So for today we started with candy in the lunchroom. I also had 5 sheets turned in from last week's take home problem. As I've mentioned before its fairly crude, but the naked bribery experiment is producing results. What I'm most excited about from today is the kids produced the three main solutions I was hoping they would find. As a result I was able to I have them demo all of them on the whiteboard.

There is a curious 5 digit number A which when you add a 1 to the end of it is three times larger than when you add a one to the front. What is A?

The first way is to setup the algebraic equation 10A + 1 = 3(A + 100000) which I wasn't sure was within their skill set. (In full disclosure I think some of the parents are working with their children)

Secondly you can treat this as decoding problem:

1ABCDE

x 3

ABCDE1

and working right to left use a little number theory to find each digit. For example E must be 7 since

only 3 x 7 ends in a 1 and so on.

Finally its also possible to do a brute force search through the number space especially with a bit of intelligent bounding.

I'm super proud of how well they all did this week.Which leads to my other observation. This years kids are really good at working during club as well. They almost always form productive groups and grind a way at the problems. I can definitely see the fourth grade vs fifth grade difference in terms of algebraic awareness. But I'm hoping I'll be able to move them forward quite a bit over the year if this keeps up.

For the main activity I had everyone do a practice Olympiad since the first real one is coming in 3 weeks. This went well. I will report that it contained the STAR * 4 = RATS problem in it yet again. This must be the third or fourth place this problem has showed up. As expected this was the hardest problem for most of fourth graders. In followup when we worked through the problems as a group it looked like the decoding procedures were understandable. Also for the followup I was able to split the club into two sections and had the smaller size groups each with an adult which is really great for focusing on listening to each other.

Finally with the extra time after we finished going over the solutions we did some match stick problems (well actually tooth pick problems in my case since I don't risk burning down the school):

Example:

Form a grid like on the left and then moving only 12 sticks form two big squares: (ignore the right hand picture)

These worked really well I presented 4 challenges which was more than enough for the end of the club. Finally I left the kids with following take home challenge.

In triangle ABC, three lines are drawn parallel to side AC dividing the altitude of the
triangle into four equal parts. If the area of the second largest part is 35 (the blue region), what is the
area of the whole triangle ABC ?