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.

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.

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.

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!

I really like your getting the kids to put their axes where they like. This is real math. More complex problems can become horrible with a bad choice of axes, and the only way to find out is to do it, not to have it done for you.

Next step – transformations of the points, to modify the picture??

Actually I was thinking of reflections first, then rotations and lastly translations (trying to think of the level of difficulty for each). Reflection around the center of their picture first, both horizontally and vertically and seeing the change in equations via DESMOS, then look at what rotations would do. I would start fairly basic with both of these transformations and then let the kids go on what type/where they decide to rotate and reflect. Then I would jump into translations.

You could push it further and do stretching (dilation in one direction), multiply all the x coordinated by a number, and shearing, new x = current x + multiple of y. Probably not on the syllabus, and not rigid, but the results are way more exiting.

I am trying to recreate your picture on desmos. I am having issues with the shaded regions. When I zoom in/out sometimes parts of the graphs disappear. Is there any way you would be willing to share your graph so I can see where I am going wrong? I just want to try and help the students as I am having them do this project! 🙂

Thank you again for the inspiration to do this project. The kids are LOVING it!

Sorry Missy, I have been a bit busy this past week getting ready for NCTM Regionals. I will get something up to help on this.

Love this project, but I am new to Desmos and am wandering if you could send me your equations that you used for your Desmos project. I am not sure on how to do all of the shading.

I am also interested in the Desmos equations and shading that you used. Can you please send them to me?