Jesse’s math homework last night included the following problem:
Jesse was stumped. So was I. How can it be that knowing the length of only one side of a shape, you can know its area? So Jesse and I talked, and it was a complicated affair for a 9-year-old. Unless I’m missing something, you have to make significant assumptions about the number of sides and the angles involved for Aiden’s assertion to be true. But if you’re working on the principle of right-angle four-sided arrays, which is what the kids have been doing for two months as they learn multiplication, Aiden doesn’t seem to have enough information at all with only the length of one side. I think he needs to know a width as well as a length. And there’s something goofy about answering “it can be true if it’s a square,” because then of course Aiden “knows” the length of all four sides of his garden. Or I suppose you could argue that if the adjoining sides of the rectangle are some factor of the one known side, like they’re exactly twice as long, then Aiden can use the one known length to measure the other sides and so on. It doesn’t feel right.
I asked Jesse to stretch her thinking by leaving straight lines in the dust. Boring. What if there were a shape with only one side… The only thing you have to assume then is the shape: it’s a circle garden. Then Aiden knows the “length” of the one “side” – the circumference – and then he can calculate the radius, and from that he can calculate the area. I think I remember these basic equations right, so I wrote them down for Jesse and suggested she stretch her third-grade teacher’s thinking.
Jesse officially thinks I’m crazy now, just a complete lunatic. I feel like I must be missing something really obvious, and it’s making me feel stupid today. What do you think?
grumpy for no reason 
Yeah,,,,,, I would think so too if I was in Jesse’s place. Kid just got good at add n subtract and you are givin’ her entry level algebra. OUCH. Still you show an amazing interest in the development of your kiddies that they will never forget. Keep up the good work girl.
The answer is he can only know the area if his garden is square. Seen it before. A little disingenuous IMO.
I like the square answer but it is tough.
How about this one, read on the interwebs recently? “If I throw a triangle out of a car going 20 mph,& wind resistance exists how many cupcakes can Pedro buy with one human soul?”
My son came home with the exact same problem. I was a bit upset at the thought of the children that struggle enough, as it is, with basic multiplication, having their confidence destroyed by a problem of this complexity IN THE THIRD GRADE!!!!???? Come on!! What ever happened to teaching the basics?? Basic Math is hard enough for some kids. This new “common core” method is geared toward advanced students and leaves those that struggle with math, dazed, confused, and second guessing themselves.
LET THEM GET COMFORTABLE WITH THE BASICS!!!!
My answer to this question is definitely NOT “Its a square”. If Aiden knows its a square then the problem should read he knows the length of ALL 4 sides and can easily figure out the area, but that is NOT the case in this problem. There are no assumptions in math.
It is not a circle either. Based on the geometric definition of a polygon, a circle has no sides or infinite sides. According to the definition, a circle cannot have sides because it isn’t made up of line segments that are connected by shared endpoints that form interior angles.
Aiden is full of it!!!
TEACH THE BASICS!!!!!