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

corners.

"What about diagonals? Would those break some sort

of rule?"

He pauses, thinks, and draws an "X" connecting the

corners. "6".

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

that.

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!