## Sunday, April 04, 2010

### 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:

## Saturday, March 20, 2010

### Difficult News

I haven't posted for a while now, and I wanted to let people know why.  My younger sister passed away suddenly about five weeks ago.  She would have been 30 next Friday.  I'm back at work now, but it is difficult just to get through the days.  I love my job, but high stress work is not the best thing when going through something like this, and it's been hard just to get the minimum done.  This has also caused me to rethink my priorities and how I lead my life, where I spend my time and energy.  I do plan on continuing this blog, and I will start posting ideas and lesson materials again, but I don't know with what regularity right now.  Thank you all for your support and understanding.

## Wednesday, February 10, 2010

### Algebra 1: Systems of Equations

We are finally getting to move beyond basic graphing and finding equations of lines.  It was a long slog, but the skills tests show that the majority of my students are starting to get the hang of it.  I always look forward to the systems of equations unit, because it is a chance for students to synthesize what they have been learning all year - and, in a situated context, no less.  My plan this year is to deepen the emphasis on representational fluency and summarizing, to help build all of those neural bridges we want the students to have.  We started the unit Monday, and I was really blown away by my classes today - all of a sudden, I have students doing algebra!  I had them solving systems in pairs, using mini-whiteboards, where one does the graphical solution and the other does the algebraic solution, and then they compare their answers.  They did a great job, and it wasn't until this activity that many students realized the answers should be the same.  I got a couple of those hilarious, indignant "you should have told us!" comments.  Next week is winter break, which doesn't come a moment too soon; however, I'm worried about how much will be lost over the seven days that nobody is asking them about starting points or rates of change.  No matter, it's worth it to have a rest.  Here are a couple of  examples of what we're doing, and the links to the lesson materials thus far.

Lesson 1 (Intro to Systems of Equations)  doc / GeoGebra files / Keynote / Powerpoint
Lesson 2 (Solving y = mx + b Systems)  doc / Keynote / Powerpoint
Lesson 3 (Practice Solving Systems)  doc

## Sunday, February 07, 2010

### Language and Retention of Math Concepts

I've been thinking lately that one of the reasons my students have such difficulty with long-term retention of mathematical concepts is due to the small number of times I ask them to thoroughly summarize what they have learned.  They do lots of problems, but the language of the problems often does not enter into their brains.  As we learned in Orwell's 1984, without language, there is no thought.  So I am going to start providing more explicit opportunities for the students to summarize and discuss what we are doing in class.

Comic Strips  (Unit 5, Lesson 9:  doc / keynote / powerpoint)
Quite a few students are still struggling with graphing lines.  They know the general process, but don't pay attention to the details - is the slope positive or negative; if a term is missing, is it the slope or the y-intercept, and how does that change the graph?  So, I had all students draw comic strips to summarize the process in these different cases.  I like how this went, but I definitely did not provide them with enough time to do all I asked.  Here are a few good examples.  The first didn't scan that well, but he did an awesome job.

Think-Pair-Share  (Unit 5, Lesson 11: doc / keynote / powerpoint)
This is a tool that our humanities classes tend to use a lot.  I got some advice from them, and will be trying these periodically during the next couple of units.  We did one so far, and it went reasonably well for a first try.  Students need a lot of practice both writing down their ideas and sharing them out.  Here is the handout I gave (it was used immediately after doing a Do Now problem of the type described).

## Tuesday, February 02, 2010

### Both Flattering and Disturbing

Students in our Numeracy support class have been working on plotting points to help them with graphing in Algebra 1.  The students just finished a connect-the-dot cartoon graph assignment.  One of my students apparently decided to dedicate her drawing to me.  Like my Speedos?

## Sunday, January 10, 2010

### Algebra 1: Representations of Linear Equations

Increasing my students' representational fluency has been something I've been working on for a while.  Our second semester started last Monday, and to start my Algebra 1 students off easy, I had them do a four-fold poster of a linear relationship to review what we did last semester: situation, equation, table, and graph.  They did the work fine overall, but quite a few students had more troubling questions than I had expected (i.e. "how do you make a table?").   I guess it just shows that we have to keep going through these different representations and their connections again and again.

We have started the new unit - working with linear equations - in which students have to write the equation of a line given its slope and a point, or two points, or a point and a parallel line.  In the past, I have done this only algebraically (except for the initial explanation of concepts); this time around, the students will have to practice the problems both algebraically and graphically.  And, more importantly, the skills tests will require them to show mastery with both methods.  Let's build those connections!

Here are the first few lessons in the unit.

Lesson 1 (Representations of Linear Functions)
Lesson 2 (Graphing Practice)
Lesson 3 (Write the Equation of a Line)
Lesson 3: Keynote / Powerpoint

And some snippets from the worksheets to illustrate what I am talking about:

## Thursday, January 07, 2010

### 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: Graphing Lines Practice

I just used this worksheet from Mr. K for the first time the other day.  I thought it had a pretty cool setup, but I didn't realize just how effective it would be until I used it in my first class.  The "solve the joke" aspect of it helps draw them in, but the hidden beauty is in its self-checking properties.  Since each line must pass through exactly one number and one letter, a line that doesn't do this must be graphed incorrectly.  Students started realizing this and would go back and find mistakes without having to check with an answer key.  The only bad part (sorry to say) is that they had absolutely no idea what the answer was supposed to mean (see earlier post).

I made up a "balloon pop" homework to go with this that was inspired by Green Globs.  I wish I had the tech access for my students play that game.

## Monday, January 04, 2010

### Algebra 1: Skills List - Spring Semester

I spent a good deal of time right before break trying to figure out exactly how far I can push my students for the second semester of Algebra 1.   These skill items will be broken down into chunks for the skills tests, and MC-ized for the benchmarks and final exam.  I regret how many concepts I had to leave out due to time pressures; and still, the list seems daunting and endless.

If you're interested, this is what my students will be doing over the coming months.

doc / pdf