## Tuesday, October 20, 2015

### 10/20 Grids and Graphs

This week I planned a series of more playful activities. We started with a review of the take home problem of the week: (September from www.moems.org/zinger.htm).  I already knew this was easier than October since 3 kids had told me the answer almost immediately when I handed it out. I had 8 kids complete the problem so I will be bringing M&M's to math club next week.  To wrap it up, we did another white board exercise with 2 kids showing their work. Listening worked better this week. My only concern was one student took fairly long to copy her work onto the board and I fretted unnecessarily that I would lose the club's attention.

After that I decided to do a quick demonstration with the distributive law why a negative times a negative is a positive.

For example:
-5 * -6 + -5 * 6 = -5 (6 + -6) = 5 * 0 = 0
Then go back to the original sum -5 * -6 + -5 * 6 = 0.
We know the second term is -30 already since its a negative times a positive.
So -5 * -6 + -30 = 0   which implies  -5 * -6 =  30.

I had each kid pick their own product and work along. This strategy worked OK but I ended needing to go over several more examples from the kids on the board. Overall this was a stretch and next time I should start with a review of factoring with the distributive law even if we did it the week before.

This entire process took about 20 minutes and we then switched to over to a 3x3 logic problem from http://www.logic-puzzles.org. I went much simpler than last year based on my previous experience and even so this was about 30+ minutes of work for most of the kids. Moral of the story I estimate a 4x4 would probably take a full hour if I want to fill one up.

Because things went longer on the logic puzzle I didn't have as much time for my main selection. I did a quick edit of my original ideas and took out the loop-de-loop exercise from: http://www.amazon.com/This-Not-Maths-Book-Activity/dp/1782402055.  As others have reported on the net this was a big hit with the kids. There were a lot of excited students who wanted to show me the different spirals and loops they had created.  I ended up shorting the time I wanted to spend on trying things out so I think I may revisit this at the beginning of next week and have a wrap discussion about what patterns everyone found.

#### Problem of the week courtesy of  Martin Gardiner:

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?

I told everyone to try some strategies on your own first and give this a little time if you get stuck before looking at the hint. This will definitely be harder than last week and I'm looking forward to seeing what the kids come up with.

Hint:
"∀ ɟo sɯɹǝʇ uᴉ sɹǝqɯnu ɹǝɥʇo ɥʇoq ɹoɟ suoᴉssǝɹdxǝ ǝʇɐlnɯɹoɟ"

#### Planning

Its time to try out a sample Olympiad next week!

1. In case your crowd is interested in my sons' loop-de-loop challenges:
Four Challenges.

We also welcome puzzles posted back to us!

Also, some ideas for further explorations:
More loop-de-loops

2. An extension exploration for your Martin Gardiner puzzle that the kids might like: this puzzle has parameters 5 (digits in the starting number), 1 (the numeral that gets appended), and 3 (ratio of the two ways of adding a digit to either side). So, let's call this is the (5, 3, 1) puzzle.

Are there solutions for the (5, 3, 2) puzzle? For all (5, a, b) puzzles, where b is a single digit 0 to 9? For all (a, b, c) puzzles?

What if we let the third parameter be multi-digit?