Wednesday, September 14, 2011

Rule-Writing: Equations for Tables

What's happening in the table to the left? Can you see the pattern?

The 7th graders began the year by analyzing patterns in tables. They first described the patterns in their own words. After a few days, they began to describe them mathematically. By the end of the first week of school, they could describe the speed in an experiment, just from looking at an equation. They could graph a line, identify the slope and y-intercept, and substitute numbers in for variables. Several of them gasped when they realized they could answer questions using the same algebra steps they practiced last year. It's an impressive group of students!

That's why I like starting the year with linear equations. Not only do we get to talk about big concepts in graphing - not only do we review equation-solving and coordinate-plotting - but we also get to do experiments with marshmallows, nose-tapping, and ball-tossing.

We start by looking for patterns in a table. That leads us into equations, graphing, and lines of best fit. Watch the videos below and see how we considered problems in class.

Sunday, September 4, 2011

Ugly Equations: Dealing with Fractions

Fractions are important. Computing with fractions is important. Nobody can be truly educated in math without remembering steps for common denominators or cross-canceling.

That said, fractions can be a real hassle, especially in an equation. Even worse, some equations can have fractions with different denominators. If I give a class an equation like that, I can see immediately what students are thinking: that is an UGLY EQUATION.

Fortunately, there is a method for dealing with this type of ugly equation - a method that transforms fractions into whole numbers. This method even works when the denominator is a variable or an algebra expression. I call this method multiplying through.

Here are two episodes of "Math with Ms. T and Betsy" that show the steps.

Notes about this method are posted under the page, "Notes on Equations with One Variable".

Getting Ready for School

I've been outside with my dog for most of this summer, but yesterday, she snuffed out the first red leaves of autumn. It's no surprise: September is a little over a week away.

But after a wonderful summer, I'm thinking often of the moment in the "You've Got Mail" movie, when Tom Hanks writes about bouquets of freshly sharpened pencils. I have always loved new school supplies: clean, flat sheets of paper and fresh pens with their matching caps. They all say, I have my tools prepared. I will fill these pages with information and thoughts and responses to new challenges. I am ready.
There are some things to do, however, to be ready. And for my math class, this is what I would recommend:

• Plenty of pencils. A bouquet of pencils. Extra lead or a mini pencil sharpener.

• Erasers. The cap erasers are good for pencils, but a large eraser is better for a larger mistake.

• Binder with lined paper and graph paper. I suggest dividing it into four sections: homework, notes, classwork, and assessments.

• Folders to hold old worksheets and printed documents.

• Scientific calculator(s). Our favorite at school is the TI-30x.

• Assignment notebook.

The following supplies aren’t essential, but would be convenient:

• Markers or colored pencils.

• Dry erase markers/eraser.

• Ruler.

• Compass.

On the first day of school, students lay out their new tools very proudly. Their aspirations are obvious. This is going to be a better year. They are ready.

And so am I.