Homeschool Math Blog

Here's an online fractions activity that is somewhat artistic and that some of you might find fun. Unitize fractions on a grid Conceptua Fractions is offering this tool for free during this summer. Here's a screenshot: First, you drag a red rectangle or a triangle that is going to be your UNIT. It corresponds to 1. Then, you make rectangles and triangles of the other colors. Your task is then to figure out their area compared to the UNIT you established in the beginning, and type it in as a fraction or a mixed number. For example, in the picture below, my UNIT is actually 4 squares. The blue rectangle is 6 squares, so its area, compare to the unit, is 6/4 = 3/2. Enjoy!

I got inspired by the blogpost Art School | Geometric Design with Islamic Art where Deborah shows how to make a neat flower design with seven circles , using a compass, and then coloring it using 2, 3, or 4 colors (or however many of your own). I think it ties in neatly with mathematics, and lets students practice drawing circles with a compass.  My girls loved the art/math project. Here are pictures they made: Here are step-by-step instructions for the flower design: 1.  Draw a line and a circle so that the circle's center point is on the line. Then mark the points where this circle intersects the line. 2. Use those points as center points, and draw two more circles. The radius is the same all the time, so make sure you don't change it on your compass!We used 5 cm as the radius, and that made the whole design fit neatly on a regular letter size paper. 3. Now note the two points marked in the picture. They will be used as center points in the next...

I was told about this free download of the book Geometry in Art , by Hilton Andrade de Mello. On the page, you need to scroll down to the words "free downloading". This book is a basic introduction to geometry in art, with topics such as polygons, spirals, polyhedrons, tessellations, perspective, the golden ratio, symmetry, geometry and symbolism, and geometry and informatics. It has lots of illustrations and artwork by various artists, and can serve as a nice introduction for anyone who hasn't studied these topics before.

Continuing on a litlte bit more with my thoughts concerning Lochart's Lament . Lockhart starts out his lament with a comparison: WHAT IF music teaching only consisted of learning to write music , write notes on paper, and only after high school level would students be allowed to actually hear and make music? WHAT IT art instruction would consist of "paint by numbers" until high school, which is when they'd actually start applying paint... Lockhart remarks that if he wanted to destroy a child's natural curiosity and love of pattern-making, " ...I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education ." He calls school mathematics "pseudo-mathematics", where emphasis is on the accurate yet mindless manipulation of symbols. These are, of course, very strong words. I don't fully agree... I don't feel all that's done at school would be pseud...

Recently there's been a lot of talk about an essay written by mathematician/teacher John Lockhart, called Lockhart's Lament . Some people praise it, some are more skeptical. Lockhart's Lament makes for good reading and he raises some really interesting points, so I can heartily recommend reading it. Personally I don't fully agree with every statement he makes there. But his MAIN point concerns mathematics as an art, and how we should teach it. I went ahead and copied a part of the essay below. This is direct quote from the essay, presenting a VERY GOOD example with the triangle problem. So let me try to explain what mathematics is, and what mathematicians do. I can hardly do better than to begin with G.H. Hardy's excellent description: A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. So mathematicians sit around making patterns of ideas. What sort of patte...