One of my favorites lesson this year was Project Runway. When I think of teaching and learning geometry I think of the most boring lessons, some of the theorems can be hands-on, but to me patty paper is not hands on. It's visual, not interactive or engaging.

We were finishing the very first lesson in circles. Students just learned about chords, radius, tangents, centers, and secants. We reviewed to start the lesson what each vocabulary word was and what it meant.

I put students in groups, you can have them choose their own groups, this class couldn't handle that though. Plus, I was still in my visibly random groups phase (#VRG).

I played the introduction to Project Runway on YouTube. https://youtu.be/cqQrdkv-WTo

I told the students you are given 20 minutes to put together a piece of clothing for a fashion show on Project Runway. You will need to include different vocabulary words from our circles unit as your creation makes its way down the runway. You need to include: secant, tangent, chord, radius.

The second part was that they needed to select a model from their group to model down the runway. The two other designers will point out each of the properties of a circle. At the end they needed upload a picture of model on Seesaw and label each of the parts.

All of the students finished in the 20 minutes. They worked extremely hard the entire time and even though they had trouble finding a path to go down and work as a group, it was a learning experience for everyone.

Here are some of the models as they go down the runway. The students convinced me to play Beyonce softly in the background.

One of the things I need to work on this activity for next year is to give students planning time in the beginning for them to gather their thoughts. Secondly, tell students that they can not write on their project runway clothing.

### Geometry Project Runway

Labels
circles,
geometry,
project runway,
radius,
tangent

### 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.

(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.

Labels
2D,
3D,
app,
crafty cut,
cutting,
geometric solids

### 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.

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 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.

Labels
app,
equations,
fidget spinners,
finger spinner,
functions,
linear

### 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.

Labels
elink,
flipped learning,
matricies,
matrix,
self paced,
student 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.

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.

Labels
annotating,
article,
Conic Section,
desmos,
discoveryvr,
paper roller coasters,
parabolas,
polygraph,
reading,
vr,
writing

### 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.

Labels
activity,
decay,
desmos,
exponential functions,
exponents,
growth,
minnows,
outside,
sharks,
tag

### 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.

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

Labels
cardboard,
expeditions,
Google expeditions,
math,
ratios,
solving. trig,
trigonometry

### Probability Through Caine's Arcade

First day of our probability unit we watched this video.

Day 1: I chose this video, because most of my students are hispanic and I think the biggest thing in our school right now is empathy. We talked about having games of chance like in the video they just watched, what does chance mean? We did our first section of probability and told them they were going to create their own games, just like Caine did.

We did a 5 question check for understanding and told the students they needed to finish the bottom half of the checklist today.

Here are other great resources including the checklist: http://cainesarcade.com/schools/activitykits/

Students designing their cardboard games. |

Day 2: We talked about conditional probability. Did another check for understanding on Kahoot. Then I got lots of cardboard boxes from our recycling bin and had to make a quick pit-stop at Dollar General for more cardboard boxes.

Day 3: I had a substitute teacher this day, but students started creating their boxes.

Day 4: We went over theoretical vs experimental probability. I gave students 7 minutes to finish their cardboard arcade games. Then we went over theoretical probability again. We talked about geometrical probability from Day 1. Students were given rulers and yardsticks and had to find the theoretical probability of successfully completing their arcade game.

Day 5: We finished the material for our probability unit. I gave students 5 minutes to make sure their game is playable and to finish anything on the checklist. Then we went over that I would give them 5 minutes to go play other games to get other groups experimental probability, then the partners would switch and the other partner would go play games.

I thought this unit was much better than the 3D dice activity from last year, this project was more hands-on and did a better job of combining the curriculum and the project together.

Labels
algebra 2,
Caine's Arcade,
designing,
maker,
pbl,
probability,
project based learning

### Statistics Sampling through Articles

In our statistics unit for Algebra 2, we talk about measures of central tendency then we go over different types of sampling. The four we talk about random, convenience, systematic, and cluster. Students don't really know what these are, we talk about when people are surveyed there are different methods to survey those people. Then we go over survey biases. It is a pretty boring lesson, students already know mean, median, mode, and range. They don't really get why we go over types of sampling.

I trimmed down and this article from The Street:

https://www.thestreet.com/story/13954993/1/pictures-of-mcdonald-s-new-big-macs-are-already-sweeping-the-internet.html

To summarize the article it is about the new Mac Jr and Grand Mac, in the article it says, "McDonald's started testing the Grand Mac and Mac Jr. in more than 120 restaurants in the central Ohio and Dallas areas in April last year." This is the basis of what I wanted the students to pick up out of the article, but thought this might be a good chance to get them inferring reading in the math classroom.

Students read the article, I gave them 5 minutes to read and answer the following 5 questions:

I trimmed down and this article from The Street:

https://www.thestreet.com/story/13954993/1/pictures-of-mcdonald-s-new-big-macs-are-already-sweeping-the-internet.html

To summarize the article it is about the new Mac Jr and Grand Mac, in the article it says, "McDonald's started testing the Grand Mac and Mac Jr. in more than 120 restaurants in the central Ohio and Dallas areas in April last year." This is the basis of what I wanted the students to pick up out of the article, but thought this might be a good chance to get them inferring reading in the math classroom.

Students read the article, I gave them 5 minutes to read and answer the following 5 questions:

- What is the main point of the article?
- What are two supporting details?
- What type of sampling method was mentioned in the article?
- Why do you think McDonald's chose that type of sampling method?
- Do you think the authors view of McDonalds were positive or negative? Why?

I was surprised about the level of detail that students put into the article here were some sticky notes and students working on the article.

Next year I will try to put the article on ActivelyLearn, last year it was my go to place for articles and mathematics for Junior Standards Math. I will have to use more articles in math class, it was a good experience for me and my students.

Labels
algebra 2,
article,
central tendency,
cloze,
reading,
sampling methods,
statistics

### License Plate Combinations

When we come back from winter break we normally start our probability and statistics unit. I normally take a week for probability and a week for statistics which normally melts into three weeks. I've always thought nothing of changing it, but during winter break Dan Meyer posted "Plates Without States" Since we were going over permutations and combinations I thought this would be an excellent way to get students thinking about how many different combinations there are in license plates and why they make them like that.

To start the lesson I had students go through Dan Meyer State-Plate Game. Students were definitely engaged and loved playing against each other in their groups.

Next we talked about license plates and I separated it from combinations and permutations.

I gave all of the students a blank license plate and a card. The card had a name of a city or state and a population that students had to take in consideration.

Here are some of the license plates that students were working on.

When students were done with their license plates, they took a picture of their license plate and put it on SeeSaw. The last part they had to do was comment on three others the number of different combinations that they had with their license plate.

Here were a few students figuring out and commenting on other students post.

I like this activity much more and students realized how license plates play a role in local governments and how the population of an area can control the different license plates possible.

I posted almost all of them in the back of my room here are a bunch of different ones that are posted.

Labels
art,
combinations,
Dan Meyer,
hands-on,
License Plates,
number sense,
probability

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