Cutting Geometric Solids with Crafty Cut

I knew there was a better way to teach what cutting geometric solids looked like and wanted it to be more hands-on and visual. I felt the normal stand-up lecture or worksheet wasn't enough for students to learn. The first thought I had was a hands on activity with Play-Doh and forming shapes. Then I stumbled across Crafty Cut.

(P.S. Make sure to use the link above or get the one with the P in the bottom right hand corner.)

Crafty Cut is a gamified version of cutting geometric solids. There are a bunch of different modes, but the free "unlocked" version only gives you Cut Mode (Most Important), Combine, and a Create Mode.

The way I did it was 1st day students played all the way through Cut Mode on their own or if they got stuck they could ask their neighbors. If they finished early they could work on combine mode, which is a little more difficult to get all 3 stars. But in Cut Mode they are given different 3D shapes and have to make different 2D shapes cutting it. Students liked the problem solving in the app.

One of the first ones you get in Easy Mode is to cut a rectangle from a Cylinder, here are some screenshots from the game.






It was a different app that let students explore cutting geometric solids instead of the typical lesson.

Is it Linear? With Fidget Spinners

Fidget spinners are all the rage right now. At my school I would say maybe 10% have them, one thing with fidget spinners that my students are using right now is an app called Finger Spinner. The point of the game is you get 5 tries to reach the highest number of spins. With each number of spins you get certain coins which you can upgrade your fidget spinner such as increasing speed or greasing the wheels.

Introduce the topic is by having out an actual fidget spinner and spin it twice and ask the students were there the same amount of spins both times? Some will say yes since it is the same fidget spinner and some will say no, because it determines how hard you spin it.

Then do the same thing with the app, projecting it on the whiteboard. Spin it once and then twice. Since it counts the number of spins it will be easier to ask if they were the same.

The next question is how many times would I have to spin it to get to 100 spins?

 

I have been using this handout from Estimation180: http://www.estimation180.com/blog/estimation-180-handout to have students record their answers in one place.

I want students to look at the data and see that each one is about the same in number of spins and looks linear. Using the whiteboard I want to project some student work start from the basic ones to the student work where they have a linear graph sketched (w/ average). Then have the student explain the processes they went through.

The last part is to get students using the app. My question to them is once you upgrade a part of the fidget spinner does it stay linear? What if you keep upgrading? What if you alternate upgrading? How does it effect the number of spins?

My goal next year is to incorporate more modeling and more hands-on uses of math concepts.


Geometrical Dodgeball

I am not the worlds greatest geometry teacher. In fact I am not the best in the school that I teach at.

One thing I dislike about teach geometry are the number of theorems and how old school geometry is in the way of teaching it. I know I hear it coming already about patty paper and all the things you can do with it, but it's not the same. There is no real life situation when you have to know the Central angle theorem. 

One thing I have been trying to do more of is getting students outside and playing games. Right now we are learning about polyhedra and their surface area and volume. Right now we are trying to remember the names of different polyhedra with different sides, triangles, quadrilaterals, pentagons, etc. Some students remember it from 7th and 8th grade, but those have become high school standards now in Nebraska. The way we learned this was by playing two groups of geometrical dodgeball, we played this outside, but would work much better in a gym.


The way the game is played is everyone is assigned a number and stands in a circle, one person throws the ball up into the air and calls out a number, when that person touches it they yell stop. All players stop and they get 2 free jumps to get closer. If they get hit, they are out, if it is caught or misses the thrower is out.

The way I mathematized it was at the beginning of the round they had to name the polygon they formed if someone was out and named it first they got to jump back in. I played it with two groups outside and worked well since there were shortened periods.

Using Elink for Self Paced Learning



These last two weeks have been crazy with the ACT test, MAP Testing, and being gone for soccer. One new tool that I have found is elink.io this tool allows me to create a place where students can access videos, sites, and anything else with a link. One of my goals from this year was to have students more in charge of their own learning. I want them to be able to take information I give them and be able to apply it accordingly, next year I will do a better job of giving students more opportunities to do this on their own and find videos that they listen to and engage with.



The one thing I love about elink is that the site looks good, it looks like it wasn't done by me, but more like a professional.

Since I was testing about 5-10 students per class, the other students had this worksheet to do in class.

It introduces students to adding/subtracting and multiplying matrices by a scalar. This is normally a lesson that takes a day, but really shouldn't.

I gave the students this link: https://elink.io/9b9c4

As I got the students started on the MAP test, I told them the link would help them with their worksheet and to take notes on each video or save it to their iPad for later.

Most students only asked questions if they were doing it correctly, now looking back I should add videos that explain odds to see if students are correct or are on the right path.

elink.io would be a great tool for flipped learning.


Conic Section Day 1-3

I always felt that my conic section unit was lacking and needed something that tied everything together. I had a bunch of activities, but nothing that was solid. I decided that the unit needed an overarching theme and some project based learning opportunities. I want it to be engaging and real world.

I settled on roller coasters.

Day 1:
Students have a virtual reality video to watch on DiscoveryVR where they ride a roller coaster. Then they have an introduction to conic sections where they are given play doh and a plastic knife to play surgery, I did this activity last year: Conic Section Surgery












Day 2:

I started with Parabolas and asked them to complete a Desmos Polygraph Activity over Parabolas.

Then I went over the first project with the students, students will construct a working paper roller coaster.









Students started their paper roller coasters.








Day 3:
Students read an article on Newsela about roller coasters and were asked to identify the main point, supporting details, essential elements, and asked them to circle words they didn't know. When they were done reading and annotating they were to summarize the article in two sentences using the essential elements.



Then we went over the first day of parabolas, where students graphed parabolas based on an equation.

Exponential Growth through TAG

After a great day of teaching exponential growth and decay, I felt like my students really knew the topic forwards and backwards. We did this Desmos activity as some students were finish up their MAP test.


It was a great Desmos activity, almost all the students wanted 100$ at the beginning and very insightful finishing questions at the end and I was pleased overall. Later that day I began to wonder if students would notice if something was exponential or not exponential if I gave it to them. I thought to myself how could I find a question that I could do that would model exponential growth or decay.

Then I found this game: 


I wanted an activity that got students out of the classroom. Since I have two periods at the beginning of the day we did inside in the gym, but the last time we went outside and played it on the Football field.

If you didn't watch the video, it is a simple game where one person is a shark, they yell "Minnows come out to play." the minnows job is to make it to the other side without getting tagged. The sharks job is to tag people, once a minnow is tagged they become a shark.

Here comes the math:
I had them start out with one shark, I made all the others line up and asked them how easy it was going to be this time down. All of them were confident that they could make it down without any real sweat, then I asked them what about the 5th time down? I was surprised how most of them thought it was still going to be easy, thinking of it linearly instead of exponential. We played it through the first time here are the pictures and the charts we did at the end.



Here is one of the charts that I made after each run down and back.


After all the students were tagged on the 4th down and back with ease. I asked them to estimate how many would get tagged on the fourth time back. Then I asked about the whole school, how many down and backs would there be playing with 576 students?

We came back after playing 2-3 more times. Then asked them how you could write an equation to model the graph. We did a short mini-lesson on finding equations of a exponential graph.



Solving Trig Ratios and Google Expeditions

Last year I did a solving trig ratios using Google Cardboards and the app Google Cardboard, but on Android devices the app is different from one platform to the next, so I needed an upgrade. I have been looking at Google Expeditions for a while now and finally had enough Google Cardboards and extra VR headsets (thanks Alice Keeler!!).

Google Expeditions was a great app and it allowed me to introduce other concepts like history combined with math. Another added benefit was that most of my students are from Mexico, Honduras, and Guatemala and some of these ruins were close to where they use to live.


My favorite thing is that I can direct students to look at something while reading and comes with questions to ask the students. I didn't use all of the questions, but I did use the intermediate question when it came to the number of steps. I could direct students to use their made sextants to find the angle of elevation to answer the questions.


Here are some of the students on their expedition.




Here is a link to the worksheet that students had to fill out and guide them: goo.gl/uRcvkR