Week 2: Fraction Sense

This week we learned about fraction sense. There are four different methods to look at fraction sense:

Spacial Relationships: having a physical picture of the number, including where it lies on a number line.

This is the most common fraction sense and should be the first method that we teach children. Spatial relationships is using our big ideas of partitioning and unit iteration in picture form to look at fractions.

Take, for example, the spacial relationship of 5/4. In the picture below, the picture of 5/4 is show in the coloured boxes. Here the student can count each 1/4 piece to make 5/4.

Simiarly, spacial relationships can be shown on a number line. The number line sort of incorporates benchmarks as well, but it's mainly to show where it lies on the line. The picture below shows this.

One/Two (units) More and Less: essentially it's knowing what is one more or less of the given unit. 

O/T, M&L was difficult to understand because it allows us to think about fractions in terms that our teachers initially forbade us to. If we look at the number line above, we can see that 1 (4/4) is one less than 5/4, and 6/4 is one more than 5/4. 

Benchmarks of 0, 1/2, 1...: being able to recognize where the given  unit is in relation to the benchmarks of 1, 1/2, 1... etc. 

Benchmarks are particularly important when trying to distinguish what fractions are larger, which is illustrated in the picture below. 

It is easy to tell why the top two fractions are greater than. 5/8 and 17/32 are both larger than 3/7 and 11/24, respectively. The bottom two are more difficult to recognize, but this is where benchmarks come in. To understand these problems, we have to think about which piece is large. A 1/10 piece is smaller than a 3/8 piece. Both fractions are less than 1/2, but which one is closer? The unit of 1/10 is closer to 1/2 than a unit of 1/8. 

Part-Part-Whole: the ability to break up the given unit into friendlier numbers. 

Basically just decomposing. Using a number line or a "tree" diagram is the most efficient way to show this method.