letters to my class

3 October 2011

October 3rd, 2011

Dear Rectangle Makers,

This week we’ll learn a few different algorithms for multiplication. While these step-by-step processes might look a lot different, they’re really all just the same. When we multiply, we’re making rectangles. One factor is the base. The other factor is the height. The product is the area. The different algorithms are just different methods for counting up the pieces of that rectangle.

The algorithms we’ll learn are the methods that people throughout history have devised to solve problems. We learn all of the algorithms because there’s never only one right way to solve a problem. Also, it’s a lot of fun to play with numbers.

Sincerely,

Mr. H
30 September 2011

September 30th, 2011

Dear Estimators,

Math is like horseshoes–most of the time, close enough is good enough. Usually, an estimate will give us the information we need. Sometimes, however, we have to be precise. Good mathematicians have to know how to do both. More importantly, good mathematicians have to know when estimates are appropriate and when it’s time to calculate precisely. As always, math thinking is about creating a method for solving a problem, not just doing the arithmetic.

Today, we’ll make magnitude estimates for products. The orders of magnitude are the powers of ten–1, 10, 100, 1000, 10,000, etc. By estimating the magnitude of the product, we’ll not only be able to check our calculations, but we’ll learn about the wonders of our number system. That’s really what it’s all about.

Sincerely,

Mr. H
29 September 2011

September 29th, 2011

Dear Geometers,

Archimedes was one of the greatest mathematicians of all time, but when he died as an old man, he was still drawing circles in the sand. Circles are an endless mystery: they are an enclosed space with infinite sides. Unlike many other shapes, circles appear in nature–ripples in a pond, craters in the moon, the eye of a hurricane, the face of a sunflower. Ancient people studied these circles and from them created the field of geometry.

Today, we’ll create circles using one of the geometer’s best friends–the compass. With this simple tool, we’ll be able to create beautiful, intricate designs. As we’re doing it, look for patterns, look for symmetry, and be prepared to be amazed.

Sincerely,

Mr. H
27 September 2011

September 27th, 2011

Dear Statisticians,

Numbers become data when we collect them and analyze them. For our data to be good, we have to go about collecting it in accurate, reliable, and precise ways. For our data to be meaningful, we have to use it to draw conclusions. The world is full of data. Some of it is good, some of it is bad. Some of it is reliable, some of it is not. Your job is to find the good data, analyze it for meaning, and use it to say something true about the world.

One tool for analyzing data is landmarks: median, maximum, minimum, range, mode, and mean. These landmarks help us make sense of data. Today we’ll collect data, organize data, and analyze data using landmarks. Then, we’ll use it to try to say something true about the world.

Sincerely,

Mr. H
26 September 2011

September 26th, 2011

Dear Problem Solvers,

When we do math, we’re learning how to think. More importantly, we’re learning how to solve problems. In the “real world,” no one actually does arithmetic, but those who know how to are better at solving problems because they’ve had lots of practice and they have a powerful method for doing so.

You’re going to have to solve problems every day of your life, numerous times, almost constantly. What should I believe? What is true? What is the good life? What kind of toothpaste should I buy? Those are the types of philosophical problems that math prepares us to tackle in analytic and truthful ways.

So when you’re doing your math today, spend less time worrying about your answers and more time thinking about your thinking. The most important thing you learn from math can’t be written on the other side of an equal sign. It’s in your head.

Sincerely,

Mr. Heimbuck
26 September 2011

September 25th, 2011

Dear Satellite Dodgers,

Did you see the news about the falling satellite? It weighed six tons and was the size of a school bus! When it re-entered the atmosphere, it broke into smaller pieces, but scientists said it had a 1 in 3200 chance of landing on a person. What do you think the odds were that it would have landed on you?

This week we’ll talk about probability. When you learn to think probabalistically, the world lets you in on its not-too-well-hidden secrets, you make better choices, and you don’t waste precious time worrying about 6-ton satellites falling on your head.

Look at the globe or the map. Where do you think the satellite probably landed?

Let’s have a great day.

Sincerely,

Mr. H.

3 October 2011

30 September 2011

29 September 2011

27 September 2011

26 September 2011

26 September 2011