# Boolean Bridges

## The Activities

1. Topic: Division: Book: One Hungry Cat by Joanne Rocklin.
2. Topic: Logic: I made several pictures of paths and rivers, where you needed bridges in one or more spots in order to be able to make it to the castle.  Each picture corresponded to a Boolean logic formula.  The kids both had to write down a formula given a picture, and draw a picture given a formula.  All the pictures can be found here, as well as the PowerPoint if you want to make your own.
 A v B A ^ (B v C) A v B v C v D (A v B) ^ (C v D)
3. Topics: Addition, Subtraction, Multiplication:  I did several “math magic” problems where each kid starts with a different number between 1 and 9, I give them instructions, and then at the end they get the same number.  The three “tricks” were “add 6, subtract 8, add 2”, “add 2, add 2, add 2, subtract 6”, and “multiply by 2, add 3, multiply by 5, subtract 15, cross off the trailing 0”.
4. Topic: Geometry:  Build some number of squares using as few fences (Keva blocks) as possible.  Later, build some number of triangles.

## How Did It Go?

#### One Hungry Cat

Kid 1 said she had heard the book before, but she didn’t remember what happened.  The kids thought it was pretty funny when the cat kept eating all the food.  Kid 2 pointed out that when there were 8 cookies left, the cat could have eaten only 2, but ate all 8 instead.

#### Castle Logic

I started with one bridge, and then showed them the pictures for “A and B” and “A or B”.  I gave them ^ and v as the “and” and “or” symbols; Kid 1 mentioned that & could stand for “and”.  Then I showed them pictures for A v B v C and A ^ B ^ C, and had them write down the formula.  They didn’t have trouble with this, except that Kid 2 left out the v on the first one, and Kids 2 and 3 both wrote v instead of ^ for the second one.  Then we did A ^ (B v C).  We ended up getting two correct answers: Kids 4 and 5 wrote A ^ B v A ^ C, while the rest wrote A ^ B v C.  This is nice, because it’s the distributive low for Boolean formulas.  Of course, no one used parentheses, but before discussing that I showed them the next one, which was (A ^ B) v C.  Again, a bunch of good answers, including both the distributed and undistributed versions.  As it happened, no one wrote down the same thing both times (they randomly varied the order, probably accidentally although it’s possible Kid 6 did it on purpose to signify which came first).  So, I wrote down A ^ B v C for both of them, and explained how the parentheses tell you the precedence.  They may or may not have understood.  Kid 6 finished these quickly and started drawing a picture of a bridge with a funny troll, and then showed it to other kids.

After this, I gave them A v B v C v D and asked them to draw a picture. Four of the kids drew the right thing; Kid 1’s was the nicest, while two of them didn’t initially connect the roads at the bottom (each road went off the paper at a different place).  Kid 6 finished early and started adding to the troll again, so I gave Kid 6 another problem, (A v B) ^ (C v D).  Kid 6 didn’t want to (and didn’t) work on it, but Kid 4 drew a correct picture for it!  I thought Kid 4 had been working on A v B v C v D, and I’m still not absolutely sure she didn’t just do that one incorrectly, but it’s quite a coincidence that she got a correct diagram for the 2nd one; and when I asked, she said that they had been working on the 2nd one.  Kid 2 had the most trouble throughout the activity, and for the final one drew A ^ B ^ C ^ D instead of A v B v C v D.