

This comes from the Common Core

Develop understanding of fractions as numbers.
1. ……
fractions on a number line diagram.
a lengths 1/b from 0. …….


The mystery is solved…….




It only has to start from zero.







L cannot be moved in the static picture.


Filed under fractions, geometry, math, Uncategorized

6 responses to “1/5 is one fifth of the length of a line segment of one unit – but how?

  1. This is so cool! I love it and I think I understand! This is a grade 3 standard, and normally we would do what you did at line “a”: start at 0 and mark off 5 evenly spaced (well, as even as possible) intervals. Then we’d label each 1/5, 2/5, etc up to 5/5 or 1 whole. So we’re starting with the partitions first. But the standard says to start with the whole first and then do the partitions. I guess my question would be: Does the difference have a significant impact later on that caused the standard to be written that way?

    • Joe: The standard is conceptually wrong. It makes no sense at all.

      I spoke to my wife on this and suggested a set of equally spaced (parallel) lines, separation immaterial, and a brick or a piece of ribbon. Set up the ribbon so that its length fits between the parallel lines, at an angle, to give five (or whatever) equal bits – and there you have one fifth of the ribbon in each section. My wife explained that she learned that at her mother’s knee in the 1960’s.
      I will do you a diagram if it helps.

  2. My thoughts are that yes you can set up a line segment and call it one unit, but you cannot assert that the point 1/5 of the way along has any real existence without a construction (a Euclidean construction). Perhaps “conceptually wrong” is a bit harsh!
    I was thinking also of angles and constructions, and it would appear that very few angles at all can be constructed. Therefore most angles have got to be measured, or deduced from measurements. These measurements are inevitably approximate

    • You can tell me to stop at any time, but I am genuinely curious because I’ve spent so much time living in this standard. So I would want to know: how would you rewrite the standard? Do you feel it’s placed appropriately?



WordPress.com Logo


Twitter picture


Facebook photo


Connecting to %s