Educating Risa

Daegan and I did a couple of activities with dominoes this morning, building on the activities we did with dice a few weeks ago. I began by dumping dominoes in a pile in front of him, and asking them how they were similar, and different, from dice:

Daegan talked about their shape, the dots, and the black line in the middle. I showed him how you could sort of think of a domino as representing the roll of two dice. For example, one of the bottom dominoes in the picture above represents the roll 5 – 3, with the black line in the middle of the domino separating the two “dice”. Then I said, “But there is one big difference from dice. What is it?” Daegan figured it out:

Zeroes! You cannot roll a zero when you roll a die.

I then had Daegan put the dominos in order, from ‘smallest roll’ to largest, just as Jim did with him working with the two dice, starting from zeros: 0-0, 0-1, 0-2, etc.

Next comes the ones, starting with 1-1, and not 1-0. In dominoes, you don’t ‘double-count’ as you do with dice (e.g., with dice 1-2 and 2-1 were treated as separate rolls). There is only one domino with a 1 and a 0 on it, and it is already in the zeroes column.

After finishing the ones column, Daegan grabbed the next domino and did something quite unexpected, and cracked me right up. He started dancing around and singing music, all with an impish grin on his face:

Figured it out yet? Why, the domino that started the twos column is 2-2, or “tutu”. A little 7-year-old math humour for ya!

He kept on ordering the dominoes until it was done. I was very pleased that he needed no help on this whatsoever. He has internalized at least one mechanism by which to put number combinations in a logical order, something he found tricky last month with the dice activity.

I asked him what patterns he saw in the dominoes. He noticed that the columns always start (bottom) with a double, and that each column had one fewer domino. He noticed each domino on the top of a column had a 6. On that note, I showed him another possible logical ordering of the dominoes, from largest to smallest. It is easy to change the arrangement above (small to large) to the one below (large to small)—just move the top domino in each column over to the correct spot. So I began by moving the 5-6 on top of the 6-6, then the 4-6 on top of the just-moved 5-6, etc. You end up with:

Daegan and I then moved on to another activity that practices addition and makes a neat bar graph—the Domino Parking Lot—which I’ve written up separately. As an extension of what is above, ask your child how many times each number appears in a set of dominoes. The answer is 7: each number appears in combination in with each other number (so that’s 5 times) as well as with itself (the 6th and 7th). You can see this in the two logical orderings above—there were 7 dominoes in the zero column when we went smallest to largest, and 7 in the sixes column when we went largest to smallest.