Friday, December 26, 2014

Puzzle for the break

I love breaking substitution ciphers. I sent one out before the first meeting in the fall and I decided I would do another one before our second quarter.

Ptdegft mg mat pkhmtc vxqcmtc. Atct'n q mpg bqcm bxiidt. Ykcnm: Rtekbatc makn vxgmt ycgf Qdket kh Pghrtcdqhr. Qdket nqun, “Dtm ft ntt: ygxc mkftn ykzt kn mptdzt, qhr ygxc mkftn nko kn makcmtth, qhr ygxc mkftn ntzth kn–ga rtqc! K naqdd htztc ltm mg mpthmu qm maqm cqmt!” Nteghrdu: Nthr ft wqej q fqkd mtddkhl patmatc makn kn egfbdtmt hghnthnt gc ky matct kn q pqu km fqjtn nthnt qhr agp. Ntt ugx nggh Wth

To get started here's a page with a copy of the letter frequency chart in english:

Thursday, December 25, 2014

Odds and Ends

So officially we're on winter break and the club will not meet up again until January. It's also reregistration time. This had led me to imagine a few scenarios. Bear in mind I'm drawing from a pool of about 250 elementary school kids in fourth and fifth grade.

1. All the kids who are interested already are coming.

2. I lose a few kids due to scheduling and/or not interesting them enough

3. I have wonderful word of mouth and lots more kids try to register forcing me to cap the enrollment.

4. A few more kids who didn't sign up the first time show up because we're now starting in the official manner rather than a month late.

It turns out the answer appears to be #4. Tentatively we're at 18 kids for the next quarter which is at about my capacity to handle. Last time a few kids appeared each week so I'll see if that happens again or not. I don't really like saying no so I'm hoping that it isn't the case.


When I talked with previous coach, she gave me a list of all the contests the club went to last year. AMC 8 was not on the list and I assumed that was because it was not open to kids below sixth grade or like Math Counts had restricted times one could participate. . It turns out that is not the case. It occurred last month so we're not going to participate this year. However, all the questions were posted online at:

So I'm excited to use them as take home exercises over the next month or two and double check them as a group.  Tentatively I think I'll give out 5 questions a week since most kids don't have enough time or interest to do a lot of work in between meetings. Stay tuned: It will be very interesting to see how everyone does on them.

Monday, December 22, 2014

Knights of Pi Math Competition

Finally, our first off site competition! Nevermind that it was scheduled for the first Saturday of the winter break so most kids couldn't come, I was really looking forward to this. Overall I had fun time and I hope the kids enjoyed it too but I left with more mixed feelings than I expected.

The good:

It was inspiring to see 300-400 kids all competing together and very excited about Math. This competition was hosted and mostly run by the high school math club at Newport H.S. which was also kind of cool.  Despite my worries the night before, everyone who signed up showed up and  I didn't have to scramble around. I also kept tabs on everyone and didn't lose any kids in the crowd. (It turns out this was my main worry during the event)

The Bad:
This competition was very focused on computation and speed. There was a 45 minute individual section with 40 questions.  See for some examples.  Then there was a speed math section and then a mental math piece on top of that. It reminded me of another blog post I read recently:

I felt that the relationship between what was being rewarded here and interesting mathematics was a bit warped. Basically, if you were serious about earning medals then you'd focus on speed drills, review a few advanced concepts like probability and permutations, exponents,  geometry perhaps solving some beginning linear systems or factoring a polynomial and focus on test strategies.

Some samples I happened to see and my thoughts.

Evaluate 14641^1/4.  Most of my kids haven't seen the definition for fractional exponents being n-roots which is what half this problem comes down to. For me I took a glance and divisibility rules popped into my head. Palindrome numbers are often multiples of 11 so I did the quick test (   and yes it was. If  11 is a factor of number to the fourth then 11^4 must also be.  A mental estimate and then a quick check showed that yes that was the answer.  On reflection if you checked an easy benchmark like 10^4 = 10000 you'd realize that it must be very close to there and you could guess and check your way also quite quickly to the answer.

However, this is a really mechanical problem. It's not really tricky so much as facilitated by experience. You could just try every number starting from 1 and get there fairly quickly. A little number theory about which digits raised to fourth end in one would speed this up.  Which is all to say I don't think this bridges much to more advanced math.

Another one asked what percentage of all numbers between 1 and 10 when plugged into x^3 - x are divisible by 6?   For anyone with a little algebra and number theory you immediately see this factors into x(x-1)(x+1) and therefore is always divisible by both 2 and 3 and by extension 6. I think again the kids probably just plugged some numbers in and after observing the pattern worked could just assume the answer.  Which for me misses the kernel of interest here.

Also as you might imagine with this type of focus, the demographics were a bit skewed among the contestants. If you're interesting in encouraging more widespread passion for math this format doesn't seem promising. On the other hand, I left thinking there's  no need to hand wring over math performance in countries like South Korea, China or Japan. We're importing and assimilating that culture. Hopefully we'll arrive at a happy medium over the years.

The Future

So the big question is whether I'd go back again. I think the answer is yes despite my previous paragraph. There aren't many fall events and this fills a hole. Its high energy and I don't think it did any harm. I did have one kid bring home a very large trophy after all. That said, I'm not interested in focusing on preparation for this style of contest.  Next year if I continue I think I will outline how to prepare at the beginning when signing up kids and leave it up to them whether they want to spend their time doing so. I'm happy to supply worksheets and mentor if requested.

Thursday, December 18, 2014

12/17 Math Olympiad 2

So MOEMS released the January test last week and I realized that given our school schedule it would  be best to run the contest this week rather than scramble when everyone came back and on the first day of the new quarter.  Thus, I tabled my ideas for this week in favor of the contest.

To start off with I had the kids play the game of 100. Where you break into pairs and each kid takes turn adding the number 1 - 10 to a sum, the first to get to 100 wins.  That went well and at least 3 kids came up with the idea that if they made it to 89 first they would win while I walked around and observed. I then had everyone talk about it. My next question was what if we play the game of 89? A few more kids finally arrived at the need to get to 78. I then repeated the question with the game of 78 and the recursion fell out very quickly then.

Onto the test. I had more problems with chatting than last time and I may want to spread the kids out next time.  This time around I stressed about checking both your answers and the question itself to make sure you answered the right thing as well as signing your name. (I still had one girl forget to do so)  Also this test had some terminology like counting numbers instead of whole numbers and meets instead of games that a few kids didn't recognize. Overall there was one 3-d surface area question that I thought would be the most difficult which proved true.  It might be useful to practice such problems again in the future and talk about strategies more.

At the end, we regrouped and talked through the answers to the problems together. At one point I had 3 kids up on the whiteboard trying to work out the surface area question which was fun to watch.  Interestingly when I graded the tests at home this turned out to be a hard one for the kids. I'm having an internal debate about whether to work more practice problems as a group next quarter vs. doing less structured explorations. I really want to go off and explore the Pythagorean theorem and the square root of 2.

I'm also reluctantly coming to the conclusion that group snack is not that great of an idea. It still causes too much boisterous behavior. I'll stick with it for this year but probably not beyond that unless things improve.

Thursday, December 11, 2014

Classroom Management

Going into the process, I worried most about handling a large group of kids at once.  I've never done anything exactly like this before and my closest experience would be teaching math one on one to my sons. As you'd guess there is not much of a relationship between individual tutoring and a group setting. Talking in front of larger groups always makes me nervous and its not something I necessarily look forward to.  The first meeting was stressful.  I prepared as much as I could. I had an agenda and materials printed out. I read as many other math circle diaries and descriptions as I could. I planned strategies for what to do if things didn't work out or the kids found the sample problems too hard.  Nevertheless, I was full of adrenalin and utterly exhausted by the end. The good news is that it its becoming easier over time.  For one thing, I'm starting to know the kids and how they react. I don't have to guess as much at leveling etc. Here's a list of my findings so far:

1. Always try to break things up with games. They tend to bring out the quieter kids and generally activate the room.

2. Get the kids to explain their problems. My goal is to talk as little as possible and let the kids drive as much of the conversation.

3. Give them time to work on things. My instinct is to jump to a conclusion. I'm working on letting the process unfold in its own time.

4. Call on the kids rather than just letting them raise hands. I'd have four kids or so who'd dominate the room if I didn't actively try to get the others to speak.

Things I'm still contemplating.

1. Assigned seating. As you might predict I typically end up with two large tables. The boys on the right and the girls on the left. My thinking is that this is a club not school and its probably fine to let this be but I might experiment in the future with asking everyone to sit next to someone they don't usually sit by.

Wednesday, December 10, 2014

12/9 Prime Climb

I've already tried a few different games out and they've always worked really well especially for drawing out kids who don't raise their hands as often. However, I've never used a honest to god board game. This week, Prime Climb, finally arrived in the mail and it seemed like a natural to test it in the group setting. Before starting I roughly thought that we'd review last weeks challenge problem, play 3 parallel games at once for maybe a half hour, and then introduce next week's challenge problem. I wasn't sure if that left a gap so I decided to talk about multiplying variable expressions and deriving the mental math trick of  using  (x + n)*(x-n)  == x^2 - n^2 to solve some problems as a backup to fill any extra time.

As usual, only some of the kids had solved the problem. See: November. The problem as defined is fairly trivially solvable via guessing and checking. Just start at 1 see if the answer works and by the time you reach 3 you're done so I asked a followup question: what if the side length was 16?  This requires fractional answers and more understanding of the problem structure. My hope was solving the easier version would be insightful for everyone.

With a little prompting that you could guess and check I guided everyone who hadn't already done so to the easy solution in a few minutes and then had the kids try to figure out the structure to solve the general problem. In the meantime I labeled the diagram with some x's for the missing portions. Adding 3x on the vertical would hopefully trigger some more thinking. Bingo, one girl stood up and declared how you needed to divide the length by five. I labelled some more and put the 3x on the horizonal side as well. When asked everyone could now say that you just needed to solve the equation 15 = 5x and changing the constant did not pose any further troubles.

We then broke out the raisin snacks and the new Prime Climb games. It turns out I had underestimated average game time based on my samples at home with my son. In groups of 3 the game actually took the entire rest of the hour. It was a total success though. All the kids were engaged, the boys in particular took to bumping each others pawns back to start. It was interesting to me as well, because the kids were trying to do calculations like is 24 * 7 < 101 and I received a peppering of questions asking me to do the mental math for them. I ended up talking them through the several examples like that. I'm going to need to find ways to subtly encourage more mental calculations over following weeks. Maybe I can find/invent a mental math tournament that we can warm up with.

Next week's challenge: 

This one is a word problem which I haven't really done yet. Its based on an AoPS one I saw that had a interesting trick to reach the solution.

Two football teams played a game with a combined score of 65.  All the points were scored via 3 point field goals or 7 point touchdowns.  One team scored 2 more touchdowns and 1 less field goal than the other team. What was the final score?

In the beginning ....


The elementary school my son goes to has a after school math club that is mostly for the fourth and fifth graders. The focus is on organizing the kids to go to the various math competitions that occur over the year. After last year the previous volunteer parent "graduated" to middle school and the club almost disappeared.  Some time went by and I responded to the call for a new volunteer at the end  of October and have been running it for about five weeks now.

Why Me?

This is my first time volunteering at school. I've always felt that there wasn't an opportunity that was worth the lost time at work. However, I've thought about getting involved with the math club in the past. Math is a passion of mine and I had some key mentoring experiences at the end of elementary school that I would love to provide for others. More generally I've found that I really enjoy watching kids learn. After a few weeks I can say that this seems to be true whether not they're my own  children.  Speaking of which although my own son isn't old enough yet for the club, I also want for it to be available for him in future years.  I'm hoping to also learn along the way myself and improve my own  teaching/facilitating skills.

The kids

My initial target was 10-15 kids. I ended up with 15 that are split almost evenly between boys and girls and skew mostly towards fifth graders. They all are doing various stages of pre-algebra using the Glencoe Mathematics Middle School book 1 or 2.


I'm running the club as a hybrid math circle / math competition club. That means in practice, I've been buying and reading a set of math circle diaries and books. I'm trying to structure the hour I have as partly preparation for the next contest and partly a mathematical exercise or game for the day. This is not always easy and I'm still evaluating week to week what seems to work and what draws out the most from the kids.