## Cool Midpoint and Distance Idea

September 14, 2012

via Lisa:

The Radical Rational had an idea to put a grid on top of a map of her school. The questions she proposed asking her students:

•Calculate the distance between Room 137 & Room 114.
•Find the coordinates between Room 137 & Room 114. What room are you closet to at this point?
•Connect Ag, Kitchen, Cafeteria & Workshop. What type of quadrilateral have your formed? How do you know? Prove it. We have not covered types quads – but they can use their BYOD to find this information if needed, right?
•Connect Library, Room 128, Room 116 and Room 114. Is it a rectangle? Or a square? (LOL) How do you know. This always comes up in discussion – I must say I love the “disagreements”.
•Connect Room 145, Room 142 and Band. What type of Triangle have you created? How do you know? Prove it.
•Connect the Gym, Library and Tan Hall – Find the perimeter & area of this triangle.
•What about having them “map” out their schedule and calculate “as the crow flies” distances between their destinations.

## Reflections – Geometry Obj. 3 and 4, Algebra 3 Obj. 3

September 6, 2012

Okay, I’m now 2 for 4 (I think) for writing reflections on B-day, and 0 for 4 writing them during 8th period. **sigh**

Geometry Obj. 3
I adore my Point, Lines, and Planes foldable! It made one of my most-dreaded sections into something not quite so painful. When I figured out I was only going to have about half a period to do Points, Lines, and Planes, I knew I had to do something to the way I had always done it (traditional notes), so I figured out how to rearrange things so that they would work as a foldable. After talking it over with S (yay! she’s back at my school!), I got my layout finalized. Then, it was a matter of fussing with the details. I think the thing that I especially like about this foldable are the marks I put on the side to show where the fold should go. I wish I’d thought of that before!

I started off the class with a warm-up going over conditional and biconditional statements (writing the converse, inverse, and contrapositive), and then I went over the homework, which was pretty much the same thing. Then we had our first quiz, and then we did the foldable.

Geometry Obj. 4
Okay, I had dreams of doing Constructing Segments and Constructing Angles in one day. Not so much.

I had an idea the other day, so I thought I’d try it out: when I handed back the quiz, I also handed out copies of my key. Their warm-up was to make quiz corrections, and to see if they could figure out where they went wrong. This worked really well! For one thing, it encouraged students to actually look at the quiz, instead of just looking at the grade and then throwing it away. Also, I informed/reminded them that since I let them use their notes on quizzes, if they corrected this quiz, it then became “notes” that they could use on future quizzes. Incentive!

Since I had been giving them holey notes, I decided it was time for them to take some actual notes. So for this lesson, they did a mathy version of Cornell notes. I also introduced construction (and gave my “Sharp Pointy Object Speech” as I handed out compasses) and we practiced constructing congruent segments and midpoints. One of my favorite parts occurred because I realized I had a little bit of time left (but not enough to start Constructing Angles), so we did a Kagan activity, “Draw What I Say”. In a group of students, one student drew a card that had a description of a figure (ex. “Point $E$ is the midpoint of $\overline{MB}$“). The student would read the card to the other member(s) of the group who would then try to draw it based on his description. The card has a diagram of what the picture should look like, so the reading student knows what to look for. Very cool activity.

Algebra 3 Obj. 1-2 Quiz
As I think will become my habit, I made copies of my solutions on bright pink paper for them to check their homework, and I then went over any additional questions they had. The main questions, somewhat distressingly, centered around converting from standard form to slope-intercept form and writing the equation of a line. They took the quiz, and I handed out the first problem set.

Algebra 3 Obj. 3
As I did with Geometry (and for the same reasons), when I handed back their quizzes, I also handed back a copy of my key. They also caught on to the incentive nature of making corrections.

Next we went over quadratic equations. This actually went fairly well in both classes. I “reviewed” how to reduce radicals, how to factor a quadratic expression, how to use the quadratic formula, and how to factor a sum or difference of cubes. In both classes, students said, “Oh, that’s how you do that!” so I’m somewhat hopeful.

I may not have written about these lessons when I first planned to, but at least I’m caught up now. Maybe by Monday (my next B-day), I’ll have things a little better in hand.

September 3, 2012

Sometimes it’s nice when necessity kicks us in the rear and makes us come up with different ways to do things.

I have always dreaded the “Points, Lines, and Planes” section of Geometry because it’s so text- and definition-heavy. (Reference this post for my original format.) Because the district has switched things up on us, PL&P is not the first section, and I need to teach it on the same day as their first quiz. I quickly decided to make this into a holey-notes foldable, but what format to use? It’s too much text for a 2-page booklet and not really enough text for a 4-page booklet. That size usually lends itself to a tabbed booklet, but how to arrange it?

My good scanner is up at school, but here is the result:

In all three classes, we got almost all the way through, and it was a lot less mind-numbing than it has been in years past.

## Reflections – Geometry Obj. 2 and Algebra 3 Obj. 2

September 3, 2012

My goal for this year was to write my reflections during 8th period (since I have that free). So far, I am 0 for 2. On the other hand, my first reflection was written on the same day as 8th period, and this is being written before the next upcoming 8th period, so it’s not too horrible, right?

I’m not sure whether it’s because I didn’t get enough sleep this week or because I’m trying to avoid coming down with a sinus infection/cold, but I have slept for most of this weekend. Literally–of the 66 hours since I left school on Friday, I have slept for 37 of them! I could probably sleep more right now, but I want to have some chance of falling asleep tonight.

Geometry
I thought this lesson went fairly well. Since I forgot to hand out homework on the first day, I used the homework (which was a worksheet on identifying patterns) as the warm-up, which reminded me of why I really like warm-ups. It (a) gives me productive time to get the roll checked because they aren’t just sitting there talking; (b) it’s a low-key form of assessment–I can go around the room and judge student understanding; and (c) it “warms up” students for thinking about math.

After we discussed the worksheet, I started the lesson on conditional and biconditional statements. Because this lesson is also text-heavy, I gave them a “holey” foldable to fill in (which also gave them practice on learning how to make a four-page booklet). Once again, however, I ran out of time before I could finish the whole booklet, so instead of giving them an exit ticket, I gave them the exit ticket as homework.

I’m thinking I may not issue textbooks at all this year. The only use I ever really made of them was for homework, and students seemed more likely to do homework if it was on worksheets. Another Geometry teacher jokingly told me that he had made his students put their books on the floor and then stand on them. “You are tougher than your textbook!” he told them. I’m not sure that’s a battle I feel like fighting though.

Algebra 3
One idea I had this year was to make copies of the solutions (on bright pink paper) so they could check their answers. I then spent some time answering questions from the homework. It was a little depressing how many students had trouble grasping the differences between the different number systems (natural, whole, integer, rational, real, and complex); although, after talking to J, an experienced Algebra 2 and PAP Algebra 2 teacher, I found out that the A2 curriculum has dropped number systems (because it’s not in the TEKS **sigh**). Normally we would then have had a quiz, but I had decided to go straight into the next lesson.

This lesson was on linear functions. Not very many students seemed to want to print out the notes I posted online, but I think they might be more inclined after going through class without them. I’m a little disappointed by how many students seemed to have trouble with writing the equation of a line, but we’ll see how they do. This will be their first homework assignment out of the book.