Wednesday, September 28, 2011

Day 26

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.

Tuesday, September 27, 2011

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 23

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

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

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.

Saturday, September 17, 2011

Baby Blogging Steps

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:
  1. Reflective Blog Post #1 - Reflect on their first week or so of school and set some goals.
  2. Explain Direct and Inverse Variation
  3. 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.

Friday, September 16, 2011

Day 20

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.

Tuesday, September 13, 2011

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).

Monday, September 12, 2011

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).

Sunday, September 11, 2011

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?