letters to my class

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
Aug 31, 2012

August 30th, 2012

Dear Dolphins,

Hey, that’s the name you picked for our class. In fact, you picked The Flaming Cheese Dolphins. I don’t really know what that means, but I can get behind a class that likes cheese, and I especially can get behind a class that likes dolphins, which are incredible animals and rumored to be one of the smartest species out there. Scientists also think they’re one of the most playful, so they are a perfect mascot for our class.

Today we’ll continue classbuilding activities including making a 5th grade song and deciding on some of the rules and norms that we have for our classroom community. It’s important that our class cares for one another, watches out for each other, and challenges one another to be the best we can be. You will remember the people you go to school with for the rest of your life. We want those memories to be filled with laughter, leaning, and joy.

Let’s have a great day,

Mr. Heimbuck
August 30, 2012

August 29th, 2012

Dear Multipliers,

Knowing your multiplication and division facts is the key to 5th grade. It makes everything easier. Adding and subtracting fractions is a piece of cake. Finding area and perimeter is a walk in the park. Doing long division is as easy as winter shaking leaves from the trees.

Sure, you could try to memorize your multiplication facts with flash cards. But I think it’s better to internalize them by playing games, drawing pictures, and doing activities that really help you understand what multiplication is. Making arrays and describing them with number models is one good exercise.

Today, we’ll talk about factors, which are the numbers we multiply to make a product. When we find a product’s factors, it’s like looking at that number’s fingerprint–factors are what make each number unique.

Sincerely,

Mr. Heimbuck
August 29, 2012

August 28th, 2012

Dear Array Makers,

I like to think of math as the process of making models. Models help us better understand things because models break those things into their parts. We don’t just make models of trains, cars, and airplanes, however; we can also make models of numbers.

One way we can make a model of a multiplication problem is with an array. You have been working with arrays since Second Grade, and you see them all the time in everyday life. For homework this week, you will collect and bring to class arrays that you notice in the real world. One of the main jobs of a mathematician is to see math coursing through everyday life. Rather than just seeing a muffin tin as a muffin tin, a mathematician sees it as a 3×4 rectangular array.

If you have a firm grasp of arrays, you will be prepared for much of what we’ll learn in 5th grade–multiplication, fractions, percents, and area, just to name a few.

Let’s have a great day,

Mr. H
August 28, 2012

August 27th, 2012

Dear Musicians,

Today, we’ll go to a concert and you’ll get the opportunity to hear and choose an instrument. I encourage each of you to take up an instrument or join the choir. Music is a gift that will last your entire life. No matter how many hours you spend practicing, there’s always more you can learn. I’ve played the guitar for 15 years, and I still learn something new everyday.

Music is also a great place to practice the skills we’re learning in class. Because math and music both deal with patterns, they are very similar. When practicing the trumpet (or whatever instrument you choose) you’ll also be practicing fractions and arithmetic and many other mathematical concepts.

Most of all, taking up an instrument or joining the choir will teach you that success and greatness are only achieved through hard work. The greatest musicians in the world got that way by spending tens of thousands of hours practicing. You can still enjoy playing an instrument without being the greatest in the world, but the hard work and dedication offers many rewards.

Play on!

Mr. Heimbuck