I gained another math student this January.
He's my youngest student yet (a third grader),
and has a head for numbers (which many of my
students don't begin with). With this student,
my task here is to keep math fun. (Yes, fun.)
His Mom was concerned that he's not engaging,
and that he's starting to complain that math
is slow and boring, so he's cutting corners,
which means he's starting to miss things.
So, at our first meeting, after he finishes
explaining his homework to me,
I pull out a clean piece of paper.
"If I draw two dots, how many lines can you
draw connecting them?" I ask.
"Two." He answers instantly.
"If I draw one dot, how many lines can I draw?"
"Um.. n o n e."
"Okay, lets make a chart to keep track, alright?"
He nods, game to see where all of this weirdness is
going to end up. I draw a T chart with "Dots" and
"Lines" as the two headers, and write up "1" dot,
"0" lines; "2" dots, 1 line.
"How many lines for 3 dots?"
"Two", he says as he draws a dot in line with our
first pair of dots.
I redraw three dots in a triangle shape, and he quickly
draws in 3 lines and changes his answer.
"What about 4?"
"4!", he shouts out, and draws lines connecting the
"What about diagonals? Would those break some sort
He pauses, thinks, and draws an "X" connecting the
We continue to onto 5 dots, in which he spots a pentagon
with a star inside. Then we move onto 6, and then 7.
We talk about ways to work methodically so you don't miss
lines. At this point we stop and look at our chart.
"Can you tell me how many lines we'll have for 8?"
He looks at the chart.
"Do you see a pattern? Take your time."
He looks, he thinks, "OH! The first time grows by
one, the second, by 2, the third by 3. So, if we
add 7 to our 7th total, we'll get number 8!"
"Shall we test that out? Shall we see if we have
28 lines for 8 dots?"
"Yes!" he said, and started drawing dots.
And, yes, his theory worked. He then accurately
predicted the 9th part of the pattern and tested
When you stop to think about it, the pattern makes
a lot of sense. Every time you add a new dot, you
connect that dot to each of the previous dots, making
a line for each preexisting dot. So the 10th dot, would
add 9 more lines to the previous total of lines.
I think it was a good lesson. He had fun, I had fun.
We both thought about numbers and patterns. We
practiced critical thinking and analyzing. I have a
paper folding project in mind for our next meeting!
As an aside, I did this same activity with another student,
one who doesn't see numbers as readily. He also had
fun drawing the lines, finding the pattern, and then
(to his own shock) predicting the next elements in the
pattern. Good number fun, all around!