Transparent Algebra

Day 26

noreply@blogger.com (Karl Fisch) — Thu, 29 Sep 2011 01:30:00 +0000

Today's opener builds on what we did yesterday, as well as the slope video they watched last night. I'm trying to help them make the connection between slope and the graph, as well as between the slope, the graph, and the equation (eventually).

Today's lesson is a look back at some of the "application" problems we've done over the last few weeks, but trying to more explicitly tie them to the starting point/y-intercept and the slope/rate of change. I'm really trying to get them to think of the meaning of the y-intercept and the slope in these problems, as well as get them to begin to connect those ideas to the visual representation (the graph).

We'll work through the first 2 or 3 together, then they'll work on the rest by themselves. Depending on how far we get we'll save #6 for a later date.

Their homework will be to finish whatever problems we didn't get done in class (again, we may save #6 for later), to take the online pre-assessment over slope on the Moodle (assessment will be Friday), and (optionally) do some practice problems at CoolMath over calculating slope.

Day 25

noreply@blogger.com (Karl Fisch) — Wed, 28 Sep 2011 01:53:00 +0000

Today's opener builds on yesterday's lesson to see if they can construct a slope triangle and/or use the slope formula to find the slope between two points. Then there are two problems seeing if they can figure out the y-intercept from an equation in slope-intercept form, then a dimensional analysis problem involving texting and driving.

Today's lesson was then an activity with bouncy balls where they compare drop height with bounce height. Each group got a bouncy ball and a meter stick and had to record the mean of 3 bounces from each of 4 heights, then plot those points, sketch a line of best fit, and then come up with an equation for that line. They then use that equation to predict drop height and bounce height for a couple of scenarios.

Their homework for tonight is watch the Slope video and, optionally, do some slope between two points problems at CoolMath (they can do none, some, or a bunch, depending on what they think they need).

Day 24

noreply@blogger.com (Karl Fisch) — Wed, 28 Sep 2011 01:45:00 +0000

We began with our assessment over Graphing Linear Equations by Using Intercepts.

Then we did an activity measuring the weight of pennies to get at the idea of slope and y-intercept. Last year I brought in 8 scales and had each group do it, but that didn't work so well. I think this year's students could probably have handled it better, but I still decided simply to do the measuring myself (figuring my goal wasn't for them to do the measuring, but to think about the mathematics). Perhaps a cop out, but that's what I did.

We ended up coming up looking at slope triangles and coming up with an equation, and interpreting the real-world meaning of the slope (weight of each penny) and the y-intercept (weight of the container). (Side note: if anyone tries this, make sure you pay attention to your pennies - their weight changed in 1982, so I made sure I had 1982 and newer pennies).

Their homework for tonight was to check the portal for the results of their assessment and make an appointment to re-assess if necessary, and then to review today's lesson to make sure they fully understood what we did.

Day 23

noreply@blogger.com (Karl Fisch) — Wed, 28 Sep 2011 01:40:00 +0000

I had to miss today, but another math teacher covered my class. It was another shortened class period due to our Homecoming Pep Assembly. They worked through this review worksheet (below is the key, posted to the class blog for them to check their work over the weekend).

Their homework for the weekend was to finish the review worksheet if necessary and to prepare for their assessment on Monday over Graphing Linear Equations by Using Intercepts.

Day 22

noreply@blogger.com (Karl Fisch) — Wed, 28 Sep 2011 01:36:00 +0000

Today's opener utilizes a hopefully interesting problem pulled "straight from the headlines" - well, okay, straight from the news, about the world's largest chocolate bar, which I then turn into a dimensional analysis problem.They then have two practice problems involving graphing using intercepts and finding the intercepts from a graph.

Today's lesson then provides an application problem to link recursive sequences to writing equations and to talk about the concept of y-intercept (we'll get more explicitly to slope shortly, but we talk a bit about it today as well).

Their homework for tonight is to review the notes from the lesson (as always, posted as a PDF to the class blog), and to complete the Graphing Linear Equations by Using Intercepts Online Pre-Assessment on the Moodle.

Day 21

noreply@blogger.com (Karl Fisch) — Wed, 28 Sep 2011 01:22:00 +0000

Today is a shortened class period due to our Homecoming Royalty Assembly. So, the bell rings and we have about 4 minutes where I'll remind them that we're going to have an assessment and briefly remind them of some things they should think about while doing the assessment, then we go to the assembly. When we get back, they take the assessment over Graphing Linear Equations by Using a Table.

After the assessment we work out the key together (to post on the blog), and then due to the shortened class period we previewed the Graphing Linear Equations Using Intercepts video that they need to watch tonight so that we could go over, once again, some good strategies to utilize while watching these videos.

Their homework was check the portal for the results of their assessment and schedule an appointment to re-assess if necessary, and to re-watch the video.

Baby Blogging Steps

noreply@blogger.com (Karl Fisch) — Sun, 18 Sep 2011 03:07:00 +0000

I've made some tentative steps into having my Algebra students blog. So far they've had three posts I've asked them to do:

Reflective Blog Post #1 - Reflect on their first week or so of school and set some goals.
Explain Direct and Inverse Variation
Explain Solving Equations with Variables on Both Sides

Some students have done a nice job, some not so much, and some haven't blogged at all. I haven't really done this well in the sense that I'm not devoting any class time to this (I'd like to, but don't feel like I can make the time for it), but it's a start. You can check out the Student Blogs Page on the class blog if you want to read and comment on some of their blogs.

Day 20

noreply@blogger.com (Karl Fisch) — Fri, 16 Sep 2011 20:08:00 +0000

Our opener today includes another sequence and some practice with graphing an equation using a table of values where they need to solve for y first.

Then today is another Carnegie Hall Day - practice, practice, practice. We'll do a bunch of graphing problems using tables of values to make sure we have the hang of it before our assessment tomorrow, and then we'll have some review problems over solving equations with variables on both sides, distributive property, proportions and percents, and dimensional analysis.

So, not a terribly interesting day, but again one I think they need periodically to reinforce some of these skills.
Their homework is to prepare for their assessment tomorrow over Graphing Linear Equations Using a Table of Values.

Day 19

noreply@blogger.com (Karl Fisch) — Tue, 13 Sep 2011 19:22:00 +0000

Today's opener gives them another sequence and an opportunity to graph an equation by using a table of values.

Today's lesson is to explore time and distance relationships and to construct and interpret a graph from collected data. I've invited two of my assistant principals and my media specialist to join us in the gym hallway (long hallway not too far from our classroom), where they will follow a set of "walking directions" for 10 seconds. (e.g., walk at about 1 m/sec for 10 seconds; or walk at about 1 m/sec for 3 seconds, stop for 2 seconds, then walk at 2 m/s for 5 seconds; etc.).

Students are spaced 1 meter apart along the tape measure and as I count off the seconds they note the walker's position (if the walker is within 1 meter of the student). (I'm considering filming this as well so that they have the video to refer to later, but I'm worried that might be one thing too many.)

We'll have a total of 6 walks, then we'll return to the classroom. I will then collate the data for the first walk (maybe the first two if we have time), and then we'll work through graphing the data and answering the questions on the last slide. Then I'll collate the rest of the data and post it on the class blog later that day and they'll have to graph the remaining walks for homework (not enough time to collate all the data in class, so just getting them started so they have the idea).

Their homework over the weekend will be to finish the remaining graphs and to take the Graphing Linear Equations by Using a Table online pre-assessment (on the moodle).

Day 18

noreply@blogger.com (Karl Fisch) — Mon, 12 Sep 2011 18:41:00 +0000

Today we begin with our assessment over Solving Equations with Variables on Both Sides, so the opener is simply this reminder slide:

The assessment is two questions, one a relatively simple equation with variables on both sides, and the second slightly more difficult as it involved using the distributive property first, then solving an equation with variables on both sides (very, very similar to the two problems on the online pre-assessment they should've completed on Day 16). I anticipate the assessment taking about 6-8 minutes (with some students being finished in two). When everyone is finished with the assessment, I then work the two problems on the smart board so they should have a pretty good idea of whether they got them right, and then that gets posted to the blog so that if they did miss them they can use that to study from for their re-assessment.

Then we move into the lesson for the day. I'll start with graphing two equations by using a table. My assumption here is that they've done this before this year, but many are probably not very comfortable with it. So we'll work through the two problems together and, for the second problem, talk about how it's often helpful to solve for y first to make this easier.

We'll then move into an application problem involving distance, rate and time.

My goal is to get them to be able to apply a recursive sequence (and looking ahead to applying a linear equation) to a semi-real-world problem, and also get some graphing practice.

Their homework for tonight is to watch the Graphing Linear Equations by Using a Table video,

and to check the portal for the results of their assessment and make an appointment to re-assess if necessary.

Day 17

noreply@blogger.com (Karl Fisch) — Mon, 12 Sep 2011 18:18:00 +0000

Today we begin to make the transition from solving equations to creating and graphing them. Today's opener reviews distributive property, quadrants on the coordinate plane, and solving equations with variables on both sides (assessment over that last one is tomorrow).

Then I briefly define recursive sequence to give them the necessary vocabulary and relate it to pattern problems they've done in previous years. Then, in their groups, they explore patterns using toothpicks to create sequences of triangles and then eventually squares. The focus is on trying to nail down the idea of a starting value and then a rule to get to each successive term in the sequence, while giving them something concrete to work with (and throwing in a tiny bit of geometry).

If we finish early I'll throw some additional patterns on the board for them to practice finding the starting value and the rule (and possibly invite them to create their own for each other).

The homework will be to prepare for the Solving Equations with Variables on Both Sides assessment tomorrow (and to complete the blog post from yesterday if they haven't done that yet).

Day 16

noreply@blogger.com (Karl Fisch) — Sun, 11 Sep 2011 22:45:00 +0000

As I mentioned in the previous post, I'm a day "behind" my original plan so that's why there's no "day 15."

The plan for today is a combination of reviewing the topics we've covered so far (proportions and percents, dimensional analysis, solving equations) and an introduction to graphing (beginning the transition from solving equations to graphing and interpreting them).

Today's opener reviews distributive property and solving equations with variables on both sides. (It's been a while since my last post, so just a reminder that we introduced that last Wednesday, reviewed it on Friday, and they were supposed to watch the video over the weekend. Day 16 is tomorrow, Monday.)

Today's lesson feels a little awkward because it's just a brief intro to graphing and then a review of other topics, but I still feel it's necessary. I think they need a little more practice with the concepts we've learned, and I also think that even though they've graphed on a coordinate plane before, they need a refresher on the basic structure (before we begin to go more in-depth over the next few weeks).

Tonight's homework includes asking them what we consider to be the x and y-axis of the Earth, what quadrant our school is in, and how the Earth is different than a coordinate plane. Then they'll need to complete the Solving Equations with Variables on Both Sides pre-assessment on the Moodle (two questions very similar to the questions they will have on the formal assessment in two days).

I then ask them to create a blog entry describing how they solve 3(x - 5) = -7x + 12. I ask them to not only solve it, but explain their thought process as if they were trying to demonstrate this for someone who didn't know anything about solving these types of equations (this won't be due for two days to give them a little more time if they need it).

I then give them some optional practice problems, directing them to Coolmath or Khan Academy if they feel like they want some additional practice (as little or as much as they think they need - completely optional but I wanted to provide them an opportunity for more practice if they want it).

So, not the most interesting day, but again one I feel is necessary. Anyone have a different opinion to share?

First Three Weeks

noreply@blogger.com (Karl Fisch) — Wed, 07 Sep 2011 22:48:00 +0000

So, it's been a while since I've written anything here. That's partly due to my other full-time job (tech coordinator for my building) dominating my time at the beginning of the school year, and partly due to not wanting to plan too far ahead until I saw how things were going with my students.

So far, things are going okay but not fantastic. I'm one day "behind" what I had blogged about (over-planned as usual, but not as badly as before) - so what I have for "Day 14" on my last post (which the plan was to teach today) won't happen until Friday, Day 15 (reminder that we don't meet on Thursdays). The students seem to be adjusting fairly well to my class (and, since most of them are freshmen, to high school), and they've done well as a class on the first couple of assessments.

On the not-so-positive side, they haven't quite bought in as much as I would like them to. It's been a struggle to get some of them to think and explore and inquire. That's not a huge surprise, but still disappointing. I'm hopeful that as we go along they'll want to sit back and receive less often and step forward and do more themselves more often. We'll see.

Here's the direct link to this year's class blog if you'd like to follow along, and note an additional page on this year's blog that pulls in the students' individual blogs. The two blogging prompts I've given have given me some interesting insights (including that it's going to be a struggle to get some of my students to blog in an Algebra class). Baby steps, I suppose.

Now that the beginning of the year madness with the tech part of my job has slowed down a bit (still there, just not quite as crazy), and now that I know my students a bit and can make some more informed plans, I hope to begin blogging again here about my plans for Day 16 and beyond.

Day 14

noreply@blogger.com (Karl Fisch) — Tue, 05 Jul 2011 18:49:00 +0000

Today's opener reviews the distributive property and solving two-step equations.

Last year I just assumed that students were pretty good at two-step equations (they've had them before and they had the video for homework), but I think I need to spend another day to help solidify this. So we'll spend some time practicing with two-step equations and then extending our procedure to deal with equations with variables on both sides.

For homework they'll watch the Solving Equations with Variables on Both Sides video.

Day 13

noreply@blogger.com (Karl Fisch) — Sun, 03 Jul 2011 15:48:00 +0000

Today's opener reviews solving one-step equations, distributive property, and direct and inverse variation.

Today's lesson is an introduction to multi-step equations. We start by doing some magic:

We then reveal the secret behind the magic:

We then talk about working "backwards" and "undoing" the steps (doing the inverse operation/opposite).

Their homework for tonight is then to watch the Solving Two-Step Equations video.

Day 12

noreply@blogger.com (Karl Fisch) — Fri, 01 Jul 2011 19:27:00 +0000

Sometime right around here I'll lose a class period to MAP Testing, so I'm just going to plug it into Day 12 as a placeholder for now (I won't know the exact date until a week or two before).

Day 11

noreply@blogger.com (Karl Fisch) — Fri, 01 Jul 2011 19:08:00 +0000

Today is a PLC day, which means we start two hours late and classes are 40 minutes long (instead of 59). Today's opener reviews one-step equations and direct/inverse variations.

Partially due to the shortened classes, and partially due to it just being time to do some skill review, today is a "Carnegie Hall" day. ("How do you get to Carnegie Hall? Practice, practice, practice.") I'll provide the students with a worksheet and they'll work in groups to complete the problems. I haven't decided yet whether to break out the whiteboards for this or not, right now I'm thinking not. With about 10 minutes left in class we'll begin working through them on the smart board so that the "key" is posted to the blog and to try to clear up any remaining questions.

While I think it's fine just to have a "boring" practice day, I'm open to suggestions for how to spice it up a little. Just keep in mind that sometimes I think the students like just cranking away on problems like this, so I don't necessarily see a big problem with it (and they definitely need a little repetition/practice).

Day 10

noreply@blogger.com (Karl Fisch) — Fri, 01 Jul 2011 16:07:00 +0000

Today's opener reviews solving one-step equations, dimensional analysis, and direct/inverse variations.

Today's lesson is looking at bicycle gears as an application problem for direct and inverse variations. I bring in my bike and put it on a stand so that it's easy to rotate the pedals and have the wheels turn. I give them the following handout (because I learned last year that it takes some students a really long time to copy down a table and that wasn't the best use of their class time even though it was more friendly to our budget).

We then begin to work through how many times the rear wheel turns for one revolution of the pedals in different gears. We start by leaving the front sprocket alone and changing just the rear sprocket. I have three students come up: one to rotate the pedals, one to catch the wheel after one revolution (this takes some practice and multiple tries), and one to write the number of revolutions (estimated to the nearest tenth of a revolution) in the table on the smart board.

This turns out to be an inverse variation. We then leave the rear sprocket alone and change the front sprocket, and then do the same thing.

This turns out to be a direct variation.We then try to come up with a proportion relating front teeth, rear teeth, wheel revolutions and 1 pedal revolution, and then try to calculate how many times we have to pedal in different gears to travel 1 km.

If we have time then I give them a couple of dimensional analysis problems involving Lance Armstrong (or possibly give them as homework on the blog).

In 2005 Lance Armstrong won the Tour de France for a record seventh time. Over the course of the race, his mean (average) speed was 41.7 km/h.

a) Find his mean (average) speed in ft/sec.

b) It took him 86 hours, 15 minutes and 2 seconds to complete the Tour de France. How many feet did he go?

If you're interested in cycling, then you might be interested in these videos - The Science of Cycling (part 1, part 2, part 3).

I really like this activity, but last year I felt like the students didn't really "get" it completely. I've simplified a few things and provided them the table (which gives us some extra time), so I'm hoping that helps, but I'm open to any brilliant suggestions on how to make sure they understand it.

Day 9

noreply@blogger.com (Karl Fisch) — Thu, 30 Jun 2011 19:27:00 +0000

Today's opener reviews Order of Operations, solving a one-step equation involving multiplication, and a Dimensional Analysis problem. While they are working on the opener I'll be walking around checking to make sure they have at least the Self-Check problems from the video they were supposed to watch for homework.

Then today's lesson is to learn about Inverse Variations in the context of speed (d = rt). First, we take a look at this.

I solicit guesses but am not counting on them guessing - at least not until I pick up a tennis ball and start tossing it in the air and catching it. Then, perhaps. Then I'll show them this:

Again, they won't see this entire slide at once. I'll show them the top two images and ask them what question(s) we could ask. Hopefully they will come up with at least "how fast is it moving" and perhaps "how high was it dropped (thrown?) from. I'll then ask how do we figure out speed (based on last year, most students don't seem to really know this). I'll then display the equations and the additional pictures (and, with the picture of the meter stick, I'll open the original so we can zoom in on it to see the markings on the meter stick better).

After we figure out speed, then we'll work through these questions:

I'll then display these pictures for context and to see whether our answer seems reasonable.

Assuming that goes well (that may not be a good assumption, the students struggled with this last year), we'll move on to another rate problem. Using an excerpt I've edited from this video, we'll see if we can figure out Rich Eisen, Tim Tebow (bonus, since he's a Denver Bronco and a hot topic around here), and Jacoby Ford's (average) speed (again, borrowed from Dan Meyer). We'll then do a quick table of values and sketch the graph to (hopefully) notice this is not a straight line, and then define inverse variation.

If we have time, we'll then do a couple of skill practice problems (if not, we'll pick up with this tomorrow).

I'm not sure at this point whether I'll give them any homework or not, depends on how it's going. Most likely their homework will be to review their notes and determine what areas they are feeling comfortable with and what areas they need some extra help on.

Day 8

noreply@blogger.com (Karl Fisch) — Wed, 29 Jun 2011 22:28:00 +0000

Today's opener reviews Order of Operations, integer operations, and Dimensional Analysis.

We then move into a lesson on Direct Variation, attempting to connect it to our work with rates and proportions (with a touch of measurement and dimensional analysis thrown in). First we do some converting between kilograms and pounds, write an equation for that relationship, and graph it.

Then we see if we can apply what we've learned to a unit rate (price) problem.

Their homework is then to watch the Solving One-Step Equations Video. This is something they theoretically already know how to do, so it should be a review for all of them.

I don't feel great about today's lesson. It's okay, but I feel like I have to lead them through so much that I'm not sure it's that helpful in terms of their learning process or the actual content, and perhaps just 40 minutes of skill practice might be more effective. What do you think, would it be better to can the semi-interesting problems and just practice a bunch of dimensional analysis and then direct and indirect variation problems?

Day 7

noreply@blogger.com (Karl Fisch) — Mon, 27 Jun 2011 21:02:00 +0000

Today is our first assessment over new material (the initial skills' assessment was theoretically over knowledge they already had). On assessment days last year when students entered the room they would see something like the following instead of an opener:

My thinking was to have them to begin to focus on the assessment as soon as they walked into class, giving them some scaffolding in terms of what I think they should be thinking about as they prepare. Then once the bell rings and everyone is settled, they begin the assessment (more on the assessment in a minute). The time it takes them to do the assessment, and for us to then go over it on the board, should be roughly equivalent to the time it takes to do a normal opener. This way we still have a "full" day of instruction even on assessment days.

While I like this plan, one thing I discovered last year was that some (many?) students really didn't prepare for the assessments. I've thought of switching to giving a short opener on assessment days, knowing they would do much better on the assessment, but I'm not sure that contributes much to their long-term understanding (and it would also reduce instruction time for the day). So I think I'm going to stick with just giving them the assessment without the opener, but I'm open to hearing your thoughts.

A very brief aside to describe my assessments just to give you an idea. My assessments are an imperfect implementation of standards-based grading. Instead of giving them a test over "chapter 3" or whatever, each assessment is over a specific skill(s). This allows both me and the student to get a better handle on what the student actually knows how to do (not "I got a 73 on Chapter 3"), and what they need more work on. It also keeps the assessments very short (usually only 2 or 3 questions) and very focused, which has the added benefit of making re-assessments take less time. (I've previously written about assessment here and here, so I won't repeat all of that.)

After the students take the assessment, I (or sometimes students) work through the actual problems on the assessment on the smart board, which then gets posted to the class blog (so students have the exact assessment, including worked out solutions, to look back at if they need to review and re-assess). To give you an idea, here's last year's (pdf).

Then we begin today's lesson with a measurement activity that will lead us into dimensional analysis.

Then I get a little more explicit about the vocabulary (rate, unit rate, dimensional analysis), and we do some unit conversions that are hopefully somewhat relevant to the students. The "Vehicle Stopping Distance" at the bottom is a link to a website that talks about average stopping distance to give a little more perspective.

We then do a couple more conversations based on track records at my school, then watch a two-minute video from Discovery Education about dimensional analysis using the cost of gasoline in Australia. I'll then have the students figure out today's cost of gasoline in Australia (in U.S. dollars per gallon). I provide them with links to the current exchange rate and average prices per liter in Australia.

While I anticipate we'll be out of time, I have one more slide where we figure out how much Steven Spielberg made per second he was awake in 2009 that we'll go to if we do have extra time.

Their homework tonight is to check their grade on the assessment on our online portal and, if necessary, make an appointment to come in and re-assess (or get help first, then re-assess) if they did not do well. Tonight is also our Back To School Night, so I'll ask them to remind their parents to come tonight.

Thoughts on today's plan?

Day 6

noreply@blogger.com (Karl Fisch) — Sat, 25 Jun 2011 21:52:00 +0000

Today's opener reviews proportions and percents and integer operations, and also gives them a more open-ended estimation problem.

As they work on the opener I'll walk around and ask each group if they had any questions about how the online pre-assessment worked last night (and I'll also talk briefly about it after we finish the openers as a class).

Today's lesson is designed to solidify their understandings of ratios, proportions and percents. We'll start with a quick skill review, with students working in groups and then coming up and explaining their work at the board (or possibly on their group-sized whiteboards, I'm not sure which yet).

Then we'll look at an example with the chemical formula for TNT and one with the stock market. (Again, note that I'm displaying the entire slide for you, but I would use the window shade function to reveal only parts at a time.)

Then, thanks to Dan Meyer, we'll watch about a minute of The Bone Collector and then I'll turn them loose (with printouts of the footprint/dollar bill and rulers handy - bottom image is hidden until we discuss it).

Their homework will be to prepare for the Solving Proportions and Percents Assessment that they will take first thing tomorrow. They can do that however they'd like: review the video, review their notes, review everything that's been posted to the blog, review the online pre-assessment, do some practice problems online or from the textbook, work with a friend/parent/sibling, etc., as much or as little as they think they need.

Thoughts?

Day 5

noreply@blogger.com (Karl Fisch) — Wed, 22 Jun 2011 19:55:00 +0000

As a reminder, this is day five of my class, but it will be Monday of the second week since my class only meets four days a week.

The opener today is designed to build off the work we did on Friday as well as the video they watched for homework.

As they are working on the opener I will be walking around and looking at their notebooks to make sure they have the "Self-Check" problems from the video written down. This is somewhat of a philosophical dilemma for me. Last year I made the philosophical decision to not check whether they had watched the video. I explained to them that I expected them to watch the videos and that they needed to watch the videos in order to be successful, but that I wasn't going to look over their shoulder to make sure they did it. I continued to talk about this throughout the year, and it worked well for some students, but unfortunately other students had real difficulty completing these videos without me "checking up on them." So this year I've decided to backtrack a bit and check that they're watching the videos/completing the self-check exercises, at least at the beginning of the year. Then hopefully gradually back away from that throughout the year as they internalize that the videos are helping them. We'll see.

After they work on the openers individually, and then in their table groups, we'll discuss them as a class. Then today's lesson is to look at ratio, proportion and percent in the context of a sampling problem. We'll begin with a 3.5 minute video from Discovery Education on the Capture-Recapture Method of estimating animal populations. After watching the video we'll simulate the capture-recapture method using paper bags and two colors of beans (in the context of sampling fish at a nearby reservoir).

After working through the simulation, we'll then see if it took hold by completing three sample "application" problems. Assuming that goes okay, we'll then talk about how we could sample our class to try to predict answers for the entire school (or a class across the hall). The "freshmen" question is designed to get them thinking about what a good sample might look like (since my class is majority freshmen, this is not a good sample for the school, but might be for an Algebra class at the school). (Note: On all these images keep in mind that they are on a smart board and I'm using the window shade to control how much is visible at one time.)

If we have time, we'll then conclude with a quick skill review..

We'll then talk briefly about their homework for tonight, which is to complete the Solving Proportions and Percents Online Pre-Assessment. My plan is to use these in a very similar way to the way I did last year. Usually two class periods before an assessment I'll have the students complete a sample online pre-assessment. This gives them an idea of how they'll do on the actual assessment and gives them some time to get help/figure it out before the assessment that "counts." I ask them to write down the problems in their notebook and work them out, then click on "Check Your Work" to see how they did (and correct if necessary). I'll also give them an optional link if they'd like more practice, but it is completely optional.

A second piece of homework, but one that's not due until Friday (four days from now), is their first reflection piece:

Looking back at your first week in Algebra (and, for some of you, your first week at AHS), how are you feeling? What's going well or you're excited about? What's challenging or are you concerned about? Then I want you to set three goals for yourself for this semester. One goal specifically related to Algebra, one goal related to AHS in general (can be related to classwork, sports, activities, or something else at AHS), and one goal outside of AHS. Make these goals fairly specific, not just "I want to get a good grade." I'll be asking you to revisit these goals toward the end of the semester and evaluate how well you're doing on them, so make them be worthwhile and achievable.

Last year we did this in Google Docs, but this year I've decided to go ahead and have them blog them. I debated about whether I wanted these private (in Google Docs, so that they could perhaps be more honest and share more information), or public (Blogger, where they might feel somewhat constrained because it's public). Last year I really didn't have anything shared that I think wouldn't have been if they'd been public, so I want to open this up for all the usual reasons for why blogging can be powerful. I'll also let the students know that if they have anything they'd like to share but not publicly, to just let me know.

I'm a little worried that's too much homework, but I figure the pre-assessment only takes 10-15 minutes and the reflection isn't due until Friday (and they have Thursday "off" of Algebra), so I'm hoping it's not too bad.

As always, I'd appreciate your thoughts/suggestions on any of the above.

Day 4

noreply@blogger.com (Karl Fisch) — Mon, 20 Jun 2011 22:17:00 +0000

As a reminder, my Algebra class meets four days a week (MTWF), so day four is going to be a Friday but it will be two days after our day three meeting on Wednesday. Today is really the first day that is my "own" in Algebra. The first semester of Algebra at my school is basically all about linear equations, and I start by taking a look at proportional thinking - more specifically, ratios and proportions.

My opener today is designed to build off the skills review/assessment they just had and help front-load some ideas for today's lesson. At the moment (assume that phrase for all planning posts on this blog), this is what it looks like:

As a reminder, students are expected to begin the opener by the time the bell rings. They then work on it for a little while individually, then discuss with their group members, then students come up to the smart board and explain them to the class (with that getting saved to PDF and posted to the class blog).

We then open the lesson with a bit of vocabulary.

Then I try to lead them into solving proportions by starting with something they hopefully can do somewhat intuitively: "When you divide some number N by 2 you get 12. What's the value of N?"

From that we move slowly toward doing the inverse operation, to "undo" dividing by 2 we would multiply by 2; to undo dividing by 4 we would multiply by 4.

But then what happens when we throw a fraction into the mix? Hopefully they'll see that the same principle applies. From there they work through several examples with the variable in the numerator, then we try to extend to having the variable in the denominator.

At this point I really want them to focus on inverse operations, so I'm not showing them to "cross-multiply" to solve proportions.

Assuming things are going reasonably well at this point, I then introduce a hopefully somewhat interesting application of proportions.

In my head we still have about 10-15 minutes left in class (but often my head is very, very wrong), so we'll try to make a quick geometry connection. (If we don't have the time, we'll skip this - perhaps taking a look at it the next day.)

How ever much we get through gets posted to the class blog as a PDF.

We will then talk briefly about how I expect them to work through (and take notes on) the videos, as their homework will be to watch/work through the Solving Proportions and Percents video.

While I'll probably tweak it, this is what I wrote last year on the blog to follow-up what we talked about in class.

We previewed the Solving Proportions and Percents video that you're going to watch for homework tonight and talked about the different pieces in it, how you should use it, and what you need to write down in your notebook. There are three main parts to the video: an Examples and Explanation part, a Guided Practice part, and a Self-Check part.

Examples and Explanation: Just what it sounds like. I explain how to do the problems and work through some examples. You don't need to write anything down (unless you want to), just watch, listen and learn. Pause the video and replay parts if you need to.

Guided Practice: I give you a problem, then ask you a series of questions with about 5 second pauses between questions for you to think about it and answer it for yourself. If you need to, pause the video to give yourself more time. Again, you don't have to write anything down here (although you can and it may be a good idea to).

Self-Check: I give you a problem, ask you to write it down in your notebook and solve it, then I show you the solution in the video. Once the problem is on the screen you need to pause the video, write it down and solve it, then play the video again to check your work. You may need to pause the video again to view the solution if you need more time. These problems you definitely need to write down in your notebook.

Remember, you can always replay any part of the video you need to go back over something.

I would love to hear your thoughts/feedback/suggestions for improvement on any/all of this.

Day 3

noreply@blogger.com (Karl Fisch) — Sat, 18 Jun 2011 17:10:00 +0000

Day three is when I give the common assessment over the Math Skills (this is the only thing all year where they are not allowed to use a calculator). I plan to start with an opener that has several problems that involve the four skills areas on the common assessment. The basic structure of my openers is that they are projected on the smart board as the students come in to class. I ask them to be in their seats and either start them before the bell rings or be ready to start as soon as the bell rings. They work on them individually for a certain amount of time (varies depending on how many and the complexity of the openers), writing them down in their notebooks. Then I ask them to take a few minutes and discuss their results with the other members of their groups (again, typically four in a group, with one or two threes to make it work out even). Then I ask for volunteers to come up and work them out on the smart board (which I then post to the class blog - sample from last year) and explain then to the class. (I go back and forth whether to ask for volunteers or just pick randomly making them all responsible for being ready and "forcing" them to come up - your thoughts?)

After we work through the openers, I'll then give the common assessment (roughly 15 minutes, although I remember last year it took some students significantly longer than that). Then, based on Dvora's comments on the previous post, I'm considering shifting some of the culture/class expectations piece to today. I'm thinking that after the assessment I may take them to the computer lab (assuming MAP testing hasn't started yet and I can get into the lab) to help them get into their Google Accounts. All of our students have Google Apps accounts, and for students that were in my district last year they may remember how to login, but I also have three students who are new to our district. Once they get logged in I'll help them with their basic Blogger setup (mostly display name and creating a reflective blog for my class), then have them read (and eventually comment on, although we may not get that far) a post on the class blog talking about culture and expectations. This may enable some of a conversation online even if they aren't quite comfortable enough yet to engage in a face-to-face discussion.

Their homework will be to check the online portal for the results of their assessment and, if necessary, make plans to re-assess over any of the areas they did poorly on. (While I'm probably going to tweak it some, here was my assessment plan for last year.) Students sign-up online to re-assess (again, here's last year's sign-up form), and they only need to re-assess over the area(s) they did poorly on (so I'll divide the assessment grade into four portions: adding and subtracting fractions, multiplying and dividing fractions, integer operations, and order of operations). In addition, depending on how far we get in class, I may ask them to comment on the class blog post about culture and expectations (perhaps not "due" until Friday as we don't meet on Thursdays).

We would then be setup to really begin "Algebra" on Friday.