## Wednesday, November 30, 2011

### Wednesday, November 30, 2011

We began with our assessment over Systems of Inequalities (key, pdf).

We then learned about function notation (lesson, pdf).

1. Check the portal for the results of your assessment, fill out your student checklist with your results, and make a plan for retake (if necessary), including making an appointment.

2. Practice with a few evaluating function problems.
3. Quarters for Kiva?

### Review for Final 12: Parallel and Perpendicular Lines

Watch the Parallel and Perpendicular Lines video.

## Tuesday, November 29, 2011

### Tuesday, November 29, 2011

We began with this awesome opener (pdf).

Then today's lesson (pdf) was learning about graphs of real-world situations.

Tonight's homework is to:
1. Prepare for the Systems of Inequalities Assessment tomorrow. There are a variety of ways to do that including, but not limited to: review the online pre-assessment; review your notebook and/or the openers and lessons posted on the blog; review the video, work some practice problems in your textbook or that you find online. You can, of course, also get help from me, another math teacher, a teacher in the Study Center, a peer tutor in the Study Center, or a parent, sibling or friend. Do whatever works best for you, but make sure you're prepared. The expectation is that you should all be able to do very well on this assessment.

2. Consider participating in our Kiva project.(Total so far: \$4.47; Last year: \$71.41 from class, \$300 total.)
3. Change the World in 5 Minutes a Day

### Review for Final 11: Writing Linear Equations in Standard Form

Watch the Writing Linear Equations in Standard Form video.

## Monday, November 28, 2011

### Monday, November 28, 2011

We began with this opener (pdf) to get our heads back in the Algebra game.

Then today was a Carnegie Hall Day (practice, practice, practice) lesson (pdf), with an emphasis on systems of inequalities and functions.

Tonight's homework is:
1. Complete the Systems of Inequalities Online Pre-Assessment on the Moodle.

2. If you haven't been playing along with watching the one-a-day-videos to begin reviewing for the final exam, you may want to start that now. This link will take you to an auto-magically updating collection of all the posts with the videos.

3. Please read this blog post about A Quarter is More Than Just a Fraction and Kiva and decide how/if you'd like to participate. No amount is too small - or too large. (Total so far: \$0.36; Last year: \$71.41 from class, \$300 total)

### Review for Final 10: Writing Linear Equations in Point-Slope Form

Watch the Writing Linear Equations in Point-Slope Form video.

## Sunday, November 27, 2011

### Families Living in Cars

Saw this on 60 Minutes tonight and thought some of you might be interested.

## Saturday, November 26, 2011

### Never Give Up

Consider watching this.

## Friday, November 25, 2011

### A Quarter is More Than Just a Fraction

Arapahoe, as you know, puts our collective might behind several causes throughout the year. Currently we are asking students and staff to bring in a toy for Toys for Tots. I encourage you to participate in that, not just by bringing in a toy, but also attending the wrapping party and going to Alice Terry Elementary on December 14th to help distribute the toys.

But I also want you to think more globally in this class. If you happened to read my blog over Thanksgiving break, then you read about Kiva and Team Shift Happens. Here’s a brief description of Kiva:
Kiva's mission is to connect people through lending for the sake of alleviating poverty.

Kiva is the world's first person-to-person micro-lending website, empowering individuals to lend directly to unique entrepreneurs in the developing world.
And here’s part of what I wrote on my blog about Team Shift Happens:
I lend \$25 to an entrepreneur (\$25 is the minimum they accept). But I also purchase two \$25 gift certificates that I then email to two members of my PLN. I’m asking those folks to then do two things.

First, they can choose which entrepreneur to loan the \$25 to. Then I’m asking them to consider doing the same thing – purchasing two \$25 gift certificates and emailing them to two members of their PLN (with the same request that those folks continue the cycle, sending two Kiva gift certificates to folks in their network - a Kiva Pay It Forward plan).
Last year I also read this post by Chris Harbeck, a teacher in Canada, and I decided to challenge last year's class in a similar way – challenge each of them to bring in \$0.25 a day for each day class met between then and the end of the semester. I'm going to challenge you guys with the same this year. Conveniently, our class meets ten times before the end of the semester, so that’s challenging you to donate a total of \$2.50.

I want to be clear – this is not a requirement. This has no effect on your grade. There’s no extra credit, nor will I berate anyone who doesn’t participate. This isn’t about you. Or about me. This is about helping empower people who haven’t had the same opportunities that we enjoy. Some folks think teenagers won’t do this kind of thing if there’s not a payoff for them in it – we’ll see if they’re right.

I wrote a couple of years ago:
Poor people in impoverished communities often don’t have access to financial institutions and capital, and microfinancing addresses this problem. It is especially helpful to women, who often are the key to raising families – and communities – out of poverty. It’s also my opinion that this is one of the best ways to help achieve peace in the world.
So I challenge you to bring in what you can. If that’s a quarter a day (or \$2.50 total), that’s great. If it’s less, or more, that’s great as well. You can bring money to class each day expressly to donate, or you can simply find me during the day when you perhaps have some change in your pocket (after lunch?) and donate (no amount is too small – or too large). You can choose to participate yourself, or you can cajole your family and friends to donate some change as well if you want – it’s up to you.

Then I’ll match whatever you donate (up to \$100 – I’m not completely crazy). So I’ll take the total of whatever you guys bring in by the last day we meet (our final is on Tuesday, December 13th), and match it with an equal amount, then I’ll take the total and lend it out on Kiva. (If you’d like to help me pick which entrepreneur to lend to, start looking around Kiva and let me know who you think we should fund.)

So, if you occasionally visit Starbucks, consider skipping it once in the next couple of weeks. Or perhaps you could skip that overpriced, not-really-very-healthy-for-you “energy” drink I see some of you drink in the morning. Or if you go out for lunch, skip the soft drink a couple of times. Not only will you be doing your body a favor by skipping one or all of these, but a minor deprivation for you could turn into a possibly life-changing loan for someone else.

It might only be a fraction of a dollar to you, but to someone in the developing world – it’s priceless.

### Review for Final 7: Slope

Watch the slope video.

## Wednesday, November 23, 2011

### Review for Final 5: Graphing Linear Equations by Using a Table

Watch the Graphing Linear Equations by Using a Table video.

## Monday, November 21, 2011

### Review for Final 3: Solving Two-Step Equations

Watch the Solving Two-Step Equations Video.

## Sunday, November 20, 2011

### Review for Final 2: Solving One-Step Equations

Watch the Solving One-Step Equations video.

## Saturday, November 19, 2011

### Review for Final 1: Proportions and Percents

Watch the Solving Proportions and Percents Video.

## Friday, November 18, 2011

### Friday, November 18, 2011

We began with our assessment over Solving and Graphing Linear Inequalities in Two Variables (key, pdf).

We then learned about relations and functions (lesson, pdf)

1. Check the portal for the results of your assessment, fill out your student checklist with your results, and make a plan for retake (if necessary), including making an appointment.

2. Watch the Solving Systems of Inequalities video.

3. Start studying for the final exam. Seriously. As I mentioned in class, an excellent way to study for the final is to watch one Algebra video a day starting tomorrow, then every day until just before finals week (yes, that includes next week when you're off, and includes weekends). Obviously you can double-up on some days if you miss a day, but if you're willing to spend 10 to 15 minutes a day over the next three weeks you'll be well-prepared for the final. Or you can wait, try to cram a couple of hours the night before, and take your chances.

I'll post one video a day on the blog, in the order we did them, starting tomorrow. Look for them.

It's up to you.

4. Have a very good, very safe break.

## Wednesday, November 16, 2011

### Wednesday, November 16, 2011

We began with our assessment over Solving and Graphing Inequalities in One Variable (key, pdf).

We then practice solving systems of inequalities, which also simultaneously reviewed graphing linear inequalities in two variables (lesson, pdf)

1. Check the portal for the results of your assessment, fill out your student checklist with your results, and make a plan for retake (if necessary), including making an appointment.

2. Complete the Solving and Graphing Linear Inequalities in Two Variables Online Pre-Assessment on the Moodle. Please note that our assessment over this will be on Friday, so make sure you do the pre-assessment tonight so if you have any questions you can get some help tomorrow.

3. Prepare for the assessment on Friday.

## Sunday, November 13, 2011

### Tuesday, November 15, 2011

We began with this heart-wrenching opener (pdf).

Then today's lesson (pdf) was investigating how to solve a system of inequalities by looking at postage rates.

Tonight's homework is to:
1. Prepare for the Solving and Graphing Inequalities in One Variable Assessment tomorrow. There are a variety of ways to do that including, but not limited to: review the online pre-assessment; review your notebook and/or the openers and lessons posted on the blog; review the video, work some practice problems in your textbook or that you find online. You can, of course, also get help from me, another math teacher, a teacher in the Study Center, a peer tutor in the Study Center, or a parent, sibling or friend. Do whatever works best for you, but make sure you're prepared. The expectation is that you should all be able to do very well on this assessment.

2. Make an appointment to come in and re-assess for any of the assessments you might need to redo. Get them done this week before the furlough days/Thanksgiving "break."

3. If you want some more practice with solving inequalities, here's an endless supply.

### Monday, November 14, 2011

We began with this inspiring opener (pdf).

Then today's lesson (pdf) was a Carnegie Hall Day (practice, practice, practice).

Tonight's homework is to:
1. Complete the Graphing Inequalities in One Variable Online Pre-Assessment on the Moodle.

2. Make an appointment to come in and re-assess for any of the assessments you might need to redo. Get them done this week before the furlough days/Thanksgiving "break."

## Friday, November 11, 2011

### Friday, November 11, 2011

We began with our assessment over Solving Systems of Equations by Elimination (key, pdf).

Then today's lesson (pdf) was learning how to graph inequalities in two variables.

1. Don't forgot your blog post about when to use the substitution method and when to use the elimination method is due before you go to bed Sunday night.

2. Watch the Solving Inequalities in Two Variables video.

## Wednesday, November 9, 2011

### Wednesday, November 9, 2011

We began with this terrific opener (pdf).

Then today's lesson (pdf) was a Carnegie Hall Day (practice, practice, practice).

1. Complete the Solving Systems of Equations by Elimination Online Pre-Assessment on the Moodle. Please note that our assessment over this will be on Friday, so make sure you do the pre-assessment tonight so if you have any questions you can get some help tomorrow (again, in the Math Department, as I will be gone tomorrow).

2. Prepare for the Solving Systems of Equations by Elimination Assessment on Friday. There are a variety of ways to do that including, but not limited to: review the online pre-assessment; review your notebook and/or the openers and lessons posted on the blog; review the video, work some practice problems in your textbook or that you find online. You can, of course, also get help from me, another math teacher, a teacher in the Study Center, a peer tutor in the Study Center, or a parent, sibling or friend. Do whatever works best for you, but make sure you're prepared. The expectation is that you should all be able to do very well on this assessment.

3. Watch the Graphing Linear Inequalities in One Variable video

## Tuesday, November 8, 2011

### Tuesday, November 8, 2011

We began with our assessment over Solving Systems of Equations by Substitution (key, pdf).

We then practiced a bit with solving systems by elimination, and then learned about solving inequalities in one variable (lesson, pdf)

1. Check the portal for the results of your assessment, fill out your student checklist with your results, and make a plan for retake (if necessary), including making an appointment.

2. A reminder about the blog post that's due by Monday. Don't wait until the last minute.

3. If you want some more practice with solving inequalities, here's an endless supply.

4. A reminder that I'm not available this Thursday for help or to re-assess.

5. Watch Solving Systems of Equations by Elimination video.

## Monday, November 7, 2011

### Monday, November 7, 2011

We began with this electrifying opener (pdf).

Then today's lesson (pdf) was a Carnegie Hall Day (practice, practice, practice).

Tonight's homework is:
1. Prepare for the Solving Systems of Equations by Substitution Assessment tomorrow. There are a variety of ways to do that including, but not limited to: review the online pre-assessment; review your notebook and/or the openers and lessons posted on the blog; review the video, work some practice problems in your textbook or that you find online. You can, of course, also get help from me, another math teacher, a teacher in the Study Center, a peer tutor in the Study Center, or a parent, sibling or friend. Do whatever works best for you, but make sure you're prepared. The expectation is that you should all be able to do very well on this assessment.

2. Another reminder that I won't be here on Thursday to help or to re-assess. If you need help, please stop by the Math Department. If you need to re-assess, please schedule an appointment for some other day this week.

3. Try out Google Gravity. Go ahead and do a search for something.

4. If you want some additional practice on solving equations by substitution or elimination, here's an endless supply of them. (Note: some would be better solved by substitution, some better by elimination.)

6. Due Monday, November 14th: On your Algebra Reflective Blog, please create a new post titled "Solving Systems of Equations: Substitution vs. Elimination." In this post explain to your readers how you decide whether to use the Substitution Method or the Elimination Method to solve a system of equations. My guess is that you will need to include some examples, including at least one that you would choose to solve by substitution, and at least one you would choose to solve by elimination. Remember, you have to assume your reader knows nothing about this process, so be specific and detailed.

## Sunday, November 6, 2011

### We See This as the Future of Higher Education

About a year ago I ran across this article in the New York Times titled, Learning in Dorm, Because Class is on the Web (two pages, make sure you click through to page two) and I'd like you to take 5-10 minutes to read it. Go ahead, go read it, then come back.

This article illustrates that many colleges – which most of you will be attending in 3-4 years – are starting to utilize some of the same video techniques we’re trying to use in our Algebra class. There are a variety of different ways colleges are using this, some are pretty similar to what I’m doing, others are very different (consider yourself lucky, you only have to watch 8-10 minutes of me, not an 85 minute streamed lecture!).

Note that some colleges are doing this primarily for financial reasons,
You have X amount of money, what are you going to do with it?
others are exploring whether it can be a more effective way of delivering instruction,
She said an advantage of the Internet is that students can stop the lecture and rewind when they do not understand something.
No matter the reason, it appears likely that more classes will be offered this way by the time you get to college.
We see this as the future of higher education.
So consider our Algebra class a chance not only to learn Algebra (and enjoy my amazing wit), but an opportunity to begin preparing yourself to be successful in college – and beyond – by learning how to learn through online components of courses.

Notice how some students don’t like this approach.
In a conventional class, “I’m someone who sits toward the front and shares my thoughts with the teacher,” she said. In the 10 or so online courses she has taken in her four years, “it’s all the same,” she said. “No comments. No feedback. And the grades are always late.”
This is one of the reasons why I believe hybrid classes – where there’s an online component and a face-to-face component - are perhaps currently the best of both worlds when done well (although that may change as we get better at implementing online courses). The way I've tried to structure our class is inquiry first - we explore the ideas together in some kind of context - and then you watch the video outside of class to reinforce the skill and to help you go from the more concrete to the abstract. But several things have to happen in order for classes like this to work.

First, students must watch/complete the “lecture” video portion of the class outside of class. Clearly some college students – as well as some of you – are not doing this. If this part isn't done, the entire model falls apart because the videos outside of class allow us the time in class for inquiry.

Second, just as critically, students must be active participants in class to maximize the value of our time together. Students must be willing to use class time as an opportunity both to explore and to practice mathematical ideas and concepts, not as a time to sit back and be “told” or “shown” what to do. This is why I continue to try to get you guys to think more on your own, to talk and work in your groups, and to take risks in your learning, instead of simply waiting for me to show you the “right” answer.

So I’m hopeful that as we continue with this approach we all will get better at it. I need you to hold up your end of the bargain (watch/complete the videos outside of class - including the Guided Practice and Self-Check portions, complete the online pre-assessments on the Moodle, actively participate/explore/think in class, and come in for help and to re-assess), and I hopefully will get better at structuring class to complement the video instruction outside of class. Together we can not only help you master Algebra, but prepare you to be successful learners in college and beyond.

So what do you think? Are you planning to go to college? If so, what are your feelings about the fact that you undoubtedly will have a large online component? If not, how do you feel about online training in general, as many jobs that don't require college now require that type of training?

What about Algebra - given that this is how I've structured the course, is there anything you can be doing better to maximize your chances for success? Be specific. Is there anything I can be doing better (keeping in mind that the basic hybrid nature is not going to change)? Do you have any other thoughts about above article and my thoughts regarding it?

(Bonus: While not specifically about using video, this post I wrote a while back is also about higher education - specifically, the University of Virginia, and the expectation that students do the preparatory work outside of class and then come in and be active participants in class. You might be interested in reading my post and the linked article).

## Friday, November 4, 2011

### Friday, November 4, 2011

We began with our assessment over Solving Systems of Equations by Graphing (key, pdf).

Then today's Carnegie Hall Day lesson (pdf) was learning about when to use substitution method, when to use elimination method, and practicing with both.

1. Check the portal for the results of your assessment (I'll hopefully get those picked up tonight and graded and on the portal either tonight or tomorrow morning), fill out your student checklist with your results, and make a plan for retake (if necessary), including making an appointment.
2. Complete the Solving Systems of Equations by Substitution Online Pre-Assessment on the Moodle. Please come to class on Monday with any questions you have.

3. Go to google and type "Do a barrel roll" (without the quotation marks).

4. If you didn't get a chance to read Can't We Just Memorize a Formula to Plug Stuff Into? last night, please take a few minutes to read it this weekend.

5. Just a heads up that I will not be available next Thursday for help or re-assessments. If you need help on Thursday, please stop by the Math Department and they will be happy to help you. If you need to re-assess next week, you'll need to make an appointment to see me on a day other than Thursday.

## Thursday, November 3, 2011

### Can't We Just Memorize a Formula to Plug Stuff Into?

I've been wanting to share something with you the last couple of days in class but just haven't had time, so I decided to just put it here on the blog instead. In The Myths of Innovation by Scott Berkun I came across a couple of passages that I thought were relevant to our class. In a section of the book talking about the myth that good ideas are hard to find, he writes:
While waiting in a city park to interview someone for this book, a nearby child played with Silly Putty and Legos at the same time. In my notepad I listed how many ideas the young boy, not more than five years old, came up with in 10 minutes. Sitting in the grass, he combined, modified, enhanced, tore apart, chewed on, licked, and buried various creations I'd never have imagined. His young mother, chatting on a phone while resting her morning coffee on the park bench, barely noticed the inventive creations her toddler unleashed on the world. After being chased away for making her nervous (an occupational risk of writers in parks), I wondered what happens to us, and what will happen to this boy, in adulthood. Why, as is popularly believed, do our creativity abilities decline, making ideas harder to find? Why aren't our conference rooms and board meetings as vibrant as childhood playgrounds and sandboxes? (p. 82)

. . . To open minds and find good ideas, return to the kid in the park. What is it about his attitude that allows fearless idea exploration? Linus Pauling, the only winner of two solo Nobel Prize awards in history, had this to say about finding ideas: "The best way to have a good idea is to have lots of ideas." This sounds idiotic to most ears because it cuts against the systemic, formulaic, efficiency-centric perspective worshiped in schools and professions. It seems wasteful to follow Pauling's advice. Can't we just skip to the good ideas? Optimize the process? Memorize a formula to plug stuff into? Well, you can't. (p. 85-86).
The passage also includes this picture of the first computer mouse with the caption, "The superficials of innovation are rarely impressive. This is a version of the first computer mouse."

(image source: Wikipedia)

What does this have to do with Algebra? Well, this is very similar to the philosophy of what I'm asking you to do in this class. Yes, we do have some formulas that you're going to need to learn and "plug stuff into." But our more important goal is for you to open your minds and be willing to explore ideas. This is why I'm always asking you to try to figure things out, both individually and as a group, and not wait for me to tell you how to do it.

Sure, we can "skip to the good ideas" and I can just show you how to do certain procedures, but that ends up not being very meaningful for you, and you're also not very likely to remember it very long. Instead, I want you - as much as possible - to play with the ideas. To be curious, and creative, and try to figure things out and find patterns and methods on your own, including exploring various real-world applications of the mathematics. And, yes, that's harder than just memorizing the formula and doing random problems out of the book. But I think it's also much, much, much more worthy of your time.

As Eric Hoffer said,
In a time of drastic change it is the learners who inherit the future. The learned usually find themselves equipped to live in a world that no longer exists.
I want you to be a learner; to take the attitude of "fearless idea exploration." In my class, in all your classes, and in life in general.

## Wednesday, November 2, 2011

### Wednesday, November 2, 2011

We began with our assessment over Essential Learning #3 (key, pdf). Please, please, please come in for help on this if you are still having difficulty.

We then reviewed solving a system of equations by substitution and learned a new method, solving by elimination (lesson, pdf).

1. In the lesson (pdf) on Atomic Weights, we got as far as solving for H. Try to complete that problem by substituting in the value of H into either original equation and then find C, then check it in the other equation. We'll go over this on Friday.

2. Prepare for the Solving Systems of Equations by Graphing Assessment. There are a variety of ways to do that including, but not limited to: review the online pre-assessment; review your notebook and/or the openers and lessons posted on the blog; review the video, work some practice problems in your textbook or that you find online. You can, of course, also get help from me, another math teacher, a teacher in the Study Center, a peer tutor in the Study Center, or a parent, sibling or friend. Do whatever works best for you, but make sure you're prepared. The expectation is that you should all be able to do very well on this assessment.

## Tuesday, November 1, 2011

### Tuesday, November 1, 2011

We began with our assessment over Parallel and Perpendicular Lines (key, pdf).

We then continue our exploration of the iPhone rate problem to continue practicing with solving a system of equations by substitution (lesson, pdf). We also reviewed for our assessment over Essential Learning #3 tomorrow.