Tag Archives: rates

Day 23: Case of the Mondays

Today was pretty rough in first period Algebra. I made it about halfway through the lesson and lost all motivation to move forward. The content was dry, students were half asleep and I realized there was almost no value in what I had prepped.

Before going into that, my next period I had to start with something to get students going and to get me going. So I had students go through this activity. It was really interesting to see students become so quickly conditioned, which makes me really think about how easy it is for ME to fall back to direct instruction at times.

Students are so used to having 20 minutes of lecture then 30 minutes of book work followed up with homework that I feel like I am abusing the system when I structure class in that way. This style is so natural for students and nice because all the expectations are already laid out on my end. But, I went into education with a different style of teaching in mind. I do not feel any passion in the subject of students when I teach that way.

Anyways…

I started today with the following slide:

More of them rates

More of them rates

Students ask for the price; so I gave it to ’em.

day23.1

Do we want $/oz or oz/$? Calculate whichever you think is the most useful.

day23.2

We had a nice discussion about how grocery stores do this for every. single. product.

Then I had a voice in the back of my mind…

“If stores do this for every product, why bother calculating these rates?”

I ignored it for a while and transitioned into more rates. After students did enough to get bored I mixed things up:

day23.3

“Where did the dollar sign go?” was the question I asked students. None of them could answer.

Perfect, this leads really well into dimensional analysis, which is exactly what I had prepped for.

We converted between feet and inch for a while then I threw up mph to ft/s and this happened:

A rounding error happened somewhere along the way.

A rounding error happened somewhere along the way.

Students were able to see what was going on behind the scenes, which I thought would be good. We checked our work using Google.

day23.5

This is the point where I broke down. What is the point of using long hand conversions when Google can do it in 0.28 seconds? Throughout the day I kept telling myself that it is important for students to see WHY something happens and where units come from, but deep down inside I just don’t believe that.

Today, there was no real foundation for why we use unit conversions, it was just there to say I had taught it. I could give students a bogus answer for why we use them and move on, but in reality Google is just flat out better. I am not really sure where to go from here, probably just keep moving forward and check this off as a great day for personal reflection.

Day 22: Rates + follow up

Concept tests in both classes today. Student’s scores are always going up which is great to see. In Geometry we finished up some practice on conditional statements and inductive reasoning. I have not been following the textbook’s sequencing of these things and feel like it is going well. With logic, students need to practice bits and pieces of all kinds of reasoning at the same time rather than simply going through them as different concepts.

In Algebra I started with a number talk:

day21

I swear I didn’t encourage any of this! Not even absolute value…

Last year I gave the same question but on May 18th or something and got this:

18 +0

17 + 1

16 + 2….

When we do number talks/visual patterns I tell students that I am only interested in how they are thinking about things, not the end result. It was really funky to begin with and students were uncomfortable with a focus other than the answer.

What I saw in the number talk today validated everything I have been doing this year.

After, students ranked the following from most expensive to least expensive.

day21.2A few students were hesitant and wanted to know how much of each, I kinda sorta ignored them. Then showed this:

day21.3

This slide got them fired up; a bottle of water for $17.99?? What? Then they started asking what each of these were measured in.

day21.4

Then they went to the power of Google to convert each into mL and re-rank the items. (Shout out to Dan for this idea)

A lot of times the blog post ends here and there isn’t much talk about the follow up. Well here is what I did.

In their notes, students wrote down the definition and examples of Ratio, Rate, and Unit Rate. We talked a little about how each of these tied into the activity. The vocab helps students communicate what they are finding; rather than saying I divided ______ by _______ they can now say I found the rate of $/mL and so on. The vocabulary is actually useful rather than just meaningless writing.

After the test I put up a few practice problems and on Monday we will continue to practice these concepts with the idea of proportions coming to surface.