Dot Paper Generator

I’ve been using dot paper (both “square” and isometric) in my grade 9 class lately, so I put together a Java application that generates it. The image files it produces are PNG files. Feel free to use it if it’s helpful. No warranty, expressed or implied, yada-yada.

Google Drive link to download .JAR application file

DotPaperSample.png

Sample PNG file.

Here are a couple of PDF examples that I produced from the PNG files:

Letter-QuarterInch-DotPaper

Letter-Isometric-QuarterInch-paper

The PNG files are set to 72dpi, not the desired dpi the user chooses… I haven’t figured out a simple way to set that information in the PNG metadata. The PDF files above are both 600 dpi, if I remember correctly. 

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Physical phenomena for quadratic relations

I’m working on a quadratics unit for my MCF3M (online) and MBF3C (F2F) classes. The Ms need to be able to do a few more things, but both groups have to be able to model quadratic “stuff” using an equation.

I’ll be using desmos.com pretty heavily, and I got some great ideas from Heather Theijsmeijer (@HTheijsmeijer).

I’m trying to find some examples of physical phenomena that I can have students in either class play with to practise/demonstrate modelling. Here are my ideas so far:

Throwing or Bouncing a Ball

This is the first thing I thought of. A ball follows a nice parabolic path in the air if it’s moving horizontally.

My plan is to have students use a phone or camera to record a video or a rapid burst of images, overlay a set of axes, and fit a curve to the path. My iPhone can record at 120fps, which is great. I also found a handy post at Stack Overflow that explains how to extract images from a video, so that might be helpful too.

Pouring Water from a Hose

Set your hose at an angle, turn on the water, and snap a picture. Parabola. Beauty. Maybe put a piece of grid paper behind it, or just import it into Desmos.

Rolling a Ball Up An Incline

This one’s messy, but I think it might work.

Dip a marble in some ink or paint. Set a piece of grid chart paper on an incline (say, a piece of plywood) and roll the ball on an angle up the paper. When it crests and rolls back down, it should have left parabolic paint. On graph paper.

Other ideas?

I’m open to suggestions. I have stuff like photos of suspensions bridges, etc., but I really want something students can generate on their own.