Cogito Ergo Nerd

  • Farica Erwin

Updated: May 6

The first real week of school is always devoted to learning routines. AND our first week is usually a four-day week! I cannot even begin to tell you the benefits of easing back into routines and the beauty of letting your body recover from the most exhausting week of the year.


To begin the year, I love using Sara VanDerWerf's Name Tents. It is a great way to get to know the students. I also provide a prompt each day, otherwise I get "I don't have a comment" on a lot of them. Since I sometimes teach the same students again, I change the prompts each year. This year, I used:

  • List 3 traits of your all-time favorite teacher

  • List 3 traits that define you

  • What is your favorite "sport" to watch or play?

  • Share a boring fact about yourself. (borrowed from @drrachelbrenner)

I do not need them to learn their names because I know who most of them are before they enter my room. I like to use them as a way to individually interact with the students. However, this week, I was horrible about remembering to return them. And reminding them to write in them. And collecting them. It was basically a disaster. None of the students seemed to notice.


Random Groups

Starting on Day 1, my students are seated randomly. Every one of the student chairs is numbered. Each student gets a number based on my roster. That is their number all year. I have a max of 16 students in each class and use 4 groups of 4. Every student is required to sit in their numbered seat every day. However, every morning I change where the seats are located based on a Random Grouping Sheets document. (All I have to do is highlight column A, click the down arrow, and choose randomize range. It then changes the group configurations.) They must get to class to find their seat before the bell rings. Best part of my day is watching them hunt for seats!


Day 1:

After having the discussion about Friday's activity, we worked through Sara VanDerWerf's 100 Number Activity. We play 2-3 rounds. After which, I always ask if they noticed me taking pictures (of either activity). It's a great discussion about how focused they are because they never know, even when I forget to silence the camera clicks.


In addition to discussing more group norms and routines, I use this time to explain my picture taking. Students (and/or their parents) sign a photo release for school. However, I still feel like I should ask and get their permission for using their picture. Everyday is different and there may be some days you just do NOT want a photo taken of you. I explain that I post everyday to Instagram through #teach180, but the pictures are of the math and not them. They will know I am taking them because I say things like "I need a picture of that," or "freeze your arms for an over the shoulder shot." If I ever take a picture of their face, I will ask them first, it will be staged, and it will be used only for the internal school slideshow or parent newsletters. I do not post their face to my Insta (even with permission). I just don't wanna deal with the mess.


Day 2:


Wrong answer! Cute boat though

About a third of my students had a field trip. Using Fawn Nguyen's Noah Ark problem (via Sara VanDerWerf's blog as the original links seem to not work anymore), I introduced the Stand-And-Talk routine that I also got from Sara. I love that the students usually see all of the important info before they ever see the problem. Many of my students even give ideas for what the question mark in the problem might mean before asked.


Day 3:

Now that everyone was back in class and I felt like I had been introducing so many routines, I decided to introduce another! Questions Stacks by Sarah Carter @mathequalslove

I love this routine. Self-paced and self-checking, the students begin to love them too.


Students are supposed to enter my class having already mastered solving equations, but ... things happen, new students arrive, assumptions are made (and we all know about those). So I spend two days having the students go through three different QS with three types of solving problems

The activity helps to remind students of their solving skills they already have, and allows me to work with those who need refreshers.

Pro Tip: If you print these on business cards, use a marker or highlighter to color the inside seam on both sides. This way you can still color-code your sets for when one ends up on the floor.



  • Farica Erwin

Updated: Jan 26

My school always starts on a Friday with a half-day. I like it because teachers have been there all week, and it is a quick way to meet everyone. Unfortunately, it makes each class about 18 minutes long. Usually, teachers are handing out their syllabus and materials list, so students can get them completed over the weekend.


I do not have a syllabus (I have a digital interactive slide-deck posted on my webpage) and I do not require any materials more than a graph paper spiral notebook and writing instrument. We are a 1-to-1 iPad school, but they are issued those, so no extra materials to buy.


Instead, on the first day, I like to give my students a group challenge. It changes each year as I teach some of the same students each year. This year, I chose the Impossible Paper Puzzle to get them thinking. I taped them to the walls, so each group had their own to look at, without being able to manipulate it.


The Rules of the Activity:

Each person gets ONE piece of paper to re-create the puzzle.

Each group gets ONE pair of scissors.

Talk to your group and plan wisely.

You may get as close to the Paper Puzzle as possible, but NO TOUCHING.

You get 8 minutes to work.



I usually have about one or two students who figure it out during this period. I immediately make them crumple the answer into a paper ball and recycle it. They are not allowed to share the answer.


During the activity, I hear many things:

"This must be trick. It's impossible!" - Really? You are literally looking at a completed puzzle!

"Are you going to give us the answer?" - Ummm, no, never ... to any problem.

"I don't want to waste/mess up my paper." - Arg! Take a risk, try something!


But I also hear:

"As a group, we have 4 papers, so 4 chances. Let's try your idea and see what it looks like."

"I WILL figure this out!"

"We know it has to fold it the middle."

"Can I have more paper?"


Before they leave class, I make them hide all evidence of attempts. Crumple and recycle. Finally, I explain the main rule of class - No Spoilers!

This means not discussing the activity for the day before others have attempted it AND not ruining it by sharing answers. This rule works for every assignment, project, test, activity, or class discussions. Then they are dismissed to think about this puzzle all weekend long. And they will. Even though it was not an "assignment."


These bits that I overhear start my discussion on Monday. We talk about risk-taking, perseverance, group discussion, problem solving, and what we learn from mistakes. It is great start to class and setting the tone to how the class will run.


I also NEVER share the answer. Those who solved it are now free to show only those who ask. Some students will continue to work on it all week.

  • Farica Erwin

Every year, I host a week long Art of Math Camp for 6-8th graders. We get to spend 3 hours each day together. I post pictures of the projects on Instagram and Twitter. Camp is always the week before school starts to help me get back into teaching mode. My room gets unpacked and organized before camp. I only work half days, but still have to get up early. AND, all of the "teacher tired" and "body aches and pains" scenarios are over before school starts!


I have a running list of ideas and projects that I use from year to year. You can have your own copy of that list here. I try to change the topics and projects because I have students who repeat the camp and I want them to get something new.


This year, I focused all of my projects around the theme "Explosion." I have never had a theme before (just doing projects I think are fun and cool), but it seems to have really helped me figure out what topics and projects to address.


Day 1: Fibonacci Circles and Explosion Books

I have always done a Fibonacci Sequence lesson of the first day. We sometimes read the book "Rabbits Rabbits Everywhere" as an intro. This year, after attending a session by Sunil Singh (@Mathgarden), we also discussed Pingala, the 500 BCE Sanskrit poet, who probably has the first record of the pattern. For the activity, I always have them make different colored Fibonacci circles. This gives them practice with a compass and measuring the radius exactly. They make circles of radius (or diameter) 1, 2, 3, 5, 8, and sometimes 13 (is they measure in cm). Then they cut those circles out and glue to a 11x17 piece of black construction paper.



This year, I wanted to do something new. I still wanted them to practice with a compass, but needed to display them differently. While reading a ton of art blogs, I found Explosion Books. Ursina Amsler blogs about them and you can find a video tutorial on her site.

My students used 2 pieces of 8.5"x14" heavy paper to make their Fibonacci circles anywhere on the page. We discussed warm vs cool colors, made a list of each, then I set them loose to paint with regular 16 count Crayola watercolors. They had to color the entire papers, and use only their chosen set of warm or cool colors. When finished with this step, I had them splatter paint with a contrast color (white or black). The paint dries pretty quickly, so they could then embellish with metallic sharpie pens.



We let these dry overnight and constructed the books the next day.

Day 2: Paper Folding and Exploding Canvases

Since we were familiar with making circles, we explored other shapes we could make. Once we discovered how to make an equilateral triangle, I challenged them to make 4 next to each other like a triforce. We explored how that made a tetrahedron net. After some Noticing and Wondering about the relationships between a triangles with sides of length 1, 2, and 3, we created out own. Realizing that it would take forever to make a bunch of our own nets, I pulled out the copies I had already made from Clarissa Grandi's blog. Students picked multiple colors and sizes to make a design that would fit on an 8x10 canvas. When tetrahedrons were cut and glued together, we used glue dots to stick them to the canvas.


Day 3: Islamic Geometry and Exploding Squares

At #TMC18 I attended the Islamic Geometry morning session with Annie Perkins (@anniek_p), Megan Schmidt (@Veganmathbeagle), and Stephen Weimar (@sweimar). I was excited to learn the techniques to bring back to Art Camp. To connect with creating shapes the day before, I began by showing them how to create a square, a hexagon, and an octagon with the compass and straight-edge. This year, I lead the students through the expanding squares construction (which I dubbed Exploding Squares to fit my theme).

After, they were allowed to choose a design to put on watercolor paper. We used watercolor pencils to color the designs and painted them with water to get a nice effect. Many chose the hexagon pattern because they liked the flowers created.


Day 4: Modular Origami and Exploding Polyhedrons

I love origami. I used to make elephants while sitting on hallway duty. I have origami constructions ALL OVER my classroom. Last year, we talked about truncated polyhedrons and made some Columbus Cubes.



This year, we discussed stellated polyhedra (which I dubbed Exploding Polyhedrons). I taught them two different modular folds. We use Sonobe units to make a stellated octahedron. Then we used a hexagon unit to make truncated stellated octahedrons. Some students needed to use tape because their hands could not hold all of the pieces together as they worked.



Day 5: Line Drawings and Exploding Fractals

On the last day, I like to have a project that does not take the whole three hours so there is time to finish up other projects. Of course, I also have back-up activities for those quick workers.


The fractal discussion started with the Sierpinski Triangle. This was a great tie-in to previous lessons as the second step looks like the triforce of the tetrahedron net. After looking at the Cantor set and the Koch Snowflake, we discussed area and perimeter. What was increasing, what was decreasing, would it get infinitely bigger...? They really had some great insight into what was happening. For the activity, we made tetrahedron kites. Their favorite part was picking out what color tissue paper to use.


For those that finished early and needed another project, we continued line drawings with parabolic curves. Jen Walshaw has some great templates on her site MumInTheMadHouse. There are some great templates here. The six pointed one looks great colored, cut out, and put on black construction paper. It makes it look like fireworks (according to the students).


Then the last 10 -15 minutes are used to clean up and put away supplies. Students wipe down desks (to get rid of glue stick marks), help put supplies back in my closet, and clean up the floor. Then, miraculously, my room is ready and put together a week before school starts!

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