## Chips for All Seasons

Yesterday’s lesson with Katie and Varya consisted of exploring various ways of using colorful game chips for doing fun math.  The first activity involved dividing the chips between the doll Nina and the bear Stanford according to specified rules (I specifically didn’t want to divide them between Katie and Varya so that no one would get upset when the amounts were unequal).  Here is a sample problem the girls had to solve:

Nina and Stanford have a total of 7 chips, but Nina has one chip more than Stanford.  How many does each have?

When I had previously tried giving Katie a problem of this type to do in her head, she would initially have trouble wrapping her head around the conditions.  She would, for example, say that Nina has eight and I would have to point out to her that there are only seven total.  I did at some point manage to talk her through the problem, but it was somewhat tedious.  However, with the manipulatives in front of them, both girls did really well.

To make things a bit more complicated, I asked the girls to divide four chips among the toys so that Stanford got one chip more than Nina.  It didn’t take them long to figure out that this was impossible, but they didn’t seem too surprised by it.  They were also starting to fool around at that point, so perhaps they just didn’t care any more.

The second activity with chips was more geometrical in nature.  I would arrange some number of chips in a pattern under a lid and then pick it up briefly.  The girls then had to determine how many chips there were.  I had played this game with Katie in the past so she was a bit better at recognizing more standard patterns.  However, when the chips were laid out more randomly, they would get the answer correct equally often.  Naturally, after a few rounds, the girls wanted to arrange the chips themselves, so I let them make puzzles for each other.  I was afraid that they would use too many chips and make it too difficult for each other, but it actually worked out quite well.

Finally, we used the chips to do some multiplication problems

and to play the really fun game Sequence, which is what the chips were intended for in the first place!