# #MTBoS30- Day 8

Putting it all together- that’s what my mind is trying to do.  There are a TON (really, there are) of great resources out there on the web via the #MTBoS.  There are times where it is hard to decide what to use, when to use it and where.  I am lucky enough to be slightly flexible in my curriculum (and also a curse because of the nature of the placement).

So, because I teach in MN and there are no “perfectly pre-packaged curriculum” (really who even wants that truly?), my mind is trying to wrap itself around what would be a good meld of components in the classroom.  Like I mentioned in my previous post, Science Practices in Math, I really believe that restructuring the lesson layout will help not only my students, but others as well.

Currently I have been using parts of David Wees a2i, an online curriculum for Algebra 1 and 2 as well as Geometry.  It has opening activities and I like the exploration of topics.  I also need to work with resources I find great (and my students do too) such as Estimation 180, Open Middle, WOBD, Would you Rather, Visual Patterns.

This summer will be interesting for me…

# Shading My Linear Art Projects

First I want to thank those who have tried my Linear Art Project in their classrooms.  I think this gives students a great experience with linear equations and how the slope/intercept impacts them.  I have had a lot of questions on how I shade my projects (thank you Missy and Jessica), and now that Hunting, NCTM and Thanksgiving is done I’m back on task to answer this.

So let’s say I created this awesome pumpkin on Desmos:

First, the challenge of actually graphing the pumpkin is something to celebrate!  (YES!!) Then the question arises, Mr. A- How do I color it?  The first thing I have to alert you to (and that I need to remember to ask Ely about) is the color limitations.  Currently in Desmos you have the following color choices:

This can make things tricky.  Trying to get a specific color becomes a problem.  Since pumpkins are Orange however, it works out well for me.

To get things to shade, you have to use an inequality.  For the above example lets look at his right eye.  I want to shade it, so instead of an equation I create an inequality. I first find the equation I want to change:

Now, I want to shade above it, so I want to use the “greater than or equal to” modifier.

You now notice that I have black covering a large chunk of my awesome pumpkin picture.  that’s because I need to provide a lower AND upper limit to my shading.  I need to find the equations of the other two lines that create the top of my pumpkin’s right eye.

Now I need to make a compound inequality where the upper limit is -2x-3 and the lower limit is -3 for the interval {-1,0}.

Now you will notice a few weird things, first half of the line for the bottom of my eye disappeared.  That is because I modified my interval to be the same as the interval for the line that created for the top of my eye.  Second, you will notice a heavy line now creating the border of my eye for that interval- showing you what part of the graph your inequality is shading.  Third, you will notice that you have it shaded!  YES!!

To complete the eye, I have to change the equation for the top left part of the eye into a compound inequality:
You have shaded in the right eye.  Going backwards in this fashion, you can complete the shading of your whole picture.  This can get frustrating to students and many will lose the equation of their original lines because they are trying to modify them.  One thing that helped me here is that I had students create their inequalities in a new line under the original equation.  This gave the picture a bolder outline of the shapes and allowed students to always have their original work.

This is a link to my BSU Beaver logo I created using compound inequalities.  It took a while, but I really liked the outcome- and students do as well!

https://www.desmos.com/calculator/guvl1g2mvf

# Math Songs

I really wish I could find my student work amidst the piles of resources I have in my storeroom, I would take a few pictures of student song samples…

this is a video I found on the web to give you and idea of what the end result would be for this project

One Project that students have really liked (and we have even made short video clips of them) is to take popular songs students listen to today and transform them into songs about math.  There are a few guidelines I present to students before we do this:

1. Choose a song that you currently listen to for the outline of your math song
2. Use only one Mathematical Concept for the song
3. Your song can either try to teach students about that concept or just give listeners some background about it and where it may be used in everyday life
4. Appropriate Language only

This is a project that I list under the “fun reflective” category.  I don’t have students do this project with the sole purpose of learning facts, I want them to think about the concept in it’s entirety, reflect how it is connected, and express that through song.  Creating short video clips will take some time, you will need to get ideas from the students on where they want to shoot, how they will express their song, and take class time to gather video, edit it and present them to the class.  Is this project worth the time?  I find that it is.  I recently had a student come up to me and ask if I still had his song copy, and he even sang me a few lines.  He told me that making the song had him think about mathematics in a different way than problem calculation, and that the concept is embedded in his memory.

Besides, who doesn’t like to create a few poetic verses and put them to music?

# Linear Art Project

This is a fun project that I started doing to support my Art teacher and show students that Algebra can make the most amazing things.

Step 1:

Have students pick out a picture.  This is a great sell to students since they have control over what type of picture, icon, avatar, etc that they use for the project.

This was the example I used, the logo from my college, the Bemidji State University Beaver.

Step 2:

Have student create a free hand drawing of the picture.  This allows them to adjust the picture, editing lines and shading that they may not want to show.  It allows them to be creative and adapt the picture for the project.

Here was my free-hand drawing of the Beaver.

Step 3:

Students recreate their free hand sketch on graph paper and using only lines.  They should try to make shapes end on grid points of the paper.  This part can take a while, if students created a large enough free hand sketch, you could allow window tracing to help transfer the image to graph paper.  I have students make 2 copies of the graph image, one they can decorate and one for the next step.

Here is my colored graph paper image.

Step 4:

Have students create an X&Y Axis on their picture.  I allow them to create them wherever they want, and usually they have them right in the center of their drawing.  Depending on the patience level of the students, I have them label points that create their drawing.  There are times I only have them do a set amount (20 or so) and times I have them label each line segment ending.  This is totally up to you.

My XY Axis image:

Step 5:

DESMOS!  Need I say anything more.  I used to have students write the equations of the lines that create their image, but with the totally awesome program DESMOS, I now have students create their image with it.  DESMOS has helped students understand how changing the slope or intercept effects the line, and with the instant drawing of the line when they enter the equation, it allows them to visually see where their line is.  This is a great error check for students, and they accept mistakes more readily than if they are writing equations on paper.

My DESMOS image.

Step 6: The Finalé

To complete this project, I have students create a collage of their sketches, and a printout of the equations from DESMOS.  I then hang these posters out in the hallway for everyone to enjoy.  This attracts students from all over the building to come check out what kind of cool activities we do in 8th grade.  I am even getting new 8th grade students asking me when we will start this project!

# Starting with the Basics CL Desmos Style

So students were a bit overwhelmed with Desmos at first, so I had them do a quick activity with horizontal and perpendicular lines: create a logo from our school initials, CL.

Here are some examples of work I received.

Thanks again Desmos, the Students are really loving playing around creating things.  It’s been a great end-of-year activity.  I hope this encourages them to use Desmos for their high school classes.

# DESMOS!

So I designed this with DESMOS to represent my Alma-mater, Bemidji State University.

It turned out pretty cool.

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# Human Histogram

Since it looks like I may have an alteration to my teaching assignment next year, I feel it is time to dust this off and pump it up.

Human Height Histogram

I started using this activity when I was teaching 7th grade.  There is a lot of physical growth that happens during the middle school years, and this is a great way for students to look at data that is meaningful- data about themselves.

We start by making predictions about which gender has the greatest average height at the beginning of the year.  Typically in 7th grade it was the girls, and we devise a way to determine it.  Students come up with a way to determine the mean height of both groups, which usually involves measurement since students are not accurate with their actual height.  We spend the day measuring all the students in the grade, and then look for the measures of central tendency.  Students will tell me the range, median, mode and mean of each gender, and they also are curious how that stacks up for the group as a whole.  I ask them how we could display this visually and they immediately tell me to graph it.  The type of graph will vary however, many 7th graders are overly “precise” in their measurement of height since they are trying to be taller than their friend.  The number one graph of choice for my students has been a bar graph, so I allow them to try this method.  After attempting to draw a bar for each student, they decide to use a different graph.  This normally results in a scatter plot where we use different colors for boys and girls.  My 7th graders are not particularly adept with reading scatter plots yet, and will complain about the representation, saying that it is more confusing than looking at a list of numbers.  So we brainstorm for a new idea.

After students struggle with other graph types, I ask them if they would want to go back to a bar graph.  I usually get a unanimous response of “YES!”  We talk about how bar graphs display data, and I ask students if instead of graphing each individual student, if we looked at graphing heights instead.  Students think on this a bit and then get into how this could help or be more complicated.  They also start arguing about the heights that we recorded, saying that there is too big of a variation of heights to graph.  I suggest “grouping” heights together.  Students really latch onto this idea, and we brainstorm on how to group the heights.  Typically students either decide on 1″ or 1/2″ intervals.  They then get to work graphing the heights and how many occurrences there are.

One thing I do during the measurement process is take a picture of each student as they are being measured.  I then print out everyone’s picture (normally a head shot, and typically multiple ones- some on colored paper) and when we as a class believe we have a good graph, allow students to “graph themselves” on the wall outside my door.  This creates a visual of the class overall.  We then create a bimodal graph slightly below it that represents each gender.  (A sample is below, but I no longer have pictures of my student ones so this is shown generically)

Students typically do not like this because some of their faces are covered.  So we represent it in another way with a vertical histogram, females on the left side and males on the right (stole this idea from Stem and Leaf plots).  This give students a great visual of the height distribution by gender.

This is what I want students to analyze, I even take them outside and take a picture of them in this format.  They make conjectures on why this distribution occurs, what it may have looked like in earlier grades, and what it will look like when they graduate.  I then ask students to make predictions on how much they will grow over the school year, and we create one last vertical histogram from that.  Then we wait.

At the end of the year, we go through the measuring process once again.  We determine the measures of central tendency and graph our results.  Students then compare their predictions to the actual results.  When I ask students to compare the two, I get all sorts of humorous reasons why things may or may not line up.  “I drank coffee every morning this year because I was tired all the time, Mom told me coffee stunts my growth,” has to be one of my favorite student comments.

Now that I will be teaching high school as well, this will be a fun multiple year project, I may have issues storing graphs for a few years until I measure my students again, but I think it will be a great extension to this.  When I dust these off for the seniors, I can’t wait to hear what their comments are, what the remembered about it, and what kind of estimations they now come up with for their height distribution.

# It’s More Than Just a Project…

Sometimes the biggest challenge in teaching Math is instilling a desire to work on complicated problems.  Many students today grew up with the idea that fun things are those that have instant gratification rewards- e.g. Video Games.  Math may hold this type of reward for the instructor but it is not always evident in the student.  This year I have tried to create a few projects that will have meaning beyond the immediate essential standard we are covering, attempting to bridge the gap between learning and real life.  One thing that my students lack is a long term goal, they dream of the future but many of those dreams are along the lines of “I want to play in the NBA” or “I want to be a millionaire” and have no real plan or focus to get there.

I asked a question in class one day about how many students thought they wanted to attend college after high school.  Except a handful of students, all indicated that they thought college was a goal they had.  At one point in my career I would have left the conversation at that, satisfied that my students had a good goal and future plan.  Now, I know better.  I followed that question up with where do you want to go to college and the handful now turned to students who actually had an idea of where they wanted to further their education.  So I decided to tweak an old project so I could give my students the opportunity to explore colleges.

I teach 8th grade Algebra.  One project I always do is a Line Art poster where students would choose a picture and convert it into a linear picture.  This year I took it one step further, which also meant I had to increase the class time spent on it.  This year their picture had to taken from a college they would like to attend.  It could be their logo or mascot.  I had students print out the original picture and sketch a draft of it (I did this because the pictures were normally small).  They then converted it into a linear art picture.  Students were asked to make 2 copies of the linear art, one to use now and one we will use in a few weeks.  Students then overlayed a Cartesian Plane on their linear art and plotted points on their picture.  Although this initial process can be used in grades as low as 5th, I discovered that many of my students were still transposing the X and Y axis so this was a good practice for them to master that skill.

They were asked to write a brief paragraph describing what college they chose, where it was located, what the college is known for, what they wanted to study there and why they chose that college.  As you can see from the picture, this is the part that received the least attention from the students.  When we go back to this project they will revise these paragraphs and produce more supporting details.  For the initial process I wanted my students to create a vision for themselves, now that they have one and have had some time for that seed to grow I will ask them to look at that vision with more depth.

In another week we will look at these posters again.  We are covering slope and writing equations in slope-intercept and standard forms.  Students will then use their second line picture to write the equations (slope-intercept) of 20 of the lines they used to create it.  They will then write those equations in standard form.  To finalize the project they will also revise their paragraph to include more supporting details.

Currently the posters are displayed in the hall over their lockers, a constant reminder of what they chose for their vision of the future.  So far I am pleased with the conversations that have happened as a result of this project, students are starting to change their outlook on classes and life.  They are starting to think about what will prepare them for their new realistic dream versus the superficial one.  They are starting to accept the struggle of a complicated problem and have the confidence that they can find an answer.  Overall I am very pleased with this project and its place in my curriculum.  I will follow up on this blog when we finalize our visions of the future.