#pythagorean spirals and other projects

[187days]

Day Eighty-Nine

Today was one of those days that made me wish I had a clone because I had so many things to do- and sometimes simultaneously! The Vice Principal asked team leaders to meet with her this morning because 8th Grade Transition Night is coming up in March, and a lot of planning goes into that, so we needed to start now. That took basically an entire block.

Then I taught World, which went pretty well. I mentioned yesterday that I thought students would be more prepared to present their mini-projects, and, for the most part, I was right. I still think next year I’ll plan on giving them one additional day to work, though. I said that to Mr. F when he came over to chat about how it had gone for his geometry students (whose mini-project was to explain the spiral they drew and decorated in the Middle Eastern style), and he totally agreed. But we’re happy with how this went. It was our first time trying a new thing, and it was cool. 

During flex time, students who were interested in helping redecorate the ninth grade house bulletin boards came to my room. Two of the boards are right next to each other, so we decided to put the Choose Love themes on one board, and put examples on the other; students brainstormed instances of courage, compassion, forgiveness, and gratitude in their lives and/or in things they’ve been studying. I left them to it while I went over a unit test with two of my APUSGOV students, and by the time I was done they’d thought of enough examples to cover the board, so we went out into the hall to start putting them up.

We ran out of time before we finished, but a few of the students had Block 5 study halls and offered to come back, which was great. I had a meeting for part of the block, but I made it as quick as possible (I think I may have annoyed half of my team, but Mr. F and Mrs. T also had other things they needed doing, so it wasn’t just me), then went back out to help. Awesome thing: there were scraps and staples on the floor- which happens during bulletin board decorating- and these kids went and found a broom and dustpan to sweep up. I didn’t even have to ask. 

There was a faculty meeting after school, so I missed most of track practice. I made it for the last half hour, though, so I was able to direct the cool down, core exercises, and stretches- which I do at every practice, that’s one of my responsibilities- and the administrative assistants offered my team all the veggies and crackers the faculty didn’t eat at the meeting. They were quite happy about that. 

Tomorrow’s going to be a busy one, too. Stay tuned!

[marco42james]

Spiraling squares – compass and straight edge

Can you see the many spirals in this design?

Students calculate the size of each increasing round of squares and consider what sort of spirals these must be.

The activity: SpiralingSquares.pdf

Working with a little mathematical art is a great way to end your school year.

Polar graph paper with initial round of squares: PolarPaper+FirstSquares.pdf

For members we have an editable Word docx, solutions to the activity, instructions for creating the design with compass and ruler, and a blank spiraling square picture for simply coloring.

SpiralingSquares.docx      SpiralingSquares-solutions.pdf

Instructions on using compass and straight edge to create this design:  SpiralingSquares-compass-directions.pdf

BlankSquares.pdf for simply coloring.

Below are some other great math/art projects to help students visualize mathematics

Wheel of Theodorus

Work with Pythagorean Theorem and visualizing irrational numbers.

Pythagorean Triples

Discover Pythagorean Triples and find patterns in their development.

Fibonacci

Learn about the Fibonacci pattern and find some of the beauty in the sequence.

Pascal’s Triangle

Modular Math – Filling in Pascal’s Triangle can be tedious and cumbersome unless you know how to use modular math. Probability – How many ways are there to put 3, 4, 5, etc events in order? Binomial Expansion – There must be an easier way than long multiplication.

from Yummy Math https://www.yummymath.com/2019/spiraling-squares-compass-and-straight-edge/

[mathematicianadda]

Spiraling squares – compass and straight edge

Can you see the many spirals in this design?

Students calculate the size of each increasing round of squares and consider what sort of spirals these must be.

The activity: SpiralingSquares.pdf

Working with a little mathematical art is a great way to end your school year.

Polar graph paper with initial round of squares: PolarPaper+FirstSquares.pdf

For members we have an editable Word docx, solutions to the activity, instructions for creating the design with compass and ruler, and a blank spiraling square picture for simply coloring.

SpiralingSquares.docx      SpiralingSquares-solutions.pdf

Instructions on using compass and straight edge to create this design:  SpiralingSquares-compass-directions.pdf

BlankSquares.pdf for simply coloring.

Below are some other great math/art projects to help students visualize mathematics

Wheel of Theodorus

Work with Pythagorean Theorem and visualizing irrational numbers.

Pythagorean Triples

Discover Pythagorean Triples and find patterns in their development.

Fibonacci

Learn about the Fibonacci pattern and find some of the beauty in the sequence.

Pascal's Triangle

Modular Math - Filling in Pascal's Triangle can be tedious and cumbersome unless you know how to use modular math. Probability - How many ways are there to put 3, 4, 5, etc events in order? Binomial Expansion - There must be an easier way than long multiplication.

from Yummy Math from Blogger http://bit.ly/2WDl6dX

[187days]

Day Eighty-Eight

One of my APUSGOV students was interning on Cory Booker’s campaign, so today was a bit heartbreaking for her. But she just Remind texted me to say that she’s proud of the campaign he ran, proud of her own work, and grateful for everything she learned. That’s a pretty mature response, and it reminded me that this is actually her second campaign; she worked on a congressional race as a sophomore... 

How lucky am I that I get to teach her, right? And all the others, too.

I wish I could say this was one of my best days of teaching, but, alas, I still have a cold, so I wasn’t on my game. It wasn’t bad, though. APUSGOV was fine. The Warren campaign has a new field organizer in town, so I let her come in and give her pitch. After that, I passed back the tests students took last week, and encouraged anyone with a low score to come and see me. Most students’ test scores are consistently high, or they’re improving, but there are a few who are just stuck, and I want to work with them to figure out what needs doing. Hopefully, they’ll take me up on it... Lastly, it was judicial branch time; students had to read Article III of the Constitution and Federalist 78. One of the boys asked me if I thought lifetime appointments would remain in place if people started living longer lives. He mentioned that some scientists think that a person who will live to be a thousand has already been born. I have no idea if any scientists actually think this, but I didn’t miss a beat before answering, “Well, yeah, it’s Ruth Bader Ginsburg.” 

That got a laugh.

In World, students had to present the mini-projects they worked on last week. The results were... inconsistent. Some students were not done at all (I gave a quick but stern lecture about time management), some were done but their work could have been more detailed, and some presented amazing stuff. I think next year I’ll give them one more day to work before they have to present. I also think, though, that the students I have tomorrow will do better- they tend to with this kind of assignment- but we’ll see. 

[187days]

Day Eighty-Six

The social studies department at my school is a pack of show-offs and overachievers. Next Friday during in-service, every department has to give a presentation on the work that’s been done in PLCs, and our reaction to this has been “Let’s bury the competition.” The CTC teachers think they’re going to have us beat, but we spent our meeting today decking out a Prezi and getting shiny student work samples, and we’re pretty sure they’ve got nothing on us. Heh.

It’s a healthy rivalry, promise. 

What else happened today... I have a student in one of my classes who bows whenever he enters a classroom. I started to curtsey in response, to the delight of my whole class. Today, a student on one of the other ninth grade teams saw me do it because I was standing in the doorway, and was like, “OMG I need to learn how to do that!!!!” Who knew that skill was going to come in handy in a rural, northern school, right?

Oh, and my World lesson was cool. The students who are taking geometry this year spent my class time working on Mr. F’s spiral project. They have to draw pythagorean spirals, do some calculations that I admittedly didn’t look at too closely, and then decorate their spirals so that they incorporate elements of traditional Middle Eastern art (which they learned about and saw examples of in a previous class). They’re going to share their work in World next week. And what were all the students who take algebra doing? A mini-project on a different aspect of Middle Eastern culture: food, tourism, holidays, sports, music and dance, wedding customs, or styles of dress (their choice). They’ll also be sharing that next week. Stay tuned to read how it goes!

Stay tuned for fun in APUSGOV, too. I gave a “halfway” unit test today because this unit is so long, and it went pretty darn well. Up next: COURT MADNESS!