How I Teach Direct Variation

I use to teach direct variation by having students take notes, but the past few years I have been using Jon Orr's Water Bottle Flip.


There is an excellent Desmos activity that goes along with it. This year I copied and edited my first Desmos activity which was this one.

https://teacher.desmos.com/activitybuilder/custom/57f788035db373e705868c8b

I added two slides:



I wanted to emphasize direct variation and ask them deep meanings of graphs. One of the questions I asked was looking at the graph on the bottom, what inferences can you draw?

On September 8, there was the NATM (Nebraska Association of Teachers of Mathematics) Conference. During Lenny VerMass presentation, Smoke and you Croak or Huffing and Puffing to Understand Slope, he had a very interesting task. 

Students had to measure how much air filled their lungs. So we exhaled into a balloon and measured (3) breaths and the circumference of the balloon. Then on a big sheet of paper we had to plot all of our data points for the following graphs and interesting things happened. Try it with your students.


Student Created Kahoot

Kahoot is the first tool that seems universally accepted tech tool in every classroom. I can see why, its fun to play against others. I remember when I was growing up we played a game in middle school called hands down, if you were the first person on the bottom and had the correct answer you scored points, it was my favorite.

But, Kahoot has been placed in a DOK 1 or DOK 2 depth of knowledge when students are playing. It is hard to find Kahoots where students are not only just remembering or applying theorems but creating and evaluating. One of the things I wanted my students to know is how teachers choose Kahoots and for them to not only review but practice and evaluate others Kahoots.

Paper Kahoots


We started in the classroom with paper Kahoots as a lesson. We talked about how long it would take to do the problem, where there answers that were misleading, and what did the student know if they got the question wrong. Here are some examples students made.

You can find a PDF version here: https://kahoot.com/files/2017/07/kahoot_paper_template-1.pdf

 

For students to create their own Kahoots I had to change my username and password, since Google Sign-in wasn't cooperating. Some students took off and were self sufficient other students struggled coming up with questions, because of the content. I had to ask them how to be a teacher and what kind of questions I would ask.

Created Kahoots


Most students took the route of pure vocabulary and no mathematical questions, but I did not specify what type of questions, now I know.

Here were some example questions they came up with:

Artist Sol LeWitt and Points, Lines, Angles

Sol LeWitt was an artist born in Hartford, Connecticut in 1928 he was most known for his conceptual art, however in this overview we are going to focus on his Instructables. Instructables are wall art where the artist has to follow a particular set of instructions. Sol LeWitt came up with a large number of different instructions, some he never did himself.

For example Wall Drawing #65 in colored pencil is of follows:
Lines are not short, not straight, crossing and touching, drawn at random using four colors, uniformly dispersed with maximum density, covering the entire surface of the wall.

This is what Sol LeWitt came up with:


This is bad example, because it does not take in the sheer size of the piece. Since it is a wall piece it is so large that you could not fully see it from one spot.

So how does this relate to math?


Sol LeWitt has hundreds of these instructions were he takes shapes such as squares, circles, and triangles. He also loves lines, some straight some not, and vertical and perpendicular angles. So to introduce and apply the first section of geometry points, lines, and planes. We attempted our own Sol LeWitt.

Our instructions were: On a wall surface, any continuous stretch of wall, using a hard pencil, place fifty points at random. The points should be evenly distributed over the area of the wall. All of the points should be connected by straight lines.

I assigned all students a letter and then had them connect to each other, so we only really had 26 points, but our artwork was just as amazing.



It did take a little bit more time than I was planning, but the picture at the top took 8 days to make.

We talked about lines and line segments and this brought up a good conversation about how we name lines. I would ask a student which one is the longest line, but would not let them get out of their seat. So it was easier for the student to name the line segment than point.

I love using art in the classroom and Sol LeWitt's Instructables are an easy way to get art in the geometry classroom.

Below is a PDF with some Instructions to do you own.



Classifying Rational & Irrational

At the beginning of the year one of the first things we do in Algebra 2 is go over types of numbers. We classify natural, whole, integers, rational, and irrational numbers. The next day we do a group formative assessment where in a group they take turns organizing different numbers into rational/irrational numbers. Then I give each of the groups a get a sheet where they have to organize a list of numbers into rational/irrational and explain why.

Students did an excellent job discussing the numbers and classifying them.

The Math Assessment Project has other amazing resources like this one at their website.






Temperature Drop Pre-Eclipse

I wanted to start the day with a Notice/Wonder introduction. So I asked students to discuss what they think would happen during the eclipse. Students shared somethings they picked up in other classes about nocturnal animals becoming away, lightning bugs might show up, and that we might be able to see stars.

My next question focused particularlly on the temperature and asked what did they think the temperature would do during the eclipse? Students discussed in groups some of my favorites:

"How close would it be to a really cloudy day?"

"Would the temperature drop more than ten degrees?"

"Would the street lights come on outside of school?"




I gave them a piece of graph paper and asked them to put temperature on the y-axis and time on the x-axis. I told them they could use their iPads and any resources they needed to answer the question and discuss in their groups. They had ten minutes to come up with a graph and post it on the wall.

Then I showed them this graphic from the 2001 eclipse in Africa.


I asked them how it would be different, how it would be the same as the eclipse on Monday. I described the activity we were going to be doing Monday and the layout of the day.

Since some of the students had questions about the eclipse, we watched this 5 minute really well done video by Vox.


Then we went outside and tried on a pair of solar glasses to see how they fit and what the sun looks like. Some students even got their camera's on their phone to take a very blurry picture. 



Beginning of the Year: Math About Me


Every year I kick off the school year by getting to know the students in a numerical way. The overall goal of the project is for me to get to know the students, do some math that everyone can do, and have other students in the class see and hear their other classmates.

The outline of Math About Me, is that students are to make a poster of themselves and include 10 numbers that represent something about their lives on a personal level.

For example on my poster I include the number of years I have been married, how many siblings I have, etc. Then students are to make their poster colorful. I eventually hang every single one up in the classroom to show to students that their work is valuable and give them ownership of the classroom.

When they have completed the Math About Me, we sit in a big circle and go around and tell the numbers we put on our poster. This lets me see who is already proficient at speaking in front of a group, who is shy, and lets me hear their name in their voice.

I like this project, I have done it the last four years, even though it changes a little every year. I read Tracy Zager's book Becoming the Math Teacher You Wish You'd Had she explains in her book that she has students write a math autiobiography, students detail their lives as mathematicians. I thought that this would be good to start our writing in math class and then in small groups read the paper and hear each other.

What do you do to start of the school year in your math class? I always hated going over the syllabus on the first day of school, seemed impersonal. Here is my last years blogpost on the beginning of the year.

iPad Apps for Number Sense

Calculator the Game (Free)

You and your calculator gang up to complete different levels. The Game where you'll manipulate numbers by adding them, subtracting them, converting them, reversing them, and stuffing them through portals. You also can change the language now for EL students. 

The best part is for students it helps build number sense and the order in which you can do the problems from front to back or the opposite way. Promotes number sense.

You can find the link here: https://itunes.apple.com/us/app/calculator-the-game/id1243055750?mt=8


Factris (Free)

Factris is a game just like Tetris, but you move each of the blocks in the number of factors of that number. For example, if you got the number 8, you would be able to get the block in a 1x8, 2x4, 4x2, or 8x1. Factris is a classic risk/reward high score game. Resize the dropping rectangles according to their factors and pack them together. Factris is challenging (there is no undo) and you need to pay close attention to the size of the rectangles coming next. Improve your numeracy, packing and knowledge of factors with Factris.

The best part is that students get use to factors of numbers, especially for primes.

You can find the link here: https://itunes.apple.com/gb/app/factris/id1248555092?mt=8

Shape Fix (Free)

Shape Fix is a game where you need to identify the center of the larger shape and try to estimate. This is a good number sense game where students try guess the center.

You can find the link here: https://itunes.apple.com/us/app/shape-fix/id1227483776?mt=8


Eclipse: Math Class

Since we are not exactly in the path of totality we are in the 98% range, I have bought 50 Eclipse glasses through Rainbow Symphony. I want students to enjoy the eclipse, this is my first solar eclipse, but I am also an astronomy geek. Below is what Schuyler, Nebraska will look like at that time.


Day Before Eclipse

I will use this video as an introduction to the eclipse: https://youtu.be/BmOR4XSZoIQ

On that day we are going to be citizen scientists, we are going to be measuring the temperature change during totality. On this day we will talk about what the temperature drop will look like and what type of graph might that be for the entire day? We will take guesses and put them up on the white board. Each student will be given one of the worksheets below and ask them to fill it out and be as specific as possible.

Here is a link to this graph: Graph Worksheet


After all of the students have recorded their own answers, I will show them the air temperature in Lusaka, Zambia during the June 21 solar eclipse. Ask them how it will differ


I will ask the students how this will be different or the same from their graph, and what the change in air temperature was and how they think they measured air temperature.

We will go outside and test our Eclipse Viewers to make sure all students know how to use them.

You can find the activity here: Temperature Change during Totality

Eclipse Day
For the 2 hours before and after the eclipse we will go outside on the soccer field and measure the air temperature every couple of minutes. For the time that the eclipse is happening, I will take the readings so the students can enjoy the eclipse.

Students will have their own recording sheet, since we are doing our more frequently than the one in the worksheet. I will have to change it.

Here is the link with all of information and this worksheet above attached here: Citizen Scientist

Day After Eclipse
I will compile all of the data that the students took and import it into GlobeObserver for the Citizen Scientist project. Also I will give all of the students the raw data and ask them to extrapolate. I want students to ask questions at the beginning of class and answer them to the group at the end of class. Example questions would include: What the graph looked like? How far were we off? What was the temperature drop? Did the air temperature drop faster or increase faster?

I want to make August 21st a learning experience, but also a chance to see something they may never see again. Some students might not see another eclipse until April 8, 2024.

What are other math teachers doing during or for the eclipse?

Orthographic Projects with Blueprints

Blueprints is a board game where you try to score the most amount of points by constructing a building out of dice, first person to win 3 games wins. That was the short version.

There are lots of different ways to incorporate this game into any math classroom. First is the way you score points, it would be a great way to review order of operations.




Basically there are four color dice, when you use them they have different point values. The orange ones increase by two by the
number that touches that specific orange one. Green ones increase by the specific number of green ones you have. Black ones increase by a specific number according to its height. Lastly, clear ones are the top number on the dice that is rolled. When you have a variety of different dice, you get a number that needs to be added in a complex way.


The next is one that I use in my classroom. I bought 4 copies on CamelCamelCamel for about 18.00$ a piece. Students were placed in groups of 4, students were taught how to play the game with a mentor game. In the game you get extra points for completing a specific build. I added extra points if they could draw an orthographic project of their build from the top, side, and front.  On the right is one of mine mid-board game night with the wife.  The cards have a unique view like most of the worksheets when searching orthographic projection, but this makes a good review game. 

Geometry Project Runway

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.

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.