WAIT! It gets better. I snapped a picture of it and threw it on Twitter for a little friendly competition. Nathan, Natalie, Fawn, and I took turns counting all of square units. Natalie came up with the best estimate and I think Chris Robinson came up with the best estimate as an online contestant.
WAIT! It gets even better. Marc Garneau took the picture and used some digital magic to calculate the exact area of Fawn's hand tracing. I decided to make the hand-tracings a theme for the last week of summer and asked Marc to find the areas for us. He generously donated some of his time and did a fantastic job giving us the answers. Marc's work really paid respect to the original images. He went above and beyond: Marc typed up the play-by-play on calculating the areas of each hand. I don't know about you guys, but I think this is such a fun way to talk about area and square units with your students.
Day 166: My amazing wife begins the week.
Day 167: My three-year-old son got a kick out of getting his hand traced.
Day 168: I asked Fawn to be apart of the week. After all, it was her idea, right?
Day 169: It was a little challenging, but my wife and I worked together to get our seven-month-old daughter's hand traced.
Day 170: My hand.
Do it with your students. Here is Marc's play-by-play on finding the area of any traced hand. Thanks again Marc!
To measure a non-regular shape on a grid, the idea is to overlay a mathematical grid and then construct a polygon around the shape to approximate it. There are various tools that can be used to do this - for these I chose to use Geogebra because it's free and accessible to all of Andrew's millions of Estimation180 fans!
(1) Scale down your image to a good resolution for your screen - too high and it looks messy when imported into Geogebra. I scaled these down to a height of about 800 pixels or so, and 72 dpi.
(2) Create a new Geogebra document with a Graphics view. Show both the axes and the grid.
(3) Under the Edit menu, insert an image from a file. The image appears overtop of the grid and has 2 points at the base. Move these points to scale and rotate the image as needed. You can simply click and drag anywhere on the image to move it where you want it.
(4) Use the "Move Graphics View" tool (4-directional arrows icon) to adjust the axes to match the grid of the image.
(5) Right-click on the image and select "ObjectProperties…" Change it to a background image.
(6) Hide the grid and axes (otherwise your points may snap to lattice points, which isn't desired in this case).
(7) Use the Polygon tool to create a polygon that approximates the shape. Basically it's tracing using segments, so your points will need to be close together to approximate curves. Once done, you can adjust some points to get a better fit.
(8) Under the Edit menu, select "Object Properties…". Select all of the points, and then un-check "Show Object" - this will hide all of those unsightly points.
(9) Use the area tool to measure the polygon, then hide the result.
(10) Create a text box to display your calculation. You can type in the text part, and reference the measurement by selecting 'poly1' from the 'Objects' pulldown menu.
(11) Change the size, etc. of the text. Show your axes and grid.
(12) Under the File menu you can export your creation as a picture.
I haven't tried this with students, but I think it would work quite well to have them do it.