Some fun(ish) worksheets

I'm going to try to get my box.net materials updated over this coming week.  In the meantime, here are a couple of decent worksheets that you may find helpful.

First, I made one to practice graphing standard form - I just ripped off Mr. K's idea.  Thanks!  And some of my students actually liked the joke (I googled Laffy Taffy jokes).

For tomorrow, students will be graphing systems of inequalities, so I decided to create a little Ohio Jones adventure (Indiana's lesser known brother).  Here is the full lesson and just the activity in pdf form. 

(UPDATE: Here is the follow-up lesson in word form - Ohio Jones and the Pyramid of Power.  Here is the follow-up lesson in pdf form if you're having trouble seeing the word doc).

Here is what the maze should look like after being solved:

Introducing Linear Inequalities

To show that a line is a representation of an infinite number of points, I like to give my algebra 1 classes an equation, like y = 2x + 3, and then give each student a couple of different ordered pairs - some that are solutions and some that aren't.  I have them each work out their points, and then go to the board to plot an open or closed circle, depending.  Once all the students sit back down, we look for patterns and see that all the closed circles fell on a straight line.  Discuss, and voila.

This extends nicely to linear inequalities (and systems of equations and inequalities).  On Tuesday, my algebra 2 students were reviewing linear inequalities so I did this activity with them.  I really like it, because it is engaging, and it helps build a mental picture that they can rely on later on when they are struggling through graphing problems on their own.  My students often get stuck on the "pick a test point" part of the process; but now, I ask them if they would have plotted a closed or open circle based on their result, and to think about what the picture on the board looked like.  This usually helps them see which side of the boundary line to shade, and to be able to explain why.

Here is what the board looks like after students plotted their points:

Then, we looked for patterns.  Usually, a student will come to the board and draw some sort of line after getting frustrated with trying to explain it in words.  Then I reveal the shading:

And there are usually some audible "ahhs" and such.  Another great benefit of this is that the string of open circles on the boundary helps students see what the dotted line is all about, and why changing the inequality to include an equals sign would create a solid line - a string of closed circles.

Here is my lesson that goes with this.  And the keynote.

Algebra 1: Introduction to Inequalities

I'm not planning our Algebra 1 classes this year, so I have not been producing much for it. But I did put together a scaffolded introduction to inequalities. The objectives are for students to:

• Compare numbers using a number line (i.e. "<" means "to the left of")
• Understand the difference between open and closed circles
• Graph the solutions of a statement like "x < 3"
  
• Understand graphically why adding/subtracting by any number or multiplying/dividing by a positive number does not change the relative position of two numbers, while multiplying/dividing by a negative number does. In other words, students should understand when and why to "flip the inequality sign" when solving inequalities.
  
• Solve and graph linear inequalities

Here is the file.

Algebra 2: Interval Notation

I went back and forth on whether or not to spend time on this, and in the end I decided to go with it. It will be helpful to students who go on to pre-calc and beyond, and it gives us a good opportunity to review solving linear inequalities and to keep working on finding domain and range of graphs. Plus, it's good to have a lesson every once and a while that is pretty easy for students to master right away - someone said today, "This is the easiest thing we've learned in like 50 years!".

Lesson 7 (Interval Notation)
Lesson 7 Keynote
Keynote Quicktime

Next Lesson: Graphing Linear Inequalities

We are finally moving on from the functions unit into a brief unit on systems of equations and inequalities. Last year, I included linear programming in this unit, because it is a great application not just of systems of inequalities, but being able to think critically about a problem, convert verbal information into a mathematical model, and so forth. Unfortunately, I think this topic will be a casualty of going so deep with functions this year. Every time I don't teach some topic, I feel like I am denying them access to ideas that other students will know. Maybe I can squeeze in a one-lesson overview just so they see the idea.

After the unit test, I gave students a homework to review graphing linear functions (horizontal and vertical, slope-intercept, standard form, finding equations of a line, etc.). I think they were happy to get something that was so "easy" for a change.

In this lesson (I actually taught it yesterday), students first were given a Do Now to explore the idea of shading a solution region. I asked them to graph x - 2y = 8. Then, I gave them a bunch of points and the inequality x - 2y < 8, and asked them to algebraically determine if each point was a solution to the inequality. If it was, they had to plot a Y at the coordinates. If not, they had to plot an N. Seeing all the Ys on one side of the line (and on the line itself) and the Ns on the other helped get across the idea of the solution region. Last year, they were taught to shade the solution region in, but I wanted to make sure that they understood what the shading really means. We talked about how the picture would look different if the inequality symbol flipped, or was exclusively greater or less than.

After we established this concept, I just did some direct instruction and showed them how to graph linear inequalities in various forms: x < c; y < c; |x| < c; |y| < c; y < mx + b; ax + by < c. After each example I did, they did a similar example on their own (switching the type of inequality symbol).

The class ended with some individual/pair practice of graphing. The practice also included determining visually if a point is a solution (given the graph), and then confirming this algebraically.

The homework includes more of the same type of practice. It also has a couple of non-linear inequality challenge problems (like y < (x - 3)^2 + 4) to help them work on their synthesis skills.

I'll post the whole lesson on ILoveMath.org