Trying to find math inside everything else

Archive for March, 2012

Design for Tracking Progress

When the ISSN came and saw my school, they had a document to show our growth in several different categories that I thought looked cool. It consisted of a circle with various rings to show your level in a category, and split into wedges for each category. The person presenting it, however, pointed it out that is was fairly flawed, because the outside ring looked so much bigger than the inside ones, so even when you reached 3/4 it looked fairly empty.

Of course, the problem was purely mathematical. Whoever had designed the chart had split the radius of each wedge into 4 parts equally, so that the first ring started 1/4 of the way down the radius, the second ring was 1/2 of the way, etc. Clearly that will make the areas very different. So I quickly made up a version where the areas were proportional, which isn’t too hard in graphing software, since the formula for a circle uses r^2 anyway.

Afterwards, I decided to make one for my own class. I also decided that, because each mark (Novice, Apprentice, Proficient, and Master) was not weighed the same (for example, Novice is a 50, worth a whole lot more than any other category from the start), I would have the areas of the circles have similar weights. Here’s what I made:

Learning Goal Checklist – Spring Semester

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3 Acts – Potatoes

I tried this out today in class (and will repeat tomorrow), and it worked out quite well. So now I want to share, my first 3 Acts problem.

Act 1

Potatoes – Act 1 from James Cleveland on Vimeo.

The question I intended to be asked was “How many of each potato do I need for the recipe?” or variants such as “What does he do now that the scale is broken?” or “Did he buy enough potatoes?” Those were all asked, along with some others.

Act 2

The video shows some things (how many potatoes I bought the first time, and the cashier says the totals), but it’s easier to lay that out when the students ask.

After that, they also wanted to know how much the potatoes cost, so I provided that.

But that’s all the information I can give: my scale is broken and I didn’t take the receipts from the cashier. Luckily, this is enough.

Act 3

After we calculated the weight, we compared when I weighed them in my “new” scale.

I wish I had my digital scale for a better Act 3, but it’s actually broken (and the calculations I had to do when it was inspired this problem) and the analog was cheaper. The solutions you calculate (.36 lb and .43 lb) are pretty close to the values on the scale (which I peg at .37 lb and .5 lb).

The problem itself, in terms of the system of equations involved, is not that complicated (because I am using it to introduce the concept of elimination), but for the students who solved it quickly, I had a trickier problem up my sleeve:

Extension

What if I had bought 3 Idaho potatoes on the second trip? How can I figure out how much each one weighs now?

The Complete Problem

Potatoes.zip

Writing by Design

Though I’m a math teacher, I also consider myself to be a writer. Unfortunately, my more prolific days were pre-teaching, mostly because of the time. But as I was going to bed tonight, I realized that thinking like a teacher (in particular using the Understanding by Design framework) would help me get past a block I’ve been having.

Back when I was in undergrad I wrote a novella that, for the most part, was pretty good. But the story only really picked up from chapter 2 onwards: my prologue and first chapter were muddled, confusing, and needed a lot of work. I’ve opened it up every once and a while since then to try to fix them, but I just didn’t know where to start.

That’s where thinking like a teacher helps me. I just had to think, well, what exactly is my goal in having those chapters? (Establishing the main character’s relationship with his aunt, his tendency towards flights of fancy, etc.) With those goals clearly established, it becomes easier to envision what I need to do.

But there’s another part. I then asked myself, why was I only trying to change things in the prologue, instead of rewriting a new chapter that meets my goals? It’s because that prologue was originally a short story that then spawned the whole book. In teaching, that would be the same thing as already having a great activity and basing a whole lesson or unit around it. Everyone knows that is a terrible way to lesson plan. Turns out it’ll hold back your writing, too.

Now that I’ve realized these things, I’ll let them simmer in the back of my mind while I sleep, and maybe the morning will look brand new.