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The
teacher should start out by saying: "Today,
I'm going to jinx everyone. Take out your
notebook or a piece of paper and do the
following steps."
1.
Choose a number from 1 to 10 and write it down.
2. Add 11.
3. Multiply by 6.
4. Subtract 3.
5. Divide by 3.
6. Add 5.
7. Divide by 2.
8. Subtract the number you started with in step
1.
9. Your answer is _____.
Teacher
waits for a student and then asks a student
who is done and looking up: "What did you
get?" (13) If the student doesn't get 13 move
on to another student and ask the same
question. Continue until there is a consensus
that you get 13.
Teacher says: Wow. All (or most) of you got
13! That must mean you all started with the
same number. Is that right? (Heads should move
side to side along with some "no" answers.)
Teacher: No? What did you start with then?
The teacher writes the numbers the students
started with on the white board.
Teacher:
Do you think it matters what number you
started with? (Students will usually
not be sure.)
Teacher: OK, let's try a few
more numbers to see if this pattern continues.
The teacher then challenges them to come up with
a number that will “break” the jinx. Students
try larger numbers, fractions, negative numbers,
etc. but come away frustrated declaring that “it
must always work” mostly because the task
becomes so tedious even with a calculator.
At this time the teacher introduces the Jinx
calculator. Actually, it’s just a spreadsheet
file in disguise that does the calculations for
them so they can try more ambitious numbers.
After lots of trial and error with no success,
the teacher tells the students to try
3000000000000000. (That’s 3 followed by 15
zeros.) Result as expected is still 13. Now
click in B1 and add a 16th zero. Surprise! You
should see 0. Now does that mean the trick no
longer works? Or is it just that our Jinx
calculator has some flaws? (It’s the latter.)
Spreadsheets “fall apart” when we use numbers
out of their range.
To prove that the trick really does work all the
time, the teachers suggest the use of something
that can represent any number chosen including
ones you can’t completely write out like pi or
the square root of 2. The teacher then uses the
marbles and bags model (first introduced to me
by W. W. Sawyer) and demonstrates why it works
using a digital white board. |
This
is one of my favorite lessons which I
usually do with a pre-algebra class.
The
“correct” answer of course is no, since we
can prove it using algebra. But since this
is a pre-algebra class the students are
usually not sure.
An Excel version is available here.
Can that number Pi be used with the Jinx
calculator? No, only an approximation like
3.14 is possible. |
