Algebra 2: nth-roots

My first unit this year is on real numbers. In the first two lessons, we learned the types of real numbers and how they are related. In this lesson, students learn what nth-roots are (they are only familiar with square roots from algebra 1). They also learn how to evaluate, estimate (including plotting on a number line), and simplify nth-roots.

Speaking of number lines, they can be a pain to make. Here is a tutorial on how to make number lines and coordinate planes in MathType. Who knew?

We have a lot of resources to work with at DCP, but one thing we are lacking in is digital projectors. We have four for the whole staff, which is adequate if they are only used for occasional movies and demonstrations. However, I started using one last year for daily lessons, and I liked it so much that I kind of reserved it every single day. It worked out ok, but I felt bad hogging a quarter of the resource for myself. So I decided to get one of my own this year. I just bought it from Amazon, and it seems like a great deal. Here is the link if you are interested. If you know anything bad about this projector, please don't tell me, since it's already being shipped!

Here are the handouts and the Keynote:
Lesson 3
Keynote (zipped)
Keynote Quictime

Update:
The projector arrived, and it is fantastic. I got the box 15 minutes before class, opened it up, plugged it in, and was good to go. It is bright enough to use with the lights on, and the colors look exactly like what's on the screen! (Neither of these things are true with our media cart projectors). And now I can take it home on the weekends and watch movies on the wall, instead of peering at the laptop screen (we don't have a TV, so...)

College Habits

I stole this idea from the teachers at Impact Academy in Oakland. I learned about it two days before classes started, and pretty much immediately decided to implement it.

The idea is that you establish a few "college habits" that students should be working toward, and then they self-assess at the end of each class on how well they demonstrated those habits.

Here are the habits I am using:

1. Punctuality: When the bell rings you are in your seat, binder and pencil/pen out, checking homework.
   
2. Materials: Every day, you need your binder, planner, pen, and pencil.
3. Supporting Others: Always support other students’ learning. Help others and ask for help when you need it. Never distract other students.
4. Focus: Focus on doing your best work. Don’t let your mind wander. Your body language should show active engagement.
   

For habits 1 and 2, students can earn either 1 or 0 points. For 3 and 4, they can earn 1, .5, or 0 points. I save the last 3 - 4 minutes of the class to do this: students think about how they did, in each category, write it in their logs, and total their scores.

The key - which at first seemed a little off-putting - is that they then say their score out loud, one by one, for the teacher to record. The point is that students are being held publicly accountable for their behaviors in class, and have to face up to it when they have been harmful to the learning environment. I made a couple of rules for this. First, no students are allowed to comment in any way on other students' scores; it is silent during this time except for the person reporting their score. Second, even if I don't agree with the score, the student has final say over their score, and it does factor into their grade (albeit, only a small percentage of the whole).

I've seen my Algebra 2 classes twice each so far, and this has gone surprisingly well. I wasn't sure how they would handle it, but they are doing a good job. For example, today I had to send a student out of the room for being distracting. (We have a cool new reflection process for this sort of thing, which I'll write about later.) She came back in, finished the class in a much better mood, and at the end, gave herself a 1 out of 4 for the day. And I overhead another girl asking her group if they thought she was focused today.

I hope that this structured reflection on behaviors, tied in with some public accountability and the ultimate control over a small piece of their grade will help build a strong classroom culture this year.

Algebra 2: Real Number System

I've taught the first lesson of Algebra 2, and it went well. I love the energy that 9th graders have, but I do have to admit that it is pleasant not to have to spend the first few weeks breaking the kids in from scratch. My first unit is on the real number system. The skills that I plan on covering are here.

In the past, students have had great difficulty dealing with the Venn Diagram of the number system. They always got tripped up with the fact that all whole numbers are integers, but not all integers are whole numbers (for example). So I decided to make my first lesson of the year about classification with Venn Diagrams. The second lesson extends that understanding to the number system. I'm hoping that this scaffolding will make the number system much easier to understand and remember.

Here are the lessons if you want to see what I am doing. (I plan to post all of my lessons as they go, so stay tuned if you are interested. And, any and all feedback on lessons would be greatly appreciated, especially if you try out something of mine in your class).

Lesson 1 (classification)
Lesson 2 (real number system)

Island Maps complex instruction skillbuilder I used in lesson 1

DCP Alviso

Today, DCP launches our second campus, located in Alviso. It is a 6th-12th grade school; right now, there are only 6th and 7th graders. Here is a link to the story shown on ABC news.

Algebra 1: Intro to square roots

Students often have trouble seeing a square root as a number when the radicand is not a perfect square. The point of this activity is to help students develop this understanding by using a geometric metaphor.

square root intro.doc

Group work skill builders

We are doing a major overhaul of our Algebra 1 and 2 program this year, and one of the elements we will be working on is increasing the use of complex instruction.

To be successful at this type of learning, students must be able to work effectively in groups - which is something that does not come naturally to most students. The designers of complex instruction have a set of skill builder activities that can be used to teach students how to accomplish group tasks. If you plan on doing any sort of group work, you should definitely check out the link and read through the activities.

Back to work

It's been a lovely summer, but now it is time to get back to work. I will be teaching Algebra 2 this year (4 sections) and Algebra 1 (1 section). So, most of my lesson posts are going to be about Algebra 2.

I have been working with H. on creating a skills mastery assessment system. She has posted a lot about it, so I won't bother repeating it. You can catch up here.

I just found out about box.net and I will be posting my files there as I go this year. There is a handy widget on the blog now (if you are reading this by RSS), and you can even subscribe to that by RSS. Feel free to look at and use anything I post, but of course nothing may be published/sold/turned in to your ed school instructor without my permission.

I describe how my system will work in one of the files, but here it is if you don't want to bother downloading it:

Each skill test will be given at least twice – the scores are added together. The purpose of this is to promote retention of concepts. If students receive a perfect score on the second administration of the test, the first score will be raised to a perfect as well. Students are able to retake these tests as many times as they want before the end of the semester, though they can’t take the same test more than once per day. The questions on the skills tests are all single topic items that reflect typical STAR questions.

Homework will be graded. To make this possible, students will be called on to grade their own work. This will require trust and buy-in on the students’ part – but, the weight is limited to 10% to limit temptations for cheating. Each class, students will be shown the answers to the problems, and five to ten problems will be selected for grading. Each problem is either right or wrong, no partial credit. However, students may do corrections to the incorrect problems and turn them in the following class to earn their points back.

Thus, a full 60% of the points are “recoverable”, and students who put in sufficient effort should be able to earn the full amount of points. A student who earns all of the recoverable points needs only a 25% average on comprehensive tests and the final in order to earn a 70% in the class. This way, the class is passable by lower ability students who are willing to work hard, and these students will hopefully be better prepared to take the STAR test. Students who want to earn a B or an A must also do well on the comprehensive tests; this allows me to create tests that are more challenging and focus on analysis and synthesis problems.

In the Unit Skills Lists, skills that are marked CE will be tested only on a comprehensive exam. These are skills that are not required by the benchmarks/released questions, but are key to progressing to higher level math.

This system is still in its development phase, so any feedback you may have would be much appreciated.