letters to my class

January 23, 2013

January 23rd, 2013

Dear Modelers,

To really understand something, it helps to make a model of it. When you make a model of something, you find out what the key parts are and you investigate the relationships between them. Today and throughout the year, we’ll think about ways to model fractions. By studying and creating models of fractions, we’ll get a better sense of fractions and be much better math thinkers.

A lot of what we’re talking about with number sense is a gut feeling you get about numbers. I want you all to be able to feel some of the key attributes about the size and characteristics of numbers. Just by looking at two fractions, we want to be able to get a rough idea about which one is bigger. Then, we investigate through various means and prove our answer. But our math gut instincts have to be strong.

Sincerely,

Mr. Heimbuck
January 22, 2013

January 22nd, 2013

Dear Climatologists,

Today we’re going to talk about climate–the average weather conditions in a place over a long period of time. When we talk about climate, we have to study a lot of different fields of knowledge: meteorology (study of the atmosphere), oceanography (study of the oceans), physical geography (the study of places), and human geography (the study of people in places). Climate affects how people live in particular places all over the world. It even affected decisions you made this morning–what did you eat for breakfast, how did you get to school, what did you wear, what jobs do your parents do, etc.

We could study how climate affects our own lives forever and keep discovering more stuff. The fun thing about knowledge is that it’s never-ending. The more we get, the more there is.

Sincerely,

Mr. Heimbuck
January 16, 2013

January 16th, 2013

Dear Solvers,

Knowing answers is overrated. Most of the stuff worth knowing is stuff we don’t know yet. The real value is in how we figure those things out. We’re going to keep practicing problem solving in math and science, and I am going to give you problems that I don’t expect you to know the answers to. But I do expect you to figure out a reasonable answer. Looking closely at something, paying attention to patterns, and thinking reasonably will take us far in life. Those skills are more important than memorizing facts and figures.

Let’s have a great day,

Mr. Heimbuck
January 15, 2013

January 15th, 2013

Dear Problem Solvers,

Math really is only about solving problems. We often use numbers to solve those problems because they let us do it more efficiently, but we could solve almost any problem by drawing a picture. Many times, such a picture takes a very, very long time to create, so numbers are more efficient, but the job of math is solving problems.

You’ve been solving problems your whole life. In many cases, you probably used math to solve these problems and didn’t even know it. Our goal in math class is to give you the tools to solve problems more efficiently and more creatively. And after you get practice solving problems, you start making up problems of our own to which math is almost perfectly suited to solve.

We’ll spend a lot of time the rest of this year thinking of problems, solving problems, and talking about our mathematical methods of doing so.

Sincerely,

Mr. Heimbuck
January 14, 2013

January 14th, 2013

Dear Risk Takers,

I am pretty bummed about the Broncos losing on Saturday, but life goes on. It’s probably foolish to take life lessons from sporting events, but if the Broncos loss teaches us anything, I think it shows us that we should always go for it.

The Broncos had many chances to win the game but they took the safe route instead. In school, sometimes it’s easier to just get along, just do enough to get by, but if we want to be excellent, we have to try for more. When we write an essay, don’t do it just to get a good grade, do it to change the way you or someone else looks at the world. When you solve a math problem, don’t just do it to get the right answer, do it in a way that reveals something profoundly interesting about the universe.

The world has enough people who are happy to fill in boxes and take the safe route. We need dreamers and risk takers and change makers.

Sincerely,

Mr. Heimbuck
January 8, 2013

January 7th, 2013

Dear Data Collectors,

It’s great to be back to school. We all had a nice, relaxing break, and now it’s time to get back to the pleasures of learning. My goals for this semester are to help you all become better readers, writers, problem solvers, and citizens. It will take a lot of hard work, but I know each of you can accomplish great things. You’ll be making your own goals for this semester, so be thinking.

Today, we’ll collect, organize, and analyze data. In math and science, we deal with data a lot. But we also use data all the time in our real lives. The important thing about data is that is has to be reliable. That means we have to be able to trust it. Anytime we crunch data, we’ll ask ourselves if our data is reliable, how we know it’s reliable, and how we can make it more reliable.

Let’s have a great first day back,

Mr. Heimbuck
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