letters to my class

December 20, 2012

December 20th, 2012

Dear Number Mavens,

Yesterday we talked about repeating and terminating decimals. In looking at whether unit fractions repeated or terminated, we found some interesting patterns. We found that having primes (except 2 or 5) as the denominator led to repeating fractions, and we saw something neat about multiples of 3. Today, we’ll look closer at the amazing repeating patterns that occur when we’re dealing with sevenths.

142857 is one of many magical numbers in our number system. When we stretch that number or cut it up into pieces, it does some mind-boggling things. If you’re still of the belief that numbers are just numbers–dry, boring things that have no relevance to your real life–142,857 is probably enough to convince you that our number system has a deep order to it, and it can model the deep order of the real world.

Sincerely,

Mr. Heimbuck
December 19, 2012

December 19th, 2012

Dear Collectors,

“The world is so full of a number of things, I’m sure we should all be as happy as kings.”

–Robert Louis Stevenson

When I was younger, I collected pennies. I had a few Indian-head pennies, and every once in a while I’d find a wheat penny, but mostly my collection was bottles full of plain, boring, 1 cent pennies. But my pennies taught me a lot–about geography, Presidents, US history, and about the nature of collecting.

Collectors pay attention to the things others overlook. Because this world is full of hidden knowledge and wonder, close attention is always rewarded with insight and beauty. It doesn’t matter what items a collector collects. It could be coins, stamps, football cards, stuffed animals, or pens. Whatever it is that you collect, your collection will teach you how to make sense of the world, and it will renew your appreciation of the wonderful world we inhabit.

Sincerely,

Mr. Heimbuck
December 18, 2012

December 18th, 2012

Dear Data Collectors,

As human beings, we’re excellent pattern detectors. Rather than looking at any one thing, we look at how things come together to form a design or to tell a story. Today as we think about ways of displaying data, we need to keep this in mind. Data displays–bar graphs, line graphs, circle graphs, etc.–help us humans see data by putting it into understandable data.

We also have to be on the lookout for misleading data. Sometimes people display data in ways that tell the story they want told. As consumers and users of data, we have to ask questions not only about how the data is displayed but also about the methods used to collect it.

We have a responsibility to make the world make sense to human beings. Data can help us do that.

Sincerely,

Mr. Heimbuck
December 17, 2012

December 17th, 2012

Dear Math Thinkers,

I’m sure you all heard about the terrible events in Connecticut on Friday. You might be sad, confused, and a little scared to come to school today–I know I am. But thinking like mathematicians might make us a feel a little bit safer and feel a whole lot better about the world.

There are over 100,000 schools in the United States with over 70 millions students in them. In recent years, the number of violent deaths at schools has been between 11 and 49 students. That’s out of 70 million. If you put that fraction on our Probability Meter, it would be so close to zero that you couldn’t even see it. The chance that any one school will have a school shooting is almost zero. The chance that any one student will die in a school shooting is extremely close to zero.

Anytime there’s a risk, however, we prepare ourselves for it. We practice our drills, keep our eyes open, and practice safety at school, so if the unthinkable ever happens, we’re prepared. And we do our best to prevent future tragedies like this from happening.

But we don’t live in fear.

Sincerely,

Mr. Heimbuck
December 14, 2012

December 14th, 2012

Dear Achievers,

I enjoyed watching the orchestra concert. You get a nice sound out of your instruments, and you played together nicely. What I’m really excited about is watching the next concert in May because I want to see how much you’ve improved. I know that it will be even better.

This world is starved for greatness. It doesn’t matter the area–it could be violin or guitar or trumpet or athletics or engineering or computer programming or construction or teaching or housecleaning–the world needs more greatness in all of them. Greatness doesn’t just solve the problems of the world (of which we have many). It also allows humans the see the previously unimaginable.

Greatness requires creativity, talent, and hard work. We don’t have much control over the first two, but the last one we do. Greatness comes from the hard work that is lit by the flames of passion. No motivations–not money, fame, or adulation–can match passion for its inspiration power. But passion can only take as as far as the hard work it inspires.

Be great,

Mr. Heimbuck
December 13, 2012

December 13th, 2012

Dear Stewards,

Stewards are people who take care of others by taking care of things. At our school, all of us are stewards. That means we pick up after ourselves, take care of things, and take pride in how our school and classroom looks. Most importantly, stewardship means we use things so they last for other people. Our responsibility is not only to the people in our community right now. We also have a responsibility to those who who will some day be in our school. We need to take care of our school so it’s even better for those people, whomever they may be.

Today, we’ll talk about how we can show stewardship of our classroom and our school, and we’ll talk about how the ethic of stewardship can be carried to other parts of our lives and our world.

Sincerely,

Mr. Heimbuck
December 12, 2012

December 12th, 2012

Dear Time Dwellers,

Today the calendar will be full of twelves. At 12:12, both clock and calendar will show only twelves–the twelfth minute of the twelfth hour of the twelfth day of the twelfth month of the twelfth year of the second millenium. That’s a lot of twelves, and it naturally gets us wondering: when was the last time the clock and calendar were full of twelves? When was the last time they were full of any number? When will it happen again?

The answers to these questions don’t really matter (unless you’re a doomsday-er), but by going through the process of figuring them out (and then coming up with more questions), we might just learn something fundamental about the clock, the calendar, and maybe even about time itself.

Also, the number twelve is awesome. Check out twelfths on your fraction-stick chart and revel in all of its equivalent fractions!

Sincerely,

Mr. Heimbuck
December 11, 2012

December 11th, 2012

Dear Number Crunchers,

Today we’ll continue to convert between fractions and decimals. One of the most important things you will learn in math is that there are many meaningful ways to express a number. Depending on what we want to do with that number determines how we express it. Do we want it as a fraction, a decimal, a percent, a sum of prime numbers, prime factorization, etc? Our number system is an amazing thing, and we’re lucky that we get to spend the entire school year learning how it works.

When we play around with numbers and express them in different ways, we start to notice some wild and crazy patterns. In the world of math, those patterns never stop and often reveal even more intricate patterns. We learn about math by playing around with those patterns, trying to find new ones, and thinking about how we can apply those patterns to other parts of life.

Sincerely,

Mr. Heimbuck
December 10, 2012

December 9th, 2012

Dear Historians,

Through its exploration and conquest of the Americas following Columbus’s journey, Spain became the most powerful country in the world. Soon, other European countries competed with Spain for power and wealth. This was a time of great change and great opportunity. European settlements began to sprout in the Americas, and the British became a world power. All of these events would shape forever shape American history.

Today, we’ll read about the defeat of the Spanish Armada, one of the most important events in World history. What made it important and how do we still feel its effects today? What important events in our lifetime will students be talking about 300 years from now?

Sincerely,

Mr. Heimbuck
December 6, 2012

December 5th, 2012

Dear Exchangers,

Movement is the way of the world. Currents, prevailing winds, train tracks, roads, flight routes–these are the things that define our world. When things move around our world, they forever change it. We’ve been reading about how radically the world changed following Columbus’s trip to the New World. Both the New World and the Old World changed in ways that we’re still feeling today.

The story of humankind is the story of unknown people meeting, trading goods and ideas (sometimes by force), and then adapting their lives to the new world that their encounters created. That was the story Columbus and the Tainos lived, the story Cortes and Montezuma lived, and it’s the story we’re still living today.

Sincerely,

Mr. Heimbuck