Prime Factorization: Maker Style


Sondra Eklund’s sweater that inspired this student project. I have never met her, but have admired her geeky attire for a long time and hope some day will have a Prime Factorization sweater vest of my own!

My students and I are very excited to share this ongoing project with you. I have always admired the attention to detail and geeky twist to cold-weather avoidance that Sondra Eklund achieved with her Prime Factorization Sweater. (more of her wonderful creations here; and inspired items here).

In our middle school mathematics program we teach the classification of numbers and prime numbers are of a big topic. In  my grade 8 program, I often refer to prime factorization to help students understand the approximation of square roots. Gifted and enrichment level students who often work beyond the scope of my expectations challenge each other to see if they can discover the next largest prime. (They love this TED talk from Adam Spencer).

At any rate, I am always trying to demonstrate to learners that mathematics is the mother of all art forms. I decided to show them Ms. Eklund’s sweater one day, and they immediately asked me if they could create something similar. What started out as a simple visualization project with markers and a piece of white paper turned into a year and a half of (borrowed) paint swatches, scratch coding and the creation of an educational technology installation that mesmerized students who chose to interact with the art piece. Below is what they came up with: 

The detail in mathematics and design that were required in this project were astonishing. Here is a little insight into what they did:

1. End design was to be a 10×10 grid that represented the numbers 1-100. They were given a piece of MDF in which they were going to use to create their final design.

2. Early into the planning, they decided that they didn’t want to simply colour the factor squares, they wanted something of constant colour throughout. They decided paint-swatches would be a good idea as there would be no shortage of colour combinations.

3. They started to determine the factors of each number 1-100. Some numbers were clearly easier than others, using one solid colour for each prime number. We had lots of great conversations particularly about what to do with the elusive “1.” The level of mathematical vocabulary that students used to complete this process was incredible.

4. Once colours were brought in from a very supportive Home Depot, the students of course limited their choices to only the “pretty” colours. The swatches were not square, and since we didn’t want to deplete the store from all of their swatches, I told them to calculate the maximum square area that one swatch would afford them.

5. They then set out to measure the total surface area that each prime number on its own required, as well as the instances where it was a prime factor of a multiple. For example, there were so many Sico branded Seafoam Breeze that I am sure we could have painted the entire academic wing.

6. The duration of this project was longer than anticipated given the prevalence of the prime factor ‘2’ in their design. It took many trips to Home Depots across the province in order to finally have enough Seafoam Breeze to finish the final display.

7. Through their planning, they worked on a piece of bristol board where they were able to perform calculations while temporarily placing the swatches.

8. Once it was time for the good copy, they used hot-glue to fix the swatches to the piece of MDF. The more prime factors, the more glue. The more the prime factors, the more cutting using the guillotine cutter.

9. It was during this process that I ordered some MakeyMakeys for the classroom. The same students instantly saw a connection between their Prime Factorization project ant the potential to turn this into an interactive art installation.

10. The students decided to choose 9 numbers from the grid in which to create “math-facts” where a user could trigger these facts simply by touching their fingers to the board.

11. After researching some of the more elusive and bizarre math facts for their chosen numbers (including perfect numbers, statistical satire and counting) they used GarageBand to record sound-bits that they would eventually program the board to trigger when the user interacted.

12. One of the most memorable aspects of this project was when a very modest students showed me the Scratch code that he created to play the sound files when someone initiated a key press via the MakeyMakey.

13. Students then thought of how to design the display in a way that provided a non-intrusive, or ugly, interface. They chose to use simple screws that protruded from the back of the MDF in order to attach the alligator clips for the MakeyMakey.

14. I have a bookshelf at the entrance of my room that I use as a kind of divider. I thought it was a great place to finally install this project.

The MakerCart: our best idea yet.

The start of our Maker Education adventure: The MakerCart

The start of our Maker Education adventure: The MakerCart

After our return from CMK2014, we sat down with our school’s community of like-minded geeks educational technology enthusiasts, and talked  about a few different levels of maker education “buy-in,” each with their own budgets. Like any good initiative that requires some thought, we came up with four levels of expense and application that could benefit our middle-level students. The options that we came up with were:

1. Placing a Makerbot Replicator 2 in our already established MSTE Lab (what we call our Technology Lab). 

The benefit of this option is that we are very lucky to already have a technology lab that includes desktops for a class of 30 students, a fully functional kitchen as well as a professional wood shop. Our students from grades 6-8 complete self-guided units of study from Scratch coding to model rocketry. Adding a 3D printer would be an obvious fit to this lab, cost effective, and would benefit all students since they each rotate through the space in a year.

2. Creating a portable Maker Cart (What quickly became an obvious choice). 

While we always had the ambitious goal of creating a makerspace, this cart idea seemed to be a popular option as it would be a portable resource so that all of our teachers could introduce students to the fundamentals of technology related to maker education. (more about this later).

3. Creating a stand-alone Makerspace in our library (This eventually happened!). 

4. Building an on-campus, separate Maker Cottage (wow…). 

It’s always good to think big – and this idea did not fail to intrigue. In the even that expense was not a concern, it would be incredible to provide a architecturally rich ‘cottage’ space that could accommodate 30+ students, outside of our building. Imagine, a live roof where students could plant their own vegetables and learn about soil composition, an attached outdoor classroom, and the latest in makerspace technology on the inside. Who knows if something like this exists, but it would be an incredible option for a school under development.

Let’s go with the Maker Cart! 

In an effort to maximize exposure to students, we put together a collection of tools, technology and tinkering materials. This fairly inexpensive option allowed teachers to simply reserve the cart for a class, a day or a week and expose their students to an element of play and planned engineering. This also allowed our staff and administration to assess if our student population would benefit from aspects of maker culture before attempting to build any of the larger options from our brainstorming list.

Here are a few photos of the completed MakerCart:

Here are a list of contents, most of the sources and approximate pricing: 

  1. Tool Cabinet $170
  2. Hook-up Wire (x5) $2.50 each
  3. Wire Strippers (x2) $4.95 each
  4. Tweezers (x4) $3.95 each
  5. Precision Screw Drivers (x4) $3.95
  6. Diagonal Wire Cutters (x4) $1.95
  7. Needle-Nose Pliers (x4) $1.95
  8. Scissors (x3) $15
  9. 15cm Rulers (x6) $7
  10. 30cm Rulers (x6) $8
  11. MakeyMakey Kits (x5) $49.95
  12. littleBits Base Kit $99
  13. littleBits Premium Kit $149
  14. littleBits Deluxe Kit (x2) $199
  15. littleBits Light-It Kit $45
  16. littleBits Touch-It Kit $41
  17. Parts Tackle Box $4.95
  18. Colourful Duct Tape (x4) $5.97
  19. Conductive Copper Tape $2.95
  20. Bare Conductive Paint (x3) $9.95
  21. Aluminium Duct Tape $11.98
  22. Painters Tape $3.99
  23. Scotch Tape $9
  24. Pipe Cleaners $5
  25. String $5
  26. Pulleys $5
  27. Zip Ties $7
  28. Sharpie Markers $15
  29. Sharpie Paint Makers $15
  30. Crayola Markers $10
  31. Elastic Bands $4
  32. Google Eyes $3
  33. Wooden Circles $5
  34. Extension Cords $3.43
  35. Crayons $2

The above list, without taxes or shipping, came in at around $1500. For maker technology, we decided to focus on MakeyMakeys and littleBits. I will feature both of these technologies in a later post as they have served to be the foundation of my maker education adventure. This cart has changed how we interact with students and their creations. Please let me know if you have any questions about how to create your own: @jmrlingley

The limit of our student’s creations lie just beyond their imagination. All we have to do is provide them with the opportunity. Thanks for reading.

The journey towards Maker Education: My 2 year blogging absence.

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This is a must read for anyone starting a similar journey.

Hi folks. It’s been a while. Please allow me to explain. Two years ago, I promised myself that I would start writing some educational thoughts pertaining to the lessons that my math students complete on a semi-regular basis. The truth is, I abandoned that goal shortly after starting the academic year in September of 2013. As teachers, we never know how a year is going to go, and I have to tell you – the last two academic years have been an incredible journey. Basically it began with having a few ideas of how to get my students creating in the math classroom, to having a state of the art MakerSpace in our middle school. It has been a journey that any teacher would be proud to say that they have seen happen, but to be a participant – it has been simply incredible. Allow me to tell you about it.

Back in the summer of 2013, I picked up the first title of my summer reading list, Invent to Learn: Making, Tinkering and Engineering in the Classroom. This book authored by Sylvia Libow Martinez and Gary Stager has become the primary resource for what my classroom has become. This book introduces educators to the idea of bringing “play” into any classroom, independent of the grade level or the resources. Formally known as Maker Education, this educational framework largely founded by the work completed by Seymour Papert, allows learners to create rather than consume. At the core of Maker Education, students are encouraged to use a range of resources from cardboard to 3D printers, to create tangible learning artifacts in which they can express their passion for academic disciplines from literacy to numeracy and beyond.

While reading Gary and Sylvia’s book (I feel that I can call them by their first names for a reason) it was easy to get lost in potential, rich learning experiences that students could have, independent of the subject area. Imagine an anxious student who really cannot stand up in front of the class to give an oral presentation about their descriptive writing piece: what if they include a QR code within in their paper that allow their teacher the ability to simply scan their assignment to open a video on the teacher’s smart phone of the student confidently reciting their presentation under their own volition. Or maybe even I could consider my math classroom – maybe I could have students building interactive polyhedra from a 3D printer? The possibilities and relevance of maker education began to be the fairy tale that I hoped would come true for my classroom.

Towards the end of that summer, my wife and I attended the educational conference: Constructing Modern Knowledge hosted by Gary and Sylvia. This intimate conference of only 200 educators from across the globe, allowed us all to simply – create. We were instructed to the most far-fetched student projects that we could fathom. There were ideas that included: animatronics, interactive art sculptures, sound gardens, robotic recycling bins and of course: our Rube Goldberg device. For 5 passionate, exhausting days, our group worked with the best in educational technology to create a 21 component Rube contraption – quite the accomplishment (if you can call all of those failures along the way the parts of what an accomplishment is composed).

Needless to say, this conference was exactly what I needed to spark my journey over the last two years. Over the next little while, I hope to post a few key events that provide some more clarity on what the Maker Movement means to my classroom. From a Maker Cart to a Maker Space – an incredible amount has happened.

Talking Place Value @ PD

Today we are at professional development. We are lucky enough to be given this opportunity to chat and rant with colleagues.

Today as middle level teachers we have been talking a fair amount about place value. Earlier this week I had students respond to this question in their math journal (no I did not show them the new wrecking ball video).

Miley Cyrus earned $12.3 million from her latest single. What would that number look like?

Students gave some interesting and incredible answers. Really all I was looking for was for students to write 12 300 000 (without the commas of course 😉 ). One answer included 12 000 003 another was 12.30000. And many answered correctly. What is fascinating was the number of varied responses. I underlines the importance of differentiation and constant assessment of numeracy ability. Many of our enrichment level students still make place value mistakes. As teachers we have to be willing to work independent of our grade level. Students need to be able to complete the work that is in front of them. Confidence in math drives appreciation for math. If a student is struggling with decimal computation maybe it’s because they just don’t truly understand the difference between a thousand and a thousandth.

Another colleague, in a separate question, wrote a number: 5 000 000 700 0023. What do you guys think the teacher was asking? What are you guys noticing about common errors in place value understanding?



Classroom Tour – Math Immersion

I know, I have been on the lag train as far as this blog goes. After quite a bit of time and effort, I have finally got my new room up and ready. No, the students have not been learning in filth (even though I tell them that math is supposed to be messy), most of what I will tell you about here has been up since the end of August.

I was reluctant to give up my old classroom – A wonderful, fully equipped science-lab, complete with lab benches for balanced math activities. While my new classroom is smaller, it is the largest of the bunch, and allows me to lots of mathing room.

Ok, now for the tour…

1. Window Math

Walking through the aisles of Staples, always gives me goosebumps of envy and desire. I wanted a way for students to  freely express their mathematical thoughts without judgement. I picked up a few window markers (Expo Neons) and threw up an enrichment level math question. I have since needed to change this window on a daily basis as my students love picking up a maker and writing where they shouldn’t be writing.

Window Math

2. Math Meets Hollywood

In an earlier post, I mentioned a book that I hope my students are going to take and turn into short films. This is my attempt at inspiring them through this bulletin board. (Not too much action yet :S)

Math Meets Hollywood

3. Math Journals 

I am lucky (others would disagree) to have 90 minutes with each of my classes, once a week. I have made a goal for them to write a journal entry every week. A link to our first two entries can be found by following this link. In addition to the constructed response entries, students will also create summary entries à la Interactive Student Notebooks. Thanks Pinterest. Will post more as I get them.


4. Sound Machine 

I picked this up at Indigo / Chapters 3 years ago. It has more uses than you would believe. I use it mainly as a positive reinforcement for when students are close to a breakthrough. A affirming DING sends them into hysterics. There is also the boo-boo sound for a wrong answer, but this is used sparingly. You may notice an x next to the whistle. There is a story to that, to which I will not divulge. Go pick one of these suckers up – you will not be sorry!


5. When will Mr. Lingley Return? 

Really I just use this to show the students how early I show up to get started on their day (7:30). They have yet to take pity. Also, many students can use a refresher on analog time.


6. Do You Have the Time? 

Yes this is a poor excuse for one of those commercial Math Clocks, however is still very functional. Students can feel free to place sticky notes in the form of expressions where the numerals should appear.


7. Enrichment Bulletin Boards 

No shortage of activities to inspire. Students are free to help themselves while waiting for further instruction. Questions are in envelopes and colour-coded for complexity.

IMG_1223 IMG_1222

8. MART Station 

Students quickly find that Mr. Lingley is more obsessed about patterns in math, rather than their associated numbers. They get to explore these patterns through MART (math+art) projects. We will work on things like string art, modular origami, and endless geometric shapes.


9. Student White Boards 

Love them. Picked up a class set from the MarkerBoard people last year. I was tired of having students resort to pulling out a random piece of paper, only for it to end up in the recycle bin at the end of class. It is amazing what motivates students to work, and I have to say, they have yet to stop working with these whiteboards. When I find exceptional answers that I would like to save, I get them to snap a photo using the classroom camera.


Wish I had a tenth, but can’t seem to find any more photos. I call my room the math immersion diversion. Students know that for every class, they will be working – no questions asked. The use of tiered and differentiated materials, have become critical for their achievement and to my clarity of thought. That and coffee.

Happy Monday!

What I am doing my (Fifth) First Day Back.

Ahh… the night before the first day of school. All of the soon-to-be-students are home thinking thoughts like:  I wonder who my homeroom teacher is going to be, will my class be full, what if I have to use the bathroom, and what should I wear? Us teachers who are heading back are thinking similar things like:

  • I wonder if I am the one who has to bring in milk tomorrow?
  • I wonder if my voice is going to crack in-front of my students,
  • What if I have to use the bathroom,
  • What should I wear?

Like our students, by days end tomorrow, we will have the answers.

I always enjoy planning the first day – try out some of my new jokes – part my hair a different way – and especially planning those engaging activities. In addition to some of my own, I have manipulated some great resources found on a couple of my favourite math blogs: I Speak Math, and Dan Meyer. Check those out.

My First Day Activities (many are not even math based)

1. Lower the Helium Stick

Back in my student leadership days, we used this icebreaker. Line students up in groups of 8-10 facing each other. Have them stick out their index fingers. Place a broom stick or a long dowel on-top of their fingers. Tell them: as a group, they must always keep their fingers touching the stick, and they must lower the stick. Challenge ensues as the stick will surely rise. For further explanation check out this site. 

2. Student Interest Inventory Screen Shot 2013-09-02 at 8.20.34 PM

Dan Meyer is always great for a nifty numeric note, as well as his rendition of a math-based student interest inventory. This activity is one of my favourites, as I keep track of some learning information and use it to guide my instruction. Last year I used a facebook themed inventory, this year, after inspiration from the source above, I came up with this. Of course I had to make an exemplar.

3. Math SLAM!  

I am always looking for ways to introduce literacy into a numeracy based class. Every week my students create math journals. This activity introduces them to this concept. The goal of the Math SLAM is to think about a situation in which math has either made you feel inept or adept (not my words of choice for instruction). Students must then “soap box” style create a three sentenced Math SLAM. Some students choose to speak of a time when they were defeated by a problem – then to disclaim that this year will be different! To celebrate the first of the year, students present these by almost yelling at the class. Some record them to video.  Feel free to use this in your class.

Math Slams.pdf

At any rate, have a great first day tomorrow.

MART (Math+Art) Goals for 2013 – 2014


A student who spent several days putting together an iicosahedron from sonobe units. Used 30 units. Very proud.

During my BEd, I was introduced to a TED talk from Mae Jemison, who in 1992 became the first African-American to enter space as an astronaut. Here proclamation for the necessity of classroom integration of art into subject areas including math, science and technology, was inspiring to say the least.

Over the last 5 years of teaching grade 8 math, I have affectionately created (amongst mocking of students) Mr. Lingley’s MArt lessons. Various lessons include string-art, tessellations and last-year’s goal: Fractal Origami. It was a huge success! What began as an enrichment project, suddenly ended up in countless trips to the local art store for more shiny, perfect squares of pythagorean perfection. (Instructions on how to fold unit here.)

How could I top it for the year 2013 – 2014? At the end of the year, I found a great little book entitled: Whodunit Math Puzzles. This children’s book published by Scholastic includes 25 classic crime whodunit puzzles that require students to use their math concepts to solve them.

While the stories are for students who are generally lower than grade 8,  they require both computational and mathematic reasoning to solve.

Ok Ready for the MArt goal? Students create, film, and produce short videos based on these stories, and post them for other students to solve in video format. Basically I see it unfolding like this: 

1. I make a fool out of myself (happens daily) and create a model from one story. 

2. Post model as a challenge on class wiki. Encourage students to upload their version of the solved problem in video format. 

3. Interested students choose other Whodunit Puzzles to script, film, edit, and post to our wiki. 

4. Students / classes from around the world post thematic solutions to the math problem posed in the video. 

That’s the goal folks, who wants in? Give me a tweet @jmrlingley

Happy Mathing.