates 3½.
They will understand how to solve "c" eventually, but we can leave "d"
to much latter.
As the students move through the grades it is up to the teachers to use
the same terminology when solving this problem, so there is no confusion
in the minds of our youngsters.
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