Educating Risa

I got the kernel of this idea from this blog, and after playing around with it a bit myself realized it connected very well with the bar graph activity Jim and Daegan did with dice last month. I began by laying out the domino parking spots, using some cards from a number / number word match-up game I had made for Gareth. Daegan then began adding the dots on the dominoes and ‘parking’ them in their correct space:

We talked about the dice activity he had done previously as he was working, and Daegan recalled that the most common sum when you roll two dice was 7. I asked him why 7 and he said “because it is in the middle [of the graph].” I asked him what he thought the most common domino sum would be and he thought 7 again. Hmmm….we’ll see.

As he worked he realized we needed to make a 0 (zero) parking lot. I pointed out that when we worked with the dice, the smallest sum (parking lot) was 2, from the roll 1-1. With dominoes we have both 0 and 1 as possible sums. Daegan thought that was sort of interesting, but didn’t think it would affect the result; we should still get more 7s than anything.

He kept adding and sorting (which also gave me some insight into which sums he had down and which he is still struggling with), and made little car noises as he did so. Vrrrrrooomm! Beep! Beep! Squeeeak! It was all I could do to keep a straight face.

Just one last domino to go, the 4-2 domino with a sum of 6.

Well, this sent Daegan into a tizzy. “I must have made a mistake! The sixes have the most! It should be seven!” After helping him calm down, I reminded him that he had told me that when it came to dice, the 7s had the most as they were in the middle of the graph. What is in the middle of your domino parking lot?

I reminded him again about how dominoes have zeroes, but dice don’t. “Zeroes change everything in math!” I emphasized. “Don’t forget that!” I showed him how the zero made the 0 and 1 parking lots possible, how the zero made a way to sum to six that doesn’t work with seven (there is a 0-6 domino, but not a 0-7), and I briefly reminded him of yesterday when he had misread 201 as “twenty-one.” I wrote 21, 201, 2001 on a piece of paper and talked VERY BRIEFLY about place value and zeroes. “Zeroes are a really big deal in math, despite being nothing,” I joked. 

Still not entirely convinced, I took away the 0 and 1 parking lots, leaving only 2 through 12—just like dice sums—and asked him to find the middle. Sure enough, the middle is now 7:

As a final step we talked about the bar graph we made with the dominoes in our parking lot, and how the shape of the graph was the same as with the dice—steps up and down to a high central point—even though the exact middle number differed:

Daegan told me later he found these domino activities “kind of fun, and kind of confusing.” Excellent son—that’s the wonderment of math!