The title of this post was a 4th grade student’s response to the question
True or false: 3/4 = .34
The student responded false, and offered the above explanation.
The inability to recognize this entity – which has not one number, but two – as a number is addressed in the Common Core’s emphasis of fraction as a number. In Grade 3, students begin with unit fractions (1 in the numerator), which are found on the number line by dividing the segment from 0 to 1 into a number (the denominator) of equal parts. A fraction can then be seen as a collection of unit fractions, with a value that can be found by counting unit fractions on the number line. For example, 5/6 is 5 copies of the unit fraction 1/6, and 20/6 is 20 copies of that same unit. This approach allows students to make sense of operations with fractions, for example, that adding/subtracting fractions means joining/separating/comparing things, just as it did for whole numbers. When multiplying, we often think about the factors as the number of groups and the size of each group. If we continually think about fractions as numbers, it is not a great leap to consider a group whose size is 1/4 of a unit, or to describe finding 1/2 of a group. In division, dividing by a fraction means finding, for example, how many groups of 1/8 teaspoons there are in 4 teaspoons, and dividing a fraction by another number simply means equally sharing a portion whose size is, for example, 3/4 of an ounce.
Think about your own instruction. Are you reinforcing the notion that fractions are something other than numbers?