The other night, my son brought home a geometry assignment on midpoints that he needed to complete. I recognized the assignment right away because it was a simple worksheet from the “binder”, a collection of district purchased worksheets from 2003. (Imagine eye rolls and a sea of long sighs…Yep!)
As ridiculously bad and basic as this worksheet was, my son had not turned it in because he did not understand how to do the work. Yes, he lives with a math teaching momma, but he’s still not a fan of being tutored by his mom. I get it. (Again…eye rolls…long sighs)
With that said, he is lucky and here is how our “homework help” played out.
His first few problems were simple number lines and after talking about the meaning of a midpoint, he eventually figured out that he could combine points and divide by two. Things changed a bit when he got to coordinates.
Me: What don’t you get?
Son: Well, it has two points. What does that have to do with the number line up top? How am I supposed to graph that?
Me: How would you prefer to graph them?
Son: Probably on a coordinate grid.
Me: Well, you don’t have one. So what’s your plan?
(Does next one and sees another horizontal line and says oh, it’s (0,-4))
Son: Cool, I get this part
Me: Wait just a sec. Let’s explore those a bit more. What would you do if the line wasn’t horizontal? What if you had coordinates that weren’t so simple to graph? How would you find it?
Son: She gave us a formula to use. (searches mounds of crumbled paper for notes) [eye rolls…long sighs]
Me: Let’s explore
This is the point where I opened the Geogebra Chrome app and placed a point that we renamed M. I then told him to place two other points anywhere on the coordinate grid. Next, I told him that Point M was his midpoint and his job was to move point M to be the midpoint of the two other points that he placed.
Me: What do you notice about point M in relation to the other points?
Son:Well, it looks like it’s still halfway.
Son: Well, look at the point (0,9) and point M. They’s like opposite corners of a rectangle that’s 4×2. (I showed him the segment tool and he outlined the lines)
Look at the point at (4,1) and point M. It’s the same. Both are 4×2. Wait, the whole thing is 8×4 and the midpoint is at 4×2. Does that work every time?
(Son knows the drill and proceeds to check several different points. He grins and says…wow)
Me: Let’s go back to your original problem. Where was your midpoint?
Son: Well, it’s at (2,5). [stares at the page a bit] (0+4)/2 = 2 and (9+1)/2 = 5
Son Screams: Oh my gosh…Does that happen every single time?
Me: You know the drill
Son: (Places points at several locations…followed by calculations) Why didn’t we do this in class? All you do is Add x’s and then divide by 2. You do the same with the Y’s. It’s like finding the average of the points.
Me: What about the next part? This time, you are given a midpoint and asked to find the other endpoint.
To be continued…