Seemed like a really interesting exercise, so I gave it a shot with the boys this morning. I like the simplicity of the task – here are some shapes, shade in 1/4 and shade in 1/3 of each shape. Definitely a great way to get kids talking about math.

A feel that my kids approach math in two different ways. My older son loves to calculate and my younger son’s approach is much less about calculation and more about feel. You’ll see that difference come through in their approach to the questions in this exercise.

First, my older son shading in 1/4 on the 4 shapes. His approach to chopping up the right triangle was pretty interesting:

Second, my younger son shading in 1/4. His approach in the triangle is also really interesting, though one clear difference from my older son is that he’s not calculating. His symmetry argument on the square was nice to hear, too:

Next up, my older son shading in 1/3. This task was a bit harder for both kids. My older son things that part of the difficulty comes from 3 being prime. His approach on the triangle, the square, and the diamond is pretty neat – he realizes that you can cut a triangle into three equal areas by dividing one side by three, and then extends that idea to the two quadrilaterals.

[also, on publication, youtube isn’t generating a thumbnail image for this video. The video seems to work fine, though, so hopefully we’ll get a non-grey thumbnail sometime soon.]

Finally, my younger son talking about 1/3. He thinks the additional difficulty in this part comes from the fact that 3 is not a power of 2. His feel for math comes through in his explanation about how to cut a triangle into three pieces of equal area. He knows there’s a way to do it and, as above, explains it without calculating:

On the Rhombus, he knows that it is easy to cut a square into thirds and figures that by first bending the rhombus into a square, cutting it, and then bending it back into a rhombus, you’ll cut the rhombus into thirds. That’s a wonderful piece of mathematical reasoning for a young kid 🙂

His explanations of the how to chop up the circle and the square into thirds are neat, too.

So, a really neat exercise for kids, and one that is really easy to implement, too. I’m always really excited to hear kids talking about math. With this exercise, you get kids thinking a little about fractions, a little about geometry, and even a little bit about symmetry. Really fun morning.