It's always a bit of a challenge to figure out what to cover next with summertime Math tutoring. During the school year, I can basically follow or anticipate the material that the student's teacher is covering, which makes it easy. But in the summer? I look at the next year's curriculum online for most of my inspiration, but often it seems like Year N+1 contains more review of Year N than anything else.
So for the student who's headed to Grade 8 in September, I decided this afternoon to combine the Pythagorean Theorem (which I've covered over the past two sessions) with a little bit of Cartesian coordinate magic. I know that the student has already learned how to plot points (x,y) in the appropriate Cartesian quadrant, so tomorrow I'm going to present him with the following three points:
If you can picture that in your head, you'll notice that the 3 points form a right-angled triangle when you join them up. So I'll then ask the student to determine the length of each side of the triangle. Two of them are relatively easy to find, as they're each parallel to one of the axes. But that third, more diagonal side... to figure that one out will require use of what good ol' Pythagoras taught us!
From there, if all goes well, I'm going to teach him how to take
any two points and figure out the distance between them. He may not need that for awhile yet, but it's still a good thing to have in your back pocket, I'd say.
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