K-12 Integer Sequences

The K-12 Integer Sequences Conference was organized by my good friend Dr. Gordon Hamilton (Dr. Pickle) of MathPickle.com and Dr. Neil J. A. Sloane, the founder of the On-line Encyclopedia of Integer Sequences (OEIS). I was fortunate enough to attend as a math educator among other educators, math professors, and curriculum developers.



The goal of the conference was to identify 13 integer sequences that could be promoted for use in classrooms from K-12. The sequences would help students practice or learn level appropriate curricular goals, but they would also introduce the students to the wonderful world of mystery found in integer sequences. You can watch our large group sessions in these videos. Three sessions were spent in smaller groups - mine sought to identify sequences for grades 10-12.



The event was hosted by the Banff International Research Station (BIRS) at the Banff Centre which means they provided the hi-tech and comfortable conference facility (pictured behind me) and the lodging for the attendees. BIRS is dedicated to math research and collaboration.



Naturally, if you are still reading this, you are keen to learn which sequences will be promoted as a result. As with many collaborative conferences, there are still some **loose ends to tie up. I will feature a few here though.



Kindergarten: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, ...

A034326 This is the clock sequence. I think it's brilliant. You can have kids do some skip counting on it where they will be exposed to factors of 12 (when you skip by 4s, you will always land on the same 4 numbers, when you skip by 5s, you don't!). There is of course the excellent recursive nature of this sequence which mimics time.

Grade 3: 14, 7, 5, 3, 1, 2, 4, 6, 8, 10, 12, 24, 22, 11, 9, 18, 16, 32, 30, 15, ...

A254873 This sequence is a modified Recamán sequence developed by a 15-year old student. Starting at the seed number (14) the sequence continues by dividing, subtracting, adding or multiplying by the step number (2). Division gets precedence over subtraction which gets precedence over addition which gets precedence over multiplication. The new number must be a positive integer and not previously listed. The sequence terminates if this is impossible.



Grade 5: 4, 9, 7, 20, 6, 33, 13, 23, 16, ...

Starting with 1, on the first step add 1/n, and on subsequent steps either add 1/n or take the reciprocal. What is the smallest number of steps needed to return to 1? This number of steps is the nth term of the sequence. (Note: the n=0 and n=1 terms are not defined, so the sequence actually starts with the 2nd term.)

eg. let n=2: 1, 3/2, 2, 1/2, 1 therefore the number generated is 4 because it took 4 steps
eg. let n=3: 1, 4/3, 5/3, 2, 7/3, 8/3, 3, 1/3, 2/3, 1 took 9 steps
eg. let n=4: 1, 5/4, 3/2, 7/4, 2, 1/2, 3/4, 1 took 7 steps

This one is a lot of work, but I think it works to help students see that just because you work with increasing fractions, it doesn't necessarily mean it will require more steps. It really depends on the factors of n.



This time, I brought Amber along since I knew she would enjoy the tranquility, beauty and opportunity to relax in such surroundings.

My mom took the kids for most of the weekend, then Jasen for the last bit - we are very grateful.



Getting away to Banff now means being able to chow down and drink at the Banff Ave Brewing Company. Their beers are notable - especially their recent addition of an imperial IPA. Their food portions are ridiculously huge. I ate one burger for two meals.



The sequences have been determined in full! Here they are at the OEIS.org.

Sukkōt: The Feast of Tabernacles

On October 9 we celebrated Sukkōt, a biblical feast commemorating the time the Israelites spent in the wilderness. My father and his wife have been observing what are traditionally Jewish holy days for a few years now. They were visiting us in Calgary when the Feast of Tabernacles began so my father rigged up a temporary tabernacle or booth or tent in the back yard and his wife prepared a terrific feast for our entire household.



You could say that Christians are living in the wilderness now - the time between the exodus (freedom) and promised land (fulfilment of the promise of the new earth). Setting aside time each year to remember this was God's intent for His people.







We feasted on kabobs, pumpkin hummus, olives, tabouli, grapes and wine.





While it cooled down substantially at sunset, we hung out for another and enjoyed more wine and laughter.

Touring Victoria, BC

Flew into Victoria Int'l on Friday night after a delayed connection in Vancouver due to fog. The flight from Van was only 13 minutes. The delay was over an hour. I walked off the plane into a light mist and then to the bus stop where the bus rolls by once per hour. I had called transit and learned the bus would depart 20 minutes after arrival. While the shuttles were filling up, I sat alone on little bus. It was a 6 minute ride to the exchange just off the highway where I waited for the 70X which goes between the ferry docks of Schwartz Bay and downtown Victoria (a 30 minute drive (or 60 minute bus ride). 70X was a little late, but I didn't care! It was a double-decker bus and there was a free seat on the upper deck. Too Cool. I got off 2 blocks from my hostel, Ocean Island Backpackers Hostel.

I arrived too late to eat at a restaurant, so I enjoyed a delicious curry bowl at the Ocean Island Cafe. I slept on a bunkbed in a dormitory and only met a couple German girls who are travelling the west coast. The other guests came in after I was sleeping and were still sleeping when I left in the morning.



As I was there for the marathon, I went for a quick 3 km run through downtown and along the shore. I watched harbour light up and absorbed the cool air. It took me right back to living in the Marshall Islands.

A quick shower and check-out/check-in to the room Marc and I shared and I was off in a light drizzle to Discovery Coffee, six blocks away. I ordered a couple baked goods and a light roast espresso which was stellar! So stellar that I ordered another.



I read by book, Culture, Commonweal and Personhood by Lazar Puhalo (just across the water), whilst taking in the coffee, cafe aromas, groovy tunes, and the torrents of rain outside. I ordered a third coffee - a pour over light roast. So yummy.



I met up with Marc at Ocean Island and we picked up our marathon package at the fitness fair. Then we were ready to carb up. I picked Swan's Brewpub and had a flight with Riley's Scotch Ale, SOS Oatmeal Stout, IPA, and Coconut Porter. Oh and a big plate of eggs, sausages, bacon and pancakes. Marc and I chatted about religion.





Marc went to visit an aunt and uncle, so I went for a walkabout in the north-central part of downtown initially hoping to sample some Phillips beer at their brewery, but it was pretty crowded with folks filling growlers and I had already tried the ones they had on tap, so I just had a look around. Most impressive was Phillips yard of fermenters and kegs ready to ship.

There was a nice furniture store and a Value Village that drew me in for a while. I browsed VV's book section and formed a nice collection of books that I had no choice but to re-shelve and leave behind. I enjoyed some edamame (so many I couldn't finish) and a giant veggie burrito at Ocean Island along with a pint of Blue Buck before heading to the theatre to see Gone Girl - which was spectacular.

Before heading to bed I laid out my marathon gear and packed up everything else. The hostel was pretty loud through the night, but I had earplugs.

Thoughts on Community Development

It's been 1 year since I boarded a plane to visit two African countries and a community development organization in each one. Since that time, I've really let the ideas and realities of what is happening in these successful enterprises percolate. Here are the thoughts that have persisted.

SOUTH AFRICA
My first stop was Bhekulwandle, Malagazi*, South Africa. I blogged about Seed of Hope when I returned from Africa and the things they are focusing on and the leadership they have in Carl Waldron - a very good friend of mine. What remains with me is slow going. I think of the hospice like service they have in providing supportive care for those dying of AIDS and those coping with HIV. Much of their clientele in this field is not in a position to respond and begin doing in the place of those that do in the present - not exactly a sustainable program - necessary and life giving, but not self-sustaining.

But, let's discuss something that does have the possibility of self-sustainability: Equipping Young Leaders. Seed of Hope has several programs targeting kids of all ages with support in areas of health, spiritual growth, educational tutoring, sports programs, and community building. Let's imagine that 50% of these kids who are equipped remain in the community long term. Then, let's imagine that half of those actually use the skills and support they have received for the betterment of their community. This is probably optimistic, but it is simply to underscore two points:

• The harvest of this investment is largely expected to emerge 10-20 years from now (of course there are immediate results, but they will likely pale in comparison with future results). So, all of the resources spent today are done with a view for a couple decades down the road. 
• The other point is the relational aspect of the initiative. With the long view in mind, less is made of current results than is made of strengthening relationships between the staff and the young people coming by Seed of Hope. I think this is a clear indicator of success.

MALAWI


Kamanzi, Malawi was my second stop. My church has been in partnership with the communities in Kamanzi, a rural collection of 5 dominant villages. World Renew has been applying principals of community development on our behalf for the past 4 years and just over a year ago, Peter Timmerman took the helm. I was really struck by Peter's dissatisfaction. From the perspective of me and my fellow church member, some real progress had been made through seed loans, ecosan latrines and goat/pig husbandry. But Peter could see the relatively low economic and probably low espousing of real change by the greater community of some of the principals. His questions: Will what we are doing have a lasting and real impact on food security in these communities? Do the dollars (or kwacha in this case) and sweat equity in these projects really pay off?

His dissatisfaction helped me see the value of the big picture view, the years of experience and training he brought to the organization. In many ways, I'm stuck in the camp of "if I can take a picture of a result, be it great or small, we have succeeded!" [I shudder as I write this, but I'm being honest.] The admission that we can do better is probably the most humble thing we can do and ultimately better for working with a community who already has a hard time dreaming of a bright, less hungry future.

Shortly after we left, Peter blogged about the second thing that has stuck with me: This is a slow, slow process. And that is a good thing. Africans understand this. Sadly, westerners have a difficult time learning the value of slowing down. Ultimately, the slower, the better long term and the more buy in from the community.

*Just realized that this community is in a different province than neighbouring Amanzimtoti and Durban which are in KwaZulu-Natal. You can see the difference on either side of the road running between the two communities.

Man Scouts: The Beer Tasting

On February 4, almost 20 man scouts converged on Rob's house and we sampled 17 very diverse beers, ales, porters, lagers, stouts, wits and bocks. Some of the guys were completely blown away by the strong bitter tastes of the IPAs. Others were impressed with the strong flavours of porter and stout. Most were pleased with drink that didn't threaten their manhood.



I helped organize the event. I brought the gear - mini beer mugs, a tray, score cards and golf pencils. A couple different guys helped pour, but I kept the evening moving by pouring and delivering the brews all night.

• Cerveza Cristal (lager, Cerveceria Bucanero, Cuba)
• Sapporo Original Draft Beer (rice lager, Sapporo Breweries, Japan)
• Grolsch Premium Lager (lager, Golsch Bierbrouwerij, Netherlands)
• Morimoto Soba Ale (soba beer*, Rogue Ales, OR) fifth place
• La Messagère (pale ale*, Microbrasserie Nouvelle-France, QC) seventh place
• Mongozo Premium Pilsener (pilsener, Mongozo, Netherlands)
• Village Wit (witbier, Village Brewery, AB) seventh place
• Rickard's Red (red lager, Molson Coors, ON) seventh place
• Black Tusk Ale (dark mild ale, Whistler Brewing Co., BC) second place
• Ayinger Weizenbock (weizenbock, Privatbrauerei Franz Inselkammer/Brauerei Aying, Germany) seventh place
• Scarborough Fair IPA (india pale ale*, Wold Top Brewery, United Kingdom)
• Blacksmith India Black Ale (american black ale, Village Brewery, AB)
• Devil's Elbow IPA (india pale ale, Howe Sound Inn & Brewing Co., BC)
• Amnesiac Double IPA (imperial IPA, Phillips Brewing Co., BC) sixth place
• Village Monk Chai Winter Porter (porter, Village Brewery, AB) second place
• Salty Scot (scotch ale, Parallel 49 Brewing Co., BC) first place
• Megadestroyer Imperial Licorice Stout (imperial stout, Howe Sound Inn & Brewing Co., BC) fourth place

*denotes a gluten free beer



My personal favourites were the Phillips Amnesiac, both Howe Sound (Devil's Elbow and Megadestroyer), and the Ayinger. Of note too were all three Village Brewery contributions - too bad they are generally sold in growlers. The best of the gluten free beers was the Morimoto Soba Ale (Rogue), in fact I'd consider buying it to drink myself.

I had a great time introducing the guys to new beer. I hadn't tried about half of them, so many were new to me too! Thanks for the fun scouts!

An Evening in Durban, SA

Despite my assertion that I didn't have to be treated like a tourist, Carl decided that I must experience an evening in Durban - I think he just wanted an excuse to show off this super gorgeous city and get out for an evening. For this, I am very grateful.

We headed out after 7 pm, already nearing my bedtime, and drove the 30 or so minutes into downtown Durban (which appeared a strange fusion of Guatemala City and New York City). He parked at John Ross House, a tower, and we shot up the elevator to the 32nd floor where the Roma Revolving Restaurant sits. Roma is very tacky. Very. I'm sure the food and service are very nice, but the decor... eek.  But we strolled through and scooted up a narrow stairwell and emerged onto the roof, the location of Gino's Sky Bar.

The 360° view of a lit up port city is quite stunning. I would have brought my better suited Nikon and probably would have stood trying to capture the dazzle if I had, so I grabbed a bit of media with my iPhone and sat down for a drink with Carl. I had a Castle Milk Stout, a local South African beer - served far too cold, but it went down well enough.



It was quite windy at the top of this building next to the Indian Ocean. Carl was beginning to get cold, so we didn't hang out any longer once our drinks were done. Plus we had some food to go buy.



We drove a few blocks down the road to the Britannia Hotel where according to National Geographic, the best cultural culinary experience can be had. We ordered at the take out window - I had the Mutton Bunny Chow (see photo below) and Carl had the Chicken Kebab Bunny Chow. I went into the bar to pay for the food and was very impressed with the waitress's acute ability to recognize talent: "Are you a model?" she asked.

Presenting the receipt, we grabbed our sweet smelling bag of food and headed to the shore. The beachfront in Durban is lined with shops, a waterpark, aquarium, hotels, eateries, etc. just like any ocean city worth its salt. We walked until we came to a pier with an open air food court and after assuring the guard that we would clean up our mess afterwards, we unwrapped our bunnies.



Bunny Chow is a traditional dish originating in Durban. It is a 1/2 or 1/4 hollowed out loaf of bread which forms a container. It is then filled with delicious curry - I'd wager that the curry is better is South Africa than it is in India thanks to the fusion of cultures and ingredients. You then tear off bits of bread and eat your curry with it.

Delicious.



Great chat during the chow, then we checked out the pier and saw the tankers and freighters waiting to be called into port and the massive waves crashing into the base of the continent.

So thanks Carl, I think I may have an overwhelmingly positive view of Durban now, but I have an idea of it at least.



"Are you a model?"
"Yes, yes I am."

Big Bird Snack

Just enjoying a little ostrich jerkey - product of South Africa - to supplement my lunch today in Bhekulwandle.

Ingredients: raw ostrich meat, spices (salt, irradiated spices: nutmeg, black pepper, cloves), sugar, yeast extract, preservative: potassium sorbate, vinegar (with caramel colorant).

New Years Eve 2012 Beer Tasting

Now becoming a tradition, the Robiroost hosted a beer tasting as a New Years Eve party. It has been and is such an event that there seems to always be a contingent of attendees who don't even like/drink beer. Happy to have them there.

Everyone attending came from our Dragonfly Cohousing circle except a contingency from Regina who was passing through bring with them some delightful drink from Bushwakker brewery and debates about workers unions.

The sampling came from those sampling and what a delicious review. The evening's top four of twelve are as follows:

• Trois Pistoles (Unibroue)
• Maximus IPA (Lagunitas)
• Innis & Gunn Spiced Rum Finish - (Innis & Gunn)
• Chimay Tripel (Bières de Chimay)

Then we had a 4-way tie. The middle ones were:

• Blackberry Mead (Bushwakker)
• Winter Beard Double Chocolate Cranberry Stout (Lakes of Muskoka)
• BNL Imperial Chocolate Stout (Flying Monkeys)
• Chico IPA (Bushwakker)

The lowest scoring, though by no means bad brews:

• XXXXX Stout (Pike)
• Trephination Double IPA (Bushwakker)
• Attilla the Honey (Mt. Begbie)
• Apricot Summer Weizen (Okanagan Spring)

A great time, hopefully to be replicated annually. Happy New Year!

Beer Tasting Nov '12

Zaakistan reader and commenter Danny B, husband of the prolific blogging sensation Aimee at Simple Bites and Under the High Chair (how's that for a qualifier Danny?), happened to be in Calgary for a conference and as I had promised months before, I organized a social event around tasting kindly beer. Amber, Jae, Anne, Heather, Patrick and later Jasen rounded out the table, each of us providing 2 beer to try.

Danny brought a couple beer from a local brewer in Québec - beer we can not yet access in Alberta. It basically won the evening. This was my order of preference:

1. Ale Écossaise (Brasseurs Illimités)
2. Green Reaper Fresh Hop IPA (Phillips Brewing Company)
3. Delirium Tremens (Brouwerij Huyghe)
4. India Pale Américaine (Brasseurs Illimités)
5. Father John's Winter Ale (Howe Sound Inn & Brewing Company)
6. Saison D'Etre Farmhouse Ale (Alley Kat Brewing Company)
7. Mr Sno'balls (Harviestoun Brewery Ltd.)
8. Hobgoblin (Wychwood Brewery Company Ltd)
9. American Dream (Mikkeller)
10. Bloed, Zweet & Tranen (Brouwerij De Molen)
11. St-Ambroise Framboise (McAuslan Brewing)
12. Begbie Cream Ale (Mt. Begbie Brewing Co.)
13. Ginger Beer (Granville Island Brewery)