Yesterday's tutoring involved an introduction to fractions in my 4th grade class. I think it's cool to see the intrinsic nature of understanding fractions. For students, doing math computations with fractions quickly becomes difficult. Even as adults, we shy away from fractions, decimals, percentages, and ratios, which all express the same ideas. It's hard to conceptually think of a quarter of a third or to add up 1/6 a teaspoon to 3/4 of a teaspoon and even more so to compute complex fraction equations. Personally, I can't verbally explain what happens when you divide a fraction by another. Completely out of my realm.
However, being able to divide something into fractions and the visual understanding of equal parts is something kids pick up quickly. Our class was dividing up 4x6 arrays into fractions, like a quarter, an eighth, thirds, and sixths. The arrays have 24 smaller units inside, but my students did very well with dividing up squares and rectangles into thirds then sixths. I pushed them further and asked what 1/3 or 1/6 of the whole represents in units, which they quickly got as well.
One of my students came up after we had finished and declared, "I like fractions!" which I thought was nice. I just hope she continues to like fractions when you start adding different denominator fractions...
Mr. Steven Strogatz's newest article is also about the existence of fractions and the ensuing chaos of irrational numbers.
More cartoons of fractions.
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