Posted on 09/15/2010 8:41:36 PM PDT by Fundamentally Fair
The illustration shows "projecting" fractions onto a common line (the top line).
The technique works, regardless of where, vertically, the segmented/fraction lines are drawn.
Some kids might have the light go on, seeing this, but most won't.
I don't know if the student is taught, or is expected to figure out a way to "commonize" different length "wholes."
One of the "wholes" is a number line carved into 6ths, the other (a different "whole" length) is carved into 8ths. The student should know that a direct comparison won't work, because the "wholes" are not the same length. Either one line has to be stretched, or the other shrunk. That right triangle figure that includes two "wholes" is one way to accomplish this equalization.
If I was teaching this to my kids, I'd describe the projection as a shadow. The shorter line has to be "closer to the light" in order to make the sames size shadow as the longer line. The comparison of is made at the "common length shadow," not at the line.
As would I, but that would be beyond standard 5th grade math. IMHO based on my 5th grader.
I think a 5th grader could learn it. Unless the idea of "bigger/smaller" fractions is too advanced.
Simple examples first. Half of a pot pie, vs. half of an apple pie (the pot pie being a small item). Either way, half is a half.
Next example, half of an inch compared with half of a foot. Obviously, half of a foot is longer, but the question is which is a bigger fraction. half=half, so the fractions are the same.
Next step, find a way to compare half and inch and half a foot, "on the same line." Or, "stretch the inch." I'd do that by drawing the triangle, and a line bisecting the bottom angle. The bisector meets at the half point of any horizontal line (segment). Could go up to half a mile, if the paper was big enough.
Then ask about a way to compare unlike fractions on unlike length lines. See if the kid sees the application of the "half=half" method.
“See post 18. Agree? I’m senseing some sarcasm...”
No, No. I’m just terrible at math and thinking my son had just called saying his 4th grader got a B in math last year, but can’t remember to “borrow” this year, and says she hasn’t learned yet to subtract from zeros by borrowing. She is struggling and gets a B?
Yes, after I saw the “triangulation” method diagram someone posted, I understand what they’re getting at. But, even though that method could work with number lines that are out of scale, you’d still need the individual segments of each line to be equidistant, which is another thing you are never supposed to assume with number lines.
Basically, by teaching this method, they probably figure they are making it easier for kids than the old “common denominator” method, but they are actually teaching kids to disregard a couple basic principles of mathematics.
I have to disagree with you here. The metric system is far superior - and makes sense. The lobs have nothing to do with it. It’s been in use in sciences for nearly 200 years because it just works better. Now we could talk about the problem of 60 seconds in a minute, but that’s already been a standard since the Babylonians or Sumerians or whomever decided it, but there is no reason to be counting base-12 at all. The big problem with is question is that no one would ever divide a meter into 8 segments, it would always be base-10, so 4/6 and 5/8 doesn’t necessarily exist in practical use of the metric system. The question is should refer to each as base-10, ie; 5/10 and 6/10, then it all becomes clear, and that is why the metric system works so well. Common denominators should be apied here, but the OP did say that was a follow up lesson, so perhaps this question was meant to be misleading on purpose. Regardless, its a horrible question to ask in hopes of furthering a student’s understanding of real numbers. This should have at least had the lines and segments the same length.
Well met.
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