One Half Is Not Two Quarters? Really, CCSS?

Clicked on a tweet hawking great lessons for the toughest parts of math CCSS standards (as defined by some research or other).

There was nothing at my level of interest (Algebra) but I spotted a lesson on equivalent fractions and went for it because fraction skills matter big time in Algebra. OK, the lesson I spotted was for the third grade (remember that) but I guessed it would still get to the crux of fractions.

Not too far along I tripped over something. Looking down at the page, I thought I saw the assertion that 1/2 and 2/4 were not equivalent. In a lesson on equivalent fractions, it was quite exciting to discover 1/2 and 2/4 were not equivalent.

A, here it is, the section had a subtitle: "To find equivalent fractions, the size of the wholes must be the same." Note that this little paragraph pops out of nowhere in the middle of a lesson on 1/2 being equivalent to 1/4. If I got lost, a third grader would...?

Of course, the subtitle is wrong. The size of the whole has no bearing on the equivalence of the fractions. A fraction of a whole is not the fraction, it is the product of the fraction and the whole. Hey, let's use algebra:

Let us call two wholes x and y. If (x > y), then (1/2x > 2/4y), but the fractions 1/2 and 2/4 are still equivalent. QED.

Oh, wait, you want to call the compound product of a fraction and some whole the fraction? Let us convene a council of mathematicians to decide if .. wait. We are springing this on third-graders right in the middle of a lesson on the equivalence of fractions?

One might want to follow the lesson on equivalence by having students contemplate why a half dollar is less than a 2/4 million dollars, just in case the equivalence lesson causes confusion by misapplication, but... is that a problem?

Every time I look at the Emperor's new CCSS clothes I see lessons more confusing than inspiring, and they are often downright incorrect if one wants to look at them rigorously.

So we are in for five years of refinement of these CCSS lessons to get them right. That is understandable -- it is hard to get anything new right on the first try -- but then should not CCSS be off somewhere in an incubator being refined and tested so it can eventually win on the merits?

CCSS principles may get an "A", but its implementation is still in the first grade and those mandating it now get an "F".