August 31 - Functions

We spent most of today going over the homework from Thursday night - drawing graphs to represent different real world functions.

I mentioned to my sixth period class something that I should have told my 1st and 3rd period classes - while you were presented a lot of information in class today, I'm not going to hold you fully responsible for it. If you forget for now that I can model how a rumor spreads with a "logistics model," that's fine. My main goal for today was to impress upon you the variety of functions that are necessary to model real world behavior.

The main concepts for today were the definition of a function and how function notation works.

August 28 - Intro to Functions

I returned the quizzes from yesterday; overall they were very good.

We played my "functions" game in class today. I like to emphasize that functions don't have to be restricted to the generic f(x) = x^2 or whatever that you are used to. The idea of an input/output relation is very broad and math is applicable to the real world because clever mathematicians find ways to apply the generic f(x) in clever ways.

There is no assignment for the weekend. We will talk about the graphs from the functions worksheet (Thursday night's hwk) in class on Monday.

August 27 - Quiz over quadratics/Functions

Most of class today was spent taking our first quiz of the year.

The homework for tomorrow is for students to draw graphs for each of 15 different functions that I have described. Many of the graphs will be fairly general, but in class, we will eventually talk about what kind of function (linear, polynomial, exponential, trigonometric, etc.) would describe the scenario best. I really like this assignment as a jumping off point for talking about functions in general.

There are no notes for me to post from today.

August 26 - Quadratics

I announced a quiz for tomorrow (Thursday) today in class. It should be a fairly short quiz over quadratic functions and calculator use will be allowed. I explained that typically, quizzes are untimed - students can take as long as they wish to complete the quiz (within the class period). I will remind you that after you turn your quiz in, you need to try and stay quiet so that others can finish their quizzes without too much distraction.

I worked an example of a somewhat tricky quadratic word problem. Note that I posted worked out solutions to the worksheet on my website.

August 25 - Quadratic Functions

We started by going over several of the homework problems from last night.

The topic for today is quadratic functions. Like yesterday with linear functions, I'm not sure that there is anything here that is new or particularly difficult. I walked through the use of the calculator for finding the equation of a parabola given three points (using the QuadReg feature). Other than that, students seemed very comfortable with today's concepts.

The one tricky thing I did was to write a problem with the x's and y's switched. I think it's good practice to be able to work problems with vertically or horizontally oriented parabolas.

Here are my notes for today.

August 24 - Linear Functions

We started by going over a couple problems from Friday's assignment over inequalities.

Today's main concept is linear functions. There is really nothing complicated about lines or linear functions. Having said that, the idea of slope (especially that slope represents rate of change) is in fact a hugely important concept, and it will eventually be one of the building blocks of calculus.

I announced in class that there will be a quiz on Thursday (covering quadratics, which we will begin tomorrow).

Here are my notes from today.

August 21 - Solving Inequalities

We reviewed a couple problems from the homework last night. Problem #151 is tricky because there are extraneous solutions - it is necessary to check your answers to determine which are the "true" solutions. I pointed out that #134 should not have been assigned b/c we did not cover solving equations with radicals in them in class on Thursday.

In class, we covered solving inequalities. The types of inequalities you are responsible for are simple linear or compound linear, absolute value, and rational. When an inequality is rational (or polynomial), the strategy for solving will be to set one side of the inequality equal to zero and then to mark the zeros of all factors (in the numerator and the denominator) on a number line. Then test intervals to determine where the expression is positive and negative.

August 20 - Solving Equations

Today in class, we reviewed solving several types of equations.

These types included linear, quadratic, quadratic-ish, absolute value and radical equations. We also talked about factoring by grouping and working with rational expressions.

Note that in all cases, the problem eventually broke down to solving a linear equation (or at least, solving several linear equations)