In her most patient, teacherly voice:
"I'm drawing a simple house, Amelia. Everything in the house is mostly 90 degrees...you don't have to be exactly accurate but it just has to be good...a triangle window and here's the front porch....compare these two houses. Can you fix this one? Good job!"
[Her explanation to me when I asked her later what she was doing: "I drew a house without angles and with angles and Amelia had to fix the house without angles up!"]
After Amelia's success, she continued the lesson with this explanation:
"There are even angles in nature -- straight up and down trees, but some are even 80 degrees, slanting. The old ones are 50 or 40 degrees."
Later, I got a look at her drawings:
In the larger house I see her thinking through the angles all starting from the bottom left vertex/corner of the house, which is forward movement from her original representations in the Map of Angles post. Below the big house is the 'house with angles' at the bottom and what I think is the 'house without angles' (all wonky looking) above that (I thought I saw a different drawing with the same ideas but that, apparently, has gotten lost in the shuffle.)
Another quiet moment found her exploring the structure of an isosceles triangle.
"See, there are eight of these triangles on each edge [above] and fifteen squares on the bottom edge," she told me. She also called the line she drew from the top vertex to the center of the bottom edge a "diameter" which she knows is how you divide a circle in half.
In addition to all our sidewalk math adventures over the last year, we've learned more about identifying and classifying geometric shapes in the Beast Academy 3A series but it's been a while since we did the polygons chapter. We got through skip counting which was perfect and, after entering the perimeter chapter decided to take a break. This drawing really shows me she's thinking very specifically about the length of each edge.
And, finally, although this may seem more in the 'art' category, I know for sure that drawing three-dimensionally has all kinds of math involved in it, I just don't know what kind, lol! Six or nine months ago she tried to sketch Platonic solids and really didn't do it very successfully. I think her eye has come a long way:
Her milk box:
An Asian ceramic bowl with some paper flowers in it:
Her electric pencil sharpener:
I love seeing (and hearing) the world through her eyes.
I especially like the drawings - especiallyestly the coconut milk carton. I too think there is "lots of maths" in this (I think of Rubik invented his cube to get students to think better in 3D - just checked - you'll like this quote: "Space always intrigued me, with its incredibly rich possibilities, space alteration by (architectural) objects, objects' transformation in space (sculpture, design), movement in space and in time, their correlation, their repercussion on mankind, the relation between man and space, the object and time. I think the CUBE arose from this interest, from this search for expression and for this always more increased acuteness of these thoughts...").
ReplyDeleteDrawing 3D pictures with triangle dotty ("isometric") paper is fun. Like here: http://www.bbc.co.uk/bitesize/ks3/maths/shape_space/3d_shapes/revision/4/
ReplyDelete(There are sites where you can download it for printing.)
Also making the things you draw and drawing the things you make with little interlinking cubes. We do things in cm over here, so that's neat because they're cm cubes:
http://en.wikipedia.org/wiki/File:Linking_cm_cubes_2.JPG