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