## The Activities

**Topic: Addition:**Book: Math Man by T. Daniels.**Topic: Programming:**We did two types of programming this week. First, we reviewed how loops work, and practiced assigning a variable to itself inside a loop (X = X + 1). Second, we introduced choosing a random noun/verb/number by drawing a word from a bag — a random version of Ask_a_Friend. Download the programs here.

**Topic: Algebra:**I attempted to show the kids how to solve algebra problems involving addition and simple multiplication using Base Ten Blocks. For example, in “X + 17 = 68”, you can first make 68, divide it into a pile of 17 and a pile of 41, and then conclude that X is 41.**Topic: Reflections:**A while ago I drew a picture that had every uppercase letter hidden in it, duplicated and reflected. E.g., reflecting “B” around the vertical line gives you a butterfly. You can download the picture here.

## How Did It Go?

All six kids attended.

#### Math Man

The kids liked the part where Math Man adds a whole bunch of prices in his head.

#### Programming

Last week, many of the kids had trouble with loops that had more than one statement inside; and also with self assignment like “X = X + 1”. We walked through a program with both of these features: “Box_X = 1; Do 5 times { Print Box_X; Box_X = Box_X + 2 }”. I think by the end of it most of the kids understood what was going on; we’ll try another in a couple weeks and see how it goes. Our daughter already had a firm grasp of these two concepts, so I gave her some harder problems to work on (second page of PowerPoint above). She got the first two but got stuck on the nested loops.

As expected, the kids really liked the programs with random nouns/verbs/numbers. For the most part, they had no problems, but one thing that turned out to be very hard/confusing was “Do Box_X times {Print “really”}”. Almost all the kids wanted to print the number; and one of the kids ended up print “2 2 really really”. So clearly they need more practice using variables in control flow rather than just printing them.

#### Algebra

One issue with this activity is that some of the kids can solve problems like “X + 17 = 63” in their head, but I had everyone work through it methodically. My approach was a bit wrong, I think; I gave everyone a paper square with “X” on it, and had them make 17 and 63. Then, I said they should split 63 into two parts, 17 and what’s left, and from that, they can conclude that X is 46. I think it would have been better to simply have them make 63, and then break it into 17 and 46 and conclude that X = 46. The problem is, I don’t think they grasped the idea that the two sides were the same, so the extra 17 didn’t really help. Another problem is that it’s a bit hard to see how to extend this to X – 17 = 63; you need to make a 17 and a 63, put them next to each other, see that if you subtract 17 from this new number, you get 17, so the sum must be the answer.

There’s a different approach as exemplified in the very nice iPad game Dragonbox Algebra which I may try next time I do this activity. The focus there is much more on the fact that both sides have to be the same. I also like how they use pictures of monsters instead of numbers, at least at first, which helps emphasize the nature of “subtracting from both sides”. I think Dragonbox Algebra still gets something wrong, which is that instead of opening the box and revealing what’s inside, the box instead eats the other side, which doesn’t make much sense. So my ideal version is to have some objects hidden inside the box, emphasize that both sides have the same objects, have them isolate the box, and then reveal it to show that it has the same thing as what’s on the other side.

#### Reflection Picture

The kids really enjoyed doing this again, working together they were able to find all the letters.