Day 24: Proportions

It was a new day today and things went great. In algebra I put up the following pictures (credit goes out to Dan)

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I wish I would have read a little more into his post before today; I lacked the strong closure and connections. After talking about these for a while, we dove into proportions.

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Students didn’t have much trouble with these, but we had some great conversations on the different methods of solving each. A lot of students were looking for patterns between the two ratios so when I threw this one up they were perplexed.

day24.5We talked about how most of the time we see a variable in the numerator of a fraction and worked on using inverse operations to get it there. I was hesitant to simply tell them the technique of cross multiplication without any reason for WHY it worked. We will get into that tomorrow and follow up with some practice for most of the period.

In Geometry we worked on syllogisms and the law of detachment. I used the witch clip from Monty Python and Direct T.V. commercials to introduce the concept then followed up by having students write their own. They really seemed to enjoy this!

Much better day today!

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.

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

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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:

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“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.

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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:

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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:

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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.

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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.

Day 21: Super Bear

Geometry wrapped up Sam’s lesson on Conditional Statements and went through a gallery walk.

IMG_0330 After we talked about what puzzled them and questions they had. One area students struggled was seeing relationships between the posters, they were hesitant to draw any conclusions which I see as a good thing. We debriefed with an example then went through some practice statements.

In Algebra students worked through Super Bear which is another of my favorites.

Here is a quick run down of the lesson:

I had students fold a scratch sheet of paper into 6 regions which will later be used for the following:

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I then played the clip and asked students to write down the first question that came to their mind. They shared that with a neighbor then we put them up on the board. After each question I asked for a show of hands for anyone who also thought the question was interesting and put + that number at the end. (This helps me focus on the big idea – brain storming – some questions are not very relevant and that is OK.)

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Typo… oh well.

Then students estimated how many mini and regular bears it would take and we threw those up on the board too with names attached.

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After this students brainstormed what info they needed to answer the question.

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Then I gave the info I had to ’em and set them loose to solve the problem.

We put our calculated answers on the board too, not so sure how productive this was. Students really wanted to just get at the answer and it felt like I was making way too many lists. I also went back to the estimates and we looked at who was the closest.

After I talked a little about rates and how it tied into this problem then students named the activity.

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Once we wrapped this up I went back to the list of questions and addressed each of them, which brought some great closure to the period.

Day 20: If… Then…

I spent a lot of time today talking about college and telling stories about my crazy roommates. It is important for students to see that I am not just a mean-lean math machine. Plus it was college day so every teacher was sharing out.

Algebra spent the rest of the time practicing absolute value and multi-step equations.

In Geometry we picked back up on Sam’s lesson. Students created big and little posters, we will gallery walk tomorrow.

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A few take-aways:

  • I did not emphasize that the black statement card is true; therefore their first statement needs to be an If Then version of it.
  • Students started off slow but quickly picked up on what was happening.
  • I am really excited for the gallery walk and giving students time tomorrow to work through and discuss which statements are logically equivalent.
  • Some students mixed up the order of the statements, this will also be interesting.

Day 19: Age Estimation

Introducing absolute value is one of my favorite lessons of the year.

Crazy.

Once again credit for this lesson goes out to Dan.

I pretty much followed his structure, just a few things are different which I will mention after we get through the good stuff:

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Copy this down in your notes, you will have 21 rows.

For the first entry; students write down the name and their guess. I provide no structure or hints, we have practiced estimating a ton, let things happen.

Team Edward; how old do you think this guy is?
Team Edward; how old do you think this guy is?

We get through all 21 slides then go through another 21 with their ages

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After ask students to total how much they were off for each celebrity then add all those together; the person who was off by the least gets a homework pass. Let them run into problems, don’t take that away from them.

After a while students realize that there is one serious issue; under estimating an age. Say one student guessed Willie was 42 and another 44. Both off by 2, how should we deal with this?

No big deal; drop the negative.

We find the totals again; I made it a competition between my four algebra classes. The lowest 5 went up on the wall and will stay there for the rest of the year.

Finally, we moved into absolute value, smooth transition for students.

In Geometry students started Sam’s lesson on conditional statements. So much good happened here, we only made it through the sketching and first discussion. I couldn’t help but laugh at some of the statements in the slide show. More on this to come tomorrow; here are a few finished products in the mean time.

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Day 18: Station Review

In Geometry we needed some time to go back and review a few concepts. Part of the reason for this is my class has been chatty and I didn’t do much about it. The other part is students have been rushing through everything, not much patient problem solving goes on during some days. And that is fine, it takes time to get there.

One activity I use for student review is stations, here is how it goes.

  • Students break into groups of 3 or 4, which I use Instant Classroom for.
  • They have 6 minutes to work on the problem at their station.
  • I set a timer, once it goes off they rotate.
  • While students are working I listen in and write some of things I heard up on the board.
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This lets students know I am listening and a part of the class.

Now after this point I am not quite sure where to go. What I have been doing is having students staple all of the group members sheets together and randomly grading one. This holds all students accountable for the work. There may be better ways out there but this has always worked for me.

For algebra we solved equations for a specific variable, have a look;

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I struggled today; my classes were pretty noisy and it felt unproductive. I was thinking about why this happened, and here is my recap: this concept is not very useful. 

Sure students will use this to solve equations for x and y and MAYBE sometime in future classes like Physics and Chemistry. But will students be doing this anytime soon? Or an even better question; Will this concept be beneficial for any conversation we will be having about math in the next few days? Weeks? Months?

I taught this purely based on where it is placed in the textbook sequence and to be honest I don’t think I will keep this next year. Another problem was I did not have much enthusiasm about this and whenever that happens the negativity goes straight to the students.

After my experiences today I want to try and do a better job of asking myself “Is this content going to be beneficial for students in the up coming weeks?” and not simply base my response to that off where the concept happens to fall within the textbook.