letters to my class

September 17, 2012

September 16th, 2012

Dear Estimators,

For most of the math we do in everyday life, close enough is good enough. When we’re figuring distance or how long something will take or how much groceries will cost at the store, we estimate. That’s because we don’t have the time or tools to figure more precisely and also because sometimes there are so many variables that a perfect reckoning is impossible. There may be times in your life when accuracy is more important–if you’re building a bridge for instance–but usually close enough is good enough.

But estimating is far different from guessing. And estimating is hard work. In many cases, estimating takes more brain work than even finding the most accurate possible because you have to make so many decisions and account for so many variables. You have to think about what unit is best, what method you will use, how close is close enough, and if your final estimate seems reasonable. You also have to think about what “reasonable” would be! Making reasonable estimates is one of the most important skills you’ll learn this year.

Happy estimating,

Mr. Heimbuck
September 14, 2012

September 13th, 2012

Dear Migrants,

Throughout human history, people have moved around. They have migrated to find a better life for themselves, their families, and their people. Usually a better life is the result of better natural resources. As we know from yesterday, resources determine how and where people live. We will look at population density maps today that illustrate that truth.

However, natural resources never stay the same. Humans used to get almost all their energy from wood burning and animal power but now have more efficient methods. We are always finding ingenious new ways to use something that’s never been used before. When we do this, we can make life possible in previously uninhabitable places. Just imagine what the future holds: perhaps humans living at the bottom of the ocean or on the moon or maybe even on Mars.

Let’s have a great day,

Mr. Heimbuck
September 13, 2012

September 12th, 2012

Dear Performers,

We’ve spent the last three weeks learning about factors, prime and composite numbers, and exponential notation. We’ve spent tons of time woodshedding our multiplication and division facts. We’ve become expert strategists at the game Factor Captor. Now, I think we’re ready to do our best on our first unit math assessment. Remember, there is a bonus for those who score a four on this test. This is not a “bribe.” It’s a reminder that in this life, excellence is rewarded.

When you take this assessment, I want you to be focused, careful, and confident. Much of how well we do on tests depends on how we approach them. If we think of the test as a chance to show all that we know, then we’ll lick that thing. If we’re afraid the test will reveal all that we do not know, we will fail.

So be confident. You’ve done the hard work of preparing for excellence; now, you must grab that excellence by the scruff of the neck and make it your own.

Good luck,

Mr. Heimbuck
September 12, 2012

September 11th, 2012

Dear Data Collectors,

Yesterday, an atmospheric scientist spoke to the other class about how scientists make reliable observations about weather, specifically precipitation. He showed us a few rain gauges and a hail pad and showed us how to make precise and accurate observations. He came because he needs our help. Because precipitation can vary so much from place to place, scientists need a whole bunch of observations to get a good picture of the weather. Our job is to make daily precipitation observations and record them.

Good observations are the foundation of science. As Harlow Shapley once said, “Theories crumble, but good observations never fade.” People once thought the sun moved around the earth. We now know better, but the observations the ancients made by looking up at the stars are still invaluable to us today. Our most powerful method of understanding the world is creating methods of gathering data, accurately collecting that data, and analyzing it fairly. That’s the method that creates our greatest theories about the world.

Sincerely,

Mr. Heimbuck
September 11, 2012

September 9th, 2012

Dear Factorers,

Last week I told you that factors are like a number’s fingerprint: they are what make numbers unique. Today, we’re going to see that prime factors are a number’s DNA: they are the building blocks and the blueprint for each number. When we break a number down into its prime factors, we get to the essential core of that number.

Like many things in math, this method of breaking something into its essential parts is useful in all walks of life. I might even argue that it’s one of the main ways us humans have of knowing about the world. When you were first learning to read and you got to a word you didn’t know, your teacher told you to break it into its sounds. When you were first learning about multi-digit numbers, you broke them up by their periods and places. When you’re learning how to do brain surgery in your final year of medical school, you’ll break the brain up into its parts to better understand it.

I don’t want to oversell it, but the ways of thinking you learn in fifth grade will last you a lifetime.

Let’s have of great day,

Mr. Heimbuck
September 10, 2012

September 9th, 2012

Dear Americans,

I love America–its geography, people, history, and cultures are a rich and wonderful heritage. It is a diverse land filled by diverse people who are united in continuing the beautiful experiment that our founders started almost 300 years ago. But American history goes much farther back than that. It includes the 300 year colonial period, the age of exploration, the great Pre-Columbian civilizations, and those who crossed the Bering strait over 12,000 years ago. The geography of the United States of America is engraved in each of those acts.

The United States includes winding rivers, snow-capped mountains, oceans, diamond deserts, wheat fields waving, and golden valleys. Today we’ll also sing the praises of that geography and talk about how it makes us who we are.

Sincerely,

Mr. Heimbuck
September 7, 2012

September 6th, 2012

Dear Searchers and Seekers,

Today’s probably my favorite lesson of the year. We’re going to find all the prime numbers through 100 by using the sieve of Eratosthenes. Eratosthenes was a Greek scientist and mathematician from over 2000 years ago, but he knew things that people would have to relearn. He not only knew the earth was round, but he was able to measure its circumference within 2%. He also drew a map of the world, was a poet, a musician, and an athlete. He’s one of my personal heroes.

Eratosthenes’s sieve shows us the power of faithfully following a simple and clever method. Today, we have supercomputers that find insanely large prime numbers, but the work of creating a method and following it will never be replaced by computers.

Remember, math is the science of patterns. As we’re messing around with multiples, be on the lookout for the beautiful and intricate patterns that dance all through our amazing number system.

To the hunt (for primes),

Mr. Heimbuck
September 6, 2012

September 5th, 2012

Dear Cartographers,

Anytime we make a map, we do the impossible: we make a sphere flat. Think about it–the earth is round, yet maps are always flat. How do humans do it? We do it, quite simply, by making distortions. While trying to be as accurate as possible, cartographers (the fancy word for map makers) have to make choices about how they’ll change the land.

Anytime we make a map, we make choices about what’s important, what’s relevant, and what belongs where. When you make your personal maps, you’re going to make similar choices. As long as you can offer a reasonable explanation for your decisions, they are the right ones, but you have to really think about what distortions are important to your world.

Sincerely,

Mr. Heimbuck
September 5, 2012

September 4th, 2012

Dear Number Classifiers,

Humans make sense of the world by classifying it. We put like things in one heap and different things in another. We do the same thing with numbers. There are endless ways to classify numbers, but mathematicians have agreed on a few ways that are most useful. You’ve already learned how to classify numbers as odd and even. Yesterday we talked about classifying numbers by their divisibility. Today we’re going to talk about classifying numbers as prime or composite (or neither!).

Prime numbers are an interesting topic, and they’re important to our everyday lives. We won’t quite get into cryptography today, but you have prime numbers to thank for keeping your secrets secure in the digital world. Mostly, we’ll think and talk about the strange but illuminating nature of prime numbers. Their charm might just convince you that there’s some kind of logic lurking behind the universe’s deepest mysteries.

Happy Classifying,

Mr. Heimbuck
September 4, 2012

September 3rd, 2012

Dear Geographers,

This year we’ll spend a lot of time looking at maps. We’ll study tons of US maps that break our country up into physical and cultural regions, but most importantly we’ll think about what maps say both about the land they describe and also the people who make them.

People really do wild and creative things with maps (I’ll show you some examples today), which is why maps will never be replaced by satellites or GPS. Maps tell stories about land, history, people, cultures, attitudes, fears, and so much more. When you study maps, you not only learn about boundaries, capitals, proximities, and regions, you also learn about how humans imagine the world.

Let’s have a great day,

Mr. Heimbuck