Day 25

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

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 22

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 19

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

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

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

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?

Day 14

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

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 10

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 8

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 5

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.