Day 72: Parallel, Perpendicular or Neither

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Today we had Guided Groups. Most of the time┬ástudents spend working on the math software that we are required to use and they are required to spend a minimum of 50 minutes on during the week. This is pretty much the only day that I get to use the computers unless one of my co-workers decides that they are not using the cart on their assigned days. It bums me out that we can’t get to more exciting opportunities but nothing I can do about that.

Today during my 8th grade guided group, we worked on the idea of parallel, perpendicular or neither. This was our second day on the topic so we started with a review. No surprise, most students remembered what that parallel lines have slopes that are the same, but the understanding of perpendicular line slopes was more challenging to grasp. Once I talked through a couple of examples it made a lot more sense to them. (Non-examples were also very useful.)

I then gave the students two sets of points that were on a line and they were asked if the lines were parallel, perpendicular or neither. Some of my lower kiddos needed an explanation that they needed to find the slope of both sets of points and then they compared the slopes. Once they did the first one, the next several problems were easier for them.

The biggest problem we had was loosing negative signs due to carelessness, but that’s pretty normal for 8th graders.

Day 71: Back at It

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Back to school we go! Break was definitely not long enough… but then again, it never is. I spent a portion at the beginning of my periods just chatting with my students. While I normally dive right back into class, I talked to them and asked them questions about their break. (We could have done this as a circle, but I literally wanted to take 5 minutes and a circle would have taken longer than I truly wanted to spend on this.) I talked to them about what the plan was for the day and we reviewed our objectives for the week. I also assured them that I was willing to ease them back into the work by reviewing some of the information with them, but they had to actually do some of the work and avoid laziness. (But they are middle schoolers, so lazy was present to some degree all day.)

8th Grade

Right away we dove into working with parallel and perpendicular lines. We need to recognize that there is a relationship between the slopes of these lines and use these relationships to develop equations for lines that are either parallel or perpendicular.

While I was tempted to start with a set of notes on the topic right away, I decided that it would be more beneficial if students recognized the relationships prior to developing a formal definition of them. Thanks to @jennbartels who posted an activity on twitter, I found a resource that walked students through the relationship and made it fairly obvious for an 8th grade student.

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Sorry… I don’t own this document, but here is a photo to give you an idea.

I was impressed by how many of my students remembered the general format for slope intercept form and how many of them rattled off the slope equation when prompted. We started with the parallel lines activity and then moved on to the perpendicular lines portion. I had to walk them through finding an equation for one of the three lines that they graphed because they were not as confident because of just coming back from break, but once I helped them with one, they were able to complete the others alone.

7th Grade

We started our unit on Ratios, Rates, and Proportions today. We kicked things off with a task to ease student in and help get their brains to think mathematically again. It did not go as smoothly as I hoped, but it wasn’t a complete disaster. Mostly my students this year are more advanced then where my students were last year. The 6th grade teacher has already spent a good deal of time with them on proportional reasoning and they were quick to jump to answers.

We did the candy jar task where students are given a candy jar and are then asked to upsize the candy jar. My students quickly recognized the ease of multiplying by 20 to increase the content contents and getting them to explore other options was a challenge. However, when we got the the part-whole relationship they struggled more. I saw two strategies but they struggled to explain their relationships as it compared with the problem.

When I recognized that this task was a bust of sorts, we moved on to the notes that I had prepared about definitions of ratios, rates, and proportions so that we could spend sometime solidifying their understanding.

Remember to Live Long and Learn!!