Polynomial Art Project

While doing a quick search on the MTBoS Search Engine for lesson ideas on using algebra tiles, I came across this really cool project idea from Hoppe Ninja Math. She had her students create works of art using the algebra tiles, and I just knew that I had to have my students do the same.

We played around with the algebra tiles for one class period and experimented with adding and subtracting polynomial expressions.

Algebra Tiles

The next day, I introduced the project guidelines and drew a practice image on the board (see my lovely dog below).

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Then, students started creating! Most began by using the actual algebra tiles to play around with building different images. Then, they sketched their designs on the paper and recorded the number of tiles they would need. After writing and simplifying their expression, they cut out the necessary amount of algebra tiles from color copies of these printouts that I made:

In all, I gave students 1.5 class periods to work on this task. Some students completely finished during this time, and the rest finished for homework or came in during homeroom or after school to work on it.

The finished designs were so awesome that I had such a difficult time choosing which ones to show off:

Overall, I loved this project for a few reasons: 1) My students loved it 2) They were able to practice simplifying polynomial expressions 3)…in a creative manner!

One change I would make for next year is regarding a simplified expression that equals zero. Many of my students thought it would be really fun to create a design in which all of the tiles negated each other and simplified to zero. This is fine in my book; however I would still want those students to write the entire expanded expression on their artwork, and then show that it equals zero. Some did this, some did not, but it would be an easy change to implement next time.

If you try this, please tweet me some pictures; I would love to see them!

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Visual Patterns Project

This Algebra 1 project was inspired by Fawn’s Visual Patterns site, and her Patterns Poster lesson.

We do one of the Visual Patterns every Tuesday for our “Tough Patterns Warm Up” activity, but I thought this would be a great culmination activity to our functions unit. Students must write both explicit and recursive formulas in this unit, so the patterns project brings both together nicely. Instead of supplying students with the patterns this time, they created their own! I encouraged students to be creative and choose an image interesting to them.

I provided them with a planning guide and scoresheet:

Students were given one class period to brainstorm ideas, start sketching, and write their equations. Once approved, they had about one week to make their posters at home. Some worked on the posters in school during homeroom, or at the end of a period if they finished their work early.

When I do this project again next year, I will more strongly stress the array of the images. For example, the apples placed in the diagonal vs. the Olaf snowmen which were placed in simply a straight line.

I love this project because it gives students a chance to be creative, and sometimes silly, but also because it directly relates to the math content we are studying.

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3D Desmos Designs

About a month ago I wrote about how I use Desmos Des-man to introduce an algebra graphic art project. I have done this project for several years now, but this time, I added a special twist… After making a design in Desmos, the students used Creo Parametric to create models of their designs which they 3D printed!

Step 1: I taped four sheets of graph paper together so that students would have a large work area. They chose a theme and started drawing. The only requirements I gave: there had to be at least one image per group member with at least 8 equations (at least 2 quadratic and 2 absolute value) and 2 inequalities

Step 2: Students divided up the drawing and started determining the equations. Some students physically cut their image apart so they could work on it at home.
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Step 3: Students took turns inputting their equations into one Desmos calculator. This took a bit of time since the students could not all be the same calculator at once. Most of the groups would save the Desmos image as a PDF to google drive, and then share that file with their group members.

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Step 4: All of my students take an Engineering class where they learn how to use Creo Parametric. I also took a PTC STEM Certificate Program this past semester where I learned the basics of 3D modeling. I had each student start with a basic rectangle and they uploaded their Desmos image to the rectangle. Then they traced the outline and extruded the lines. That’s it! Some students who are very comfortable with Creo decided to add special features and colors.
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Step 5: I printed the designs using our Stratasys uPrint machine and the students created 3-Dimensional Displays to showcase their work.

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Some groups did not complete a 3-Dimensional Display, so I will be turning their designs into magnets!
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My students were so engaged in this project and so proud of the models they created. It felt so natural to have them continue working with their Desmos designs and turn them into actual 3d prints. One aspect of the project that I didn’t stress with the students this year was the scale of their models. Next year I will have students determine a group scale, so that each component of the image fits together better.

I feel very lucky to have access to a 3D printer at school, and I will be looking for new ways to bring 3D printing to my students naturally. If you have any ideas, please share!

Update: I shared this project during Twitter Math Camp 2015. Here is a video of my presentation:

Calendar Project

Our first unit in Algebra 1 is “Solving Equations and Inequalities.” This also includes dimensional analysis and rearranging formulas. Since this unit should mostly be a review, I assign this Calendar Project. The answer to each problem in the September calendar is the date. So the answer to the problem on Thursday, September 1st is x = 1. At first, this greatly confuses students as to why I gave them the answer. But my objective of this assignment is for students to show me the steps they use to solve each problem so we can focus on our methods rather than just trying to find the correct answer.

 

The second part of the project is for students to write their own problems. In the past, I have had students choose a month and write 30 problems for that month. However, this turned out to be too time consuming and challenging. This year I am going to have students write 10 problems, and I am going to assign them the numbers for their answers. It’s much harder for students to write a problem with 27 as the answer as compared to 3, so I’ll use this to differentiate.

 

At the end of the month, I think I’m going to have each student design an 8.5 x 11 inch sheet of paper with one of their problems on it. Then, we’ll make a massive calendar in the hallway with everyone’s days put together. Pictures to come!

 

Summer To Do List

 

Our school year ended on Monday and everyone I bump into keeps asking me what I’m going to do all summer. A lot actually! I’ll definitely be enjoying some days at the beach, nights at the drive in, vacations to DisneyWorld, New Jersey, and Bermuda, but there will also be a lot of schoolwork happening…

Professional Development 

  • Data Coach Training – About 40 administrators and educators from my district elected to take part in this training sponsored by Research for Better Teaching (RBT) to learn how to “Unleash the Power of Collaborative Inquiry.” We will become data coaches and lead data teams this coming school year.
  • Twitter Math Camp ’13 – Woot woot!
  • Laying the Foundation Pre-Ap Training – I’ll be attending the Year 3 HS Math Training sponsored by the National Math and Science Initiative.
  • How to Learn Math – An online course from Stanford Math Ed Professor Jo Boaler

Books to Read

  • Teach Like A Pirate by Dave Burgess
  • Embedded Formative Assessment by Dylan William
  • Invent to Learn by Sylvia Libow Martinez and Gary Stager

Curriculum to Work On

  • STEM Stuff – My team is meeting for a few days to debrief the past year, set up new norms, and most importantly, decide what we liked about the projects we did and what we want to change. The majority of our time will be spent editing project guidelines/rubrics and making new ones.
  • Algebra 1 – I’m feeling pretty good about Algebra 1 since I’m teaching it for the 3rd year in a row; however, I’ve signed up for this morning session at TMC13 and know I’ll come back with lots of new ideas to work on! I’m also getting together with a group of teachers from my school in August to create common assessments for each of the eight Algebra 1 units we have.
  • Algebra 2 – I’m teaching two college prep sections next year, and haven’t taught it for two years. I need to spend some time organizing those materials to figure out what can be used again and what needs to be changed.

Other Stuff to Work On

  • Classroom Posters – I want to print some pretty, inspirational signs to add color and  pizzazz to my room. The only ones I’m keeping from this past year are: 1) Boston University Banner 2) Excellence Surfer Poster 3) Favorite Quote from Howard Thurman

    Surfer

    Passion

  • Daily Warm Ups – My students do a warm up at the beginning of every class, and I’ve been awful at keeping track of them over the past three years. Some are in word docs, some powerpoint, some I make up 30 seconds before class starts and scribble on the white board. I want to put them all in one place.
  • Blogging – I have a lot of posts on my “To Write” list, and this will be forever expanding as I attend the aforementioned PD sessions and read the aforementioned books.

STEM ECHS Overview

Since starting to blog over the summer, writing about my school’s STEM Early College High School has seemed like a daunting task. However, I think it’s time to explain a little bit about this exciting program I get to be a part of!

Our STEM program currently consists of 6th and 7th graders at the middle school, and 9th and 10th graders at the high school. We will continue to add two new grades until we are officially grades 6-12. Juniors and Seniors will have the ability to take courses at a local university to earn college credit early. Since I’m the 9th grade STEM math teacher, I’m going to focus on the high school aspects of the program. The biggest difference between our program and the regular high school is that all STEM students must take engineering and they receive a laptop to use during the school year. The students also complete four term-long, interdisciplinary, group projects that count for 20% of the term grade in each of their STEM classes. Along with teaching skills and concepts, we are teaching the students how to collaborate and work with students they might not get along with. On some days, students do not attend math, science, English, or history class, but they stay in an assigned classroom for most of the day to work on their projects.

The biggest difference for the teachers is that we are a team comprised of one math, one science, one English, one history, and two engineering teachers, and we have one 48-minute common planning period. Every. Single. Day! We use this time to plan our projects, meet with parents, meet with the Special Education and ELL teachers, discuss student issues, and plan interventions. I truly believe the success of this program lies in having this common planning time every day and having the opportunity to work so closely with a group of teachers invested in one cohort of students.

The biggest difference in my classroom specifically is how I try to integrate the physics and engineering concepts in my lessons. For example, when teaching slope, I use some of the graphs that the physics teacher uses in his classroom. He uses a distance/time graph to have students calculate velocity. I can use the same graph and ask them to calculate the slope of the line. Then we talk about how they are calculating the same thing and they don’t really have to memorize the formula for velocity. This is surprising to students at first, but they get used to seeing the same data in our classes. And the physics teacher and I strive to use the same terminology so that we don’t confuse our students.

I teach two STEM Honors Algebra 1 classes, two STEM Honors Geometry classes, and one Senior Topics class outside of STEM. All of the STEM students take an honors class even though they might not have been placed in an honors class outside of STEM. Although it’s definitely a challenge and I spend more time planning than I did when the program didn’t exist, I absolutely love being a part of it and I think my students really benefit from this school within a school.

This is just a brief overview, as I could go on forever about the program, so let me know if you have any questions! If your school has tried anything like this too, I would love to hear about it!