A Murder Mystery ala Precalculus

A team member of mine has a really great lesson using Newton’s Law of Cooling to solve a murder. We like to make it more fun than just “doing the math” to solve the problem, so we create a little scene to inspire our students! Here is this year’s set up complete with a dead body under a sheet and a “chalk” outline on the floor (gotta thank my son for getting on the floor so I could create that part!). We got smart this year and did one set up in a central location so all the precalc classes could use it (why we had never thought of that before this year is a mystery in and of itself!) I love this day and this activity!

Speaker and Scribe – Calculator Style

Knowing how to work your own calculator is sometimes just as important as knowing how to solve a math problem especially when it comes to logs! In my precalculus class we did an activity through our notes the other day to practice calculator work. We were focusing on word problems using log, ln and e. Once we got the problem set up to solve it was time for “Speaker and Scribe!” Here are the instructions:

It was very revealing for students if they knew how to operate their own calculator real quick! Knowing the right amount of parentheses to use was a huge eye opener! Plus this way they couldn’t just fake their way thought it, they were forced to work with someone and they only way to get the answer was with their partner.

I have heard about “Speaker and Scribe” used in other ways, but this really worked out well for my precalc kids!

Making Examples…Not My Job Today!

They say (whoever they are!) that the best way to learn something is to teach it. Today as part of my Precalc lesson on log rules they students did just that! We went over the rules, which are actually a review from last year’s math class, and then we did one example together. Then it was the students’ turn to be the teacher. Each student created their own example on their whiteboard. Then they traded whiteboards with a someone around them. Students then had to solve the problem in front of them and when they had completed it give it back to the author for checking. Students were thinking at that higher level that we strive for when they were creating their own problems. A lot of students found that creating and correcting their problem was not as easy as they first thought it would be. It was a simple thing to change in my lesson and it had great benefits. A deeper understanding of log rules…yes, a deeper appreciation for their lovely teacher…maybe that too! 🙂

Rational Exponents – “Teach My Lesson”

(#MTBoS Blogging Initiative Assignments #4)

Second semester has just begun and we spent the first four days of Precalc doing a little SBAC preparation by taking the computer based ICA and the performance task, and then going over it as a class. (Another post on that later.) So yesterday was our first time being back to our “normal” schedule. We started our chapter on Exponents and Logs (which makes students terrified because they totally didn’t “get” this topic last year in Algebra 2/Trig) and first up was “Rational Exponents.”

Janelle’s Brain: That was a good idea I had to make them grab their whiteboard when they came in the room – I hate passing out those things and the students just do it so very slowly. Having that reminder right on the first slide of the PowerPoint a good idea.

First was to review the “rules.”

Janelle’s Brain: This slide is super overwhelming! Good thing I have it showing just a bit at time. And is there a better way to get this info out to the students? I mean, these rules go way back to Algebra 1 class, they do still mix them up sometimes and but really the lesson isn’t designed to LEARN these, just be reminded of them, so maybe it is okay. Plus I know the lesson gets better later. But maybe this is not the best way to start.

The first example we do together. The students have whiteboards because of another part of the lesson, I decide to have them do the first part of the question on their whiteboards – writing the expression in radical form.

Janelle’s Brain: Good thing I did, because – yay!!! – spur of the moment teaching moment. I noticed that across the class the kids had three types of answers and only two of them were correct. I nab three boards from kids in the front and show them to the class. We talk about how they are the same and how they are different and how two of them are great and one of them could be better and how important parentheses are and remind them about order of operations. I reassure the one I grab the “not so good one” from that she was totally not the only one who had that answer and she is good with that. I think I have developed that “safe classroom culture” that experts always talk about so students are okay with making mistakes. Win – high five to self.

Now we get to the part of the lesson I am proud of and that we adapted a couple of years ago – “Two Truths and a Lie.” It is a good way to have lots of examples and the students can get exposure to common mistakes that they themselves might make. Plus we ask them to fix the mistakes and say what went wrong.

Janelle’s Brain: Hmmmm, these exponents, especially the fractions ones are super hard to read!! I hustle up to the front and read each problem off in my super slow teacher voice. I am reminded that I DESPERATELY NEED (okay, WANT) a new projector with higher lumins. And how do I even spell that word? And who do I need to talk to to make that happen. I thought that one day the Assistant Supe was in here we talked about that. Hmmmm…oh yeah, I am teaching right now…back to the students.

We plug along. We do one example together and then “Two Truths and a Lie” for another set.

Janelle’s Brain: Ooh, let’s explain WHAT we are going to have to do, before we do it for this example. I tell them to quickly write on their board what they have to do to simply with those fractional exponents. As a “class” they come up with a good answer. I have three students read off what their board says and we have the idea.

Last set of examples.

Janelle’s Brain: Yikes, this last set is crazy…30 seconds in I instruct the students to work together with their peeps around them. That new girl in the back who just transferred to me is working super well with the girl in front of her – good for them, that was easy.

Last example, a word problem, the students favorite. They answer it on their whiteboards.

Janelle’s Brain: Yep, they all got the right number, but not all of them put the units. I am usually super lazy about labels, so I remember that I am not supposed to be lazy and I am supposed to “attend to precision” so I make them all look around at each other whiteboards and put them back down to fix something if they feel they are missing something. Good teaching moment, even if it was a short moment. And a good reminder to myself.

Lesson over. Boards go back into the bin.

Janelle’s Brain: Overall that was good…I liked the discussions we had about the mistakes we made ourselves as well as the mistakes from the “Lie.” Lunch is next, happy face. I wonder if lessons like this are okay. Was it too boring? Was it effective? We will see when it comes to Monday and I see how the homework went.

 

Questions on Tests…Okay to Better

I have attended some trainings lately that have focused on asking better questions on tests, not just the same ol’ solve ’em kind. Here is a few that we had come up for our last Precalc test.

• We added this one. It really showed if the students knew their vocabulary and the differences between the graphs. (We were proud of this one!)

• We also added this one. I like that the students had to categorize the choices into what worked and what doesn’t. It felt very SBAC-ish.

• I had thought of including this question, but it ended up on the cutting room floor. Mostly this is because i felt we didn’t give the names of these tools quality time in class and this particular problem may be better suited to a group quiz situation where the students can discuss it with one another and then formulate a response. (So I am keeping in my brain as a quiz question for next year!)

• This last one was a test question, but I really felt it could have been better. I could have made it more open and creative for the students. I think a better version would have been to ask students to create their own polynomial of a particular degree, say 4, that had a specific number of each of the roots. Maybe next year on that one!

Writing test questions that cover the material but at the same time challenge the students to really show their mathematical understanding is a hard job! But I am always trying to improve and increase the amount of thinking I ask my students to demonstrate to me!