Reading Assignment September 28th

I will admit that at this point in the school year I’m falling behind on my reading. Even so, here are a few interesting things I had time to look at:

First Day of School at the ABS on Islesford
Via Diane Ravitch, this is a close look at a tiny community coming together for the first day of school. This reminded me a little of my school because it’s so small and community-oriented. I love their goals!

Toddlers Know More Math Than You Think, Study Says This is encouraging! Young minds are intuitively able to pick up on patterns and absorb knowledge quickly. Totally worth staying for the last statement!

A Not-So-Simple Majority
Another reason to love This American Life. This story seems simple at first – a group of parents whose students do not attend public school have control over the school board. Left at that, the situation is clearly problematic. The whole story, however, is much more nuanced and it’s less clear what should be done in the community. This is a great examination of race, class, education funding, and education inequality.

Publisher Accidentally Puts Porn Star on Math Textbook
Pretty self-explanatory.

8 Mistakes Parents Make When They Help Kids Apply to College
The first one is key – we ask our students to consult Colleges that Change Lives a good amount of the time. Small schools usually have smaller class sizes, specialties, and a smaller pool of applicants (in general and for financial aid), but applicants are less likely to have heard of them. It’s not true that more well-known colleges will provide a better college experience! The rest of this is mainly about financial stuff, which is extra important nowadays, and spins into:

Congress Didn’t Pay a Lot to Go to College. Today’s Students Shouldn’t Either.
College degrees are becoming simultaneously more essential and less affordable. This is a great reminder that many middle class desires said to be unrealistic were the same conditions that were not just realistic but reality for lawmakers.

OK, I have to go get some yarn – I need to crochet an owl hat for yet another co-worker baby shower.


Rectangle Pattern Task

I am so into this lesson by Cynthia Lanius! She wasn’t on my radar before but I’m definitely taking a look at her website. I like that the first word of the title is “fun!” Fun, along with Mutual Respect and Safe Place, is one of the three pillars of HGS, and so it is near and dear to my heart.

Even though these rectangle patterns are definitely fun and look deceptively simple, they contain some fairly complex patterns.

lanius rectangle

Can you sense the quadratic equations?!

I changed the task just slightly. I thought it would help them to synthesize their thinking on the patterns if I initially asked them to describe them in words before writing an equation. In fact, for most of the students, I taught a teacher-led lesson on writing expressions before I had them do that. Some did not need any help at all, so I just furnished them with every single problem in this article (which is also great!).

My favorite question on the task as written was the third one, “Will the design use 42 blue squares in any stage? Will it use 102 red squares? Will it ever use 830 squares in all? If so, state the stage number for each answer.” I also loved that it wanted them to predict step 0, that definitely helped them grasp some of the pattern.

I asked them to predict stage 8 by observing the patterns, and to my great surprise every single group actually drew out what step 8 would look like – even though they had all CLEARLY gotten that the blue ones just added 4 every time, and the other colors were two pyramids whose new steps were just 2 boxes longer than the previous ones. Some of them even counted every single box instead of relying on these patterns – disappointing! I bet if I had them predict step 20 they wouldn’t have done that, 8 is too small a number I guess. NEXT TIME!

I overall loved this problem because it is so approachable and has patterns of various levels of complication. It’s got something for everyone! This is encouraging me to try use more visual methods for algebraic topics, especially boring things like factoring that use important skills and practices but that are so boring they don’t deserve a fancy different synonym for boring. Stay tuned for that (if it works).

Reading Assignment September 14th

After a solid week of teaching, let’s take a look at what else is out there in the world of education.

Like “gaydar,” only for people on the spectrum. This is another interesting first-person perspective about autism and what it means to live in the same world as everyone else but see things differently. I was nodding and seeing my kids in this piece, even though at the same time, I feel like I’ll never know enough about autism.

Shit My (Non-Biological) Kids Say About Race and Gender
While this article was from the perspective of a teacher of much younger children, I have absolutely observed similar from my students. There is so much that our students don’t know, and race/ethnicity in particular is such a blind spot because it is often considered a taboo topic. That definitely can’t be the case if we want to live in a more equitable world.

Ideas Taking Shape: Geometric Inspiration
This is a great reminder that math – in particular geometry – can be beautiful and playful and accessible to everyone. Who doesn’t need “a daily dose of Euclidean-based pleasure”?

Crappy Fiskars Compass Fix
I am so excited to see if this works for me!

The Day I LOST It Doing Homework With My Kid
What purpose are these homework assignments serving?

The End of Britain?
I’m not linking to this because it’s about education (it’s about Scottish independence), I just think that the graph is a great representation of inverses!

That’s all I had time to get to – be back soon!


Mathematical Standards of Practice Stations

My second annual “intro to math week” just concluded, and all in all I’d say things went well. Starting on the first day, I set up eight stations around the classroom, each corresponding with a different common core standard.


Look how welcoming my classroom is!

In case you’re not as focused on those as I’m trying to be this year, I’ll note the standard as I describe each station.

1. Make sense of problems and persevere in solving them.

This station was a list of number and letter puzzles that students needed to decode. I’ve heard it called the mental flexibility test. For example, 7 W of the W would stand for “7 wonders of the world.” A handful of the kids got all of these with little trouble, and several were entirely lost. I distinctly remember being handed a sheet of these in sixth grade and being very mad about 57 H V because I hated ketchup and there would be absolutely no way I could have gotten that one.

2. Reason abstractly and quantitatively.

I filled a jar of jelly beans and asked them to estimate how many were in there. The vast majority of students guessed about 100 too few jelly beans, but a couple of them had guesses in the 1000’s, so the average was still eerily close to the real answer. Ironically, I failed at quantitative reasoning when I purchased the jelly beans, buying over twice as many as I really needed.

3. Construct viable arguments and critique the reasoning of others.

Here I found some statements containing logical fallacies and asked students to say where the logic broke down. I made sure to let the classes know we’d be doing proofs – this year 3/4 of them will be.

4. Model with mathematics.

I got this great problem from nrich, walk and ride.

5. Use appropriate tools strategically

This standard is really important, but mainly requires students to properly apply a new strategy they’ve encountered or that I’ve shown them, perhaps in a new situation. I do really like this as a concept, and I’m sure it will happen, but it’s not really something that can be done as a station – it’s kind of a long-term thing. So I decided to focus on the “strategically” part of the standard, and asked them to play the dots and boxes game and note an effective strategy. Here’s a cool website where you play a computer – good luck, because it is formidable.

6. Attend to precision.

For this one they had to cut a strip of cardboard to fit perfectly inside one of the circles in the back of my chairs without bending. Shockingly few rulers were used during this station.

7. Look for and make use of structure.

I made an IRL version of this NLVM manipulative, fill and pour. The downside: my cups do not actually hold the number of ounces I labeled them as, so what was supposed to be 1 ounce was half the 5-ounce glass. This may have thrown them off, I’ll admit. Next time I may just set up my laptop with the virtual one – and that way when they get the answer there’s a duck!

8. Look for and express regularity in repeated reasoning.

I made my sweet little tower of Hanoi.


One of the pegs fell out, but one of the students kindly taped it up with a significant amount of masking tape. How sweet. This station went over well with the students because it’s so physical – I’ll have to keep that in mind.

This was good – students worked well together, got a lot accomplished, and seemed to feel comfortable with the difficulty level, regardless of prior knowledge or skill. I’m optimistic moving forward.

On Whimsy

I do not know a precise dictionary definition of the word whimsy, but I hope that after reading this blog post you’ll know what it means at HGS. We just concluded bonding week, our first week of school, and this year it was especially heavy on the whimsy. The very first day of school we introduced ourselves and noted things around the physical plant. But we also spent a big chunk of time on some limited resource challenges. Students were divided into small groups and asked to build the tallest possible structure out of dry spaghetti that would hold up a marshmallow. Here’s the winning structure:

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That’s pretty whimsical

We then watched this TED talk about the challenge and the importance of prototyping – we’re hoping to come back to this concept at other points in the year. Hoping that they had learned from the first experience and the talk, we then asked them to create a structure out of index cards to hold the maximum number of glass beads.

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Did you know that a slightly more whimsical name for those things is Dragon Tears?

Sure enough, we had five very successful teams. All of this was designed to lead into the most large-scale and whimsical limited resource challenge of all – building a boat out of trash bags and duct tape. The challenge was announced Project Runway style by none other than Heidi Klum! JK it was me, dressed in the wedding dress we happen to have at school, as Heidi Klum. I’m not sure that any of our kids watch Project Runway, but wearing a costume and attempting an accent felt pretty whimsical to me. I’ve written about the lessons about collaboration that show provides in the past. The groups will be launching their boats next week.

We started the next day with some Minute to Win It challenges. I didn’t take any pictures, but I’ll poach this one from the newsletter because I’m somewhat in it. Neal’s task was to get a playing card to stick into the watermelon.

Some of our activities this week wouldn’t necessarily qualify as whimsy. In a rotation through our classrooms in small groups, students set up their email, signed up for electives, and agreed to our drug and alcohol policy. Another teacher, Drew, and I had groups brainstorm what they wanted to see happen at school this year. Telling students how many of their suggestions got used last year (about 80%), and “yes, and”-ing even their most ridiculous ideas shows kids that they are listened to at HGS. That’s a really important thing for kids to know.

The work students did on our yard, planting flowers, pulling invasives, cleaning buses, maintaining trails, and building a bench, isn’t necessarily whimsy either, but it does help foster connections between students, staff, and school. Look how sweet the front of the building looks now!

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Our culminating activity was mainly an exercise in estimation – basically Mathematical Standard of Practice 2, Reason Abstractly and Quantitatively. Students were to ponder 6 un-googleable questions, like “when placed in the main room, which classroom would the cat enter first?,” and “could we all hold hands and circle the school building?” (it turns out we could). Here we are answering “how many paper clips would you need to span the length of the green bus?”

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Well actually at this point we had all of the paper clips in a chain and were jumping rope with them.

I have to admit, when I first came to HGS I was unsure about the whole bonding week concept. It seems like a waste of instructional time to devote three entire days to non-academic pursuits. But education is all about relationships, especially at our school. This week is valuable time for students to get acclimated to a very different educational setting if they’re new, and to get to know the classmates and teachers they’ll be working with all year. It allows us to make connections with students and understand who they are as people before we attempt to meet their needs as learners. It is absolutely a luxury to be on such familiar terms right off the bat, but it’s a luxury I wish more schools would grant themselves. Why couldn’t larger schools devote time to whimsy?