This is me abusing the fact that there are many talented, resourceful math teachers who read this. This is me asking for your help. It’s similar to a question I would have posed on Twitter, but the question is much too big, so I’m also abusing the fact that I have a blog. Sidenote: this is another wonderful benefit to being a member of the blogotwittersphere – that instead of asking my department for resources, I get to ask the whole world!

I’m preparing for a unit on area and, based on an informal exit ticket I gave a few days ago, my students don’t know very much about area even on a conceptual level. Which is sort of exciting to me, since it means I get to teach them from scratch. One thing I want to impress on them is how the choice of units effects the type of answer you get. I want to impress this on them visually – to show them a 1 cm x 1 cm square, then a 1 in x 1 in square, then a 1 ft x 1 ft square, then… etc etc etc. If area is determining the number of squares that can fit inside a shape, then I want them to know that the size of the square is a big deal.

To do this, I thought of xkcd. They have several incredible charts of different objects that are to scale. The most recent one, and one of my favorites, is the comparative cost and distribution of wealth:

They also have the height of the observable universe and depth of a computer circuit to the neuron level. The important thing is that all three of these diagrams are to scale, which paints a powerful visual picture for comparisons.

What I just spent 30 minutes fruitlessly Google searching for: A chart/image/visual that has a to scale representation of several different area measurements – all side-by-side – so I can show it to my students and we can compare them. I imagine it would look something like this (only prettier and more accurate and better in every way because I made this in 30 seconds):

Finally he gets to the point: Do you, dear reader, know of any such chart? Any place on the internet that sounds like that I’m looking for? Something visual that I can show to my students and we can explore this idea that the bigger the unit, the larger the square, so the smaller the area – and the smaller the unit, the smaller the square, so the larger the area. The most important thing to me is that it is to scale – the accuracy matters and my kids deserve it and I’m a little OCD like that. If you know of any such resource, please please please tell me in the comments.

From → Curriculum, Math

1. Not sure if this is exactly what you are looking for, but over at http://incompetech.com/graphpaper/plain/ you can print out graph paper with diff spacing between the lines. The bigger the grid, the less squares it takes to cover the page. A bit of a different angle than what I think you are going for, but it’s a way to get a bunch of squares quickly even if it’s not side by side until you print a few.

2. If you end making one, be sure to post it; I’d love to see it.

I should also mention while I don’t have a lot of lesson plans posted, I do have my introduction to area up:

http://numberwarrior.wordpress.com/2010/01/20/crowd-stuffing-revisited-introduction-to-area/

• Jason – I’m doing something similar re: here’s a grid and some shapes, estimate the area before I tell you the formula. I didn’t think to start with irregular shapes – I wish I had included Texas and Arizona. I really like the hooks you have in your area unit and your question progression on the 2nd day.

I’m wanting this unit to segue into ‘I can find the area of irregular shapes by breaking them up into triangles’ because, well, that’s how it’s done in the real world anyway. If I can get a computer situation setup, I want to do a variation of Bowman DIckson’s area estimation in Geogebra: http://samjshah.com/2011/07/13/make-it-better-drawing-with-geogebra/. He has his students use calculus to find areas of images they’ve imported into Geogebra – I would have them do the same with tiny triangles or other familiar shapes. But I dunno – we’ll see what happens and how crunched for time I am.

3. Check out the one I threw together. It’s not the prettiest, but it is accurate to the nearest tenth of an inch. Conversions are included at the top of each file.

http://nicholashussain.wordpress.com/2012/01/23/area-diagrams-to-scale/

• Thanks Nick! I’m gonna use that with one of my classes tomorrow – we’ll see how it goes. Maybe one of these days one of us can make a flashier, more extensive version