Modeling Fractions

Modeling fractions involves visually representing a fraction using different models like area, linear, or set models. To use an area model, you divide a shape (like a circle or rectangle) into equal parts based on the denominator and shade the number of parts indicated by the numerator. A linear model uses a number line to show a fraction as a part of a whole length, while a set model represents a fraction of a group of objects.  

This video demonstrates how to model improper fractions and mixed numbers using rectangles:

Area models

• What it is: A visual representation of a fraction as a part of a whole shape. 

• How to use it: Draw a shape (e.g., a rectangle or circle) and divide it into a number of equal parts equal to the denominator. Shade in the number of parts indicated by the numerator. 

• Example: To model 4/6, draw a rectangle, divide it into 6 equal parts, and shade 4 of them. 

Linear models

• What it is: A number line where the distance from zero to one represents the whole.

• How to use it: Divide the space between 0 and 1 on the number line into equal segments based on the denominator. For example, to model 3/4, you would mark the number line at the point that is 3 out of 4 equal segments from 0.

• Example: A ruler is a type of linear model where marks indicate different fractions of an inch. 

Set models

• What it is: A model that represents a fraction of a set of objects. 

• How to use it: Use physical or virtual objects, such as counters, to represent the whole set. For example, if you have 12 counters and want to model 1/4, you could group them into 3 equal groups of 4 counters each, then select one of the groups to show 1/3 of the total. 

• Example: To show 2/5 of a group of 10 circles, you would divide the 10 circles into 5 equal groups, which would be 2 circles per group. Then, you would select 2 of those groups (which equals 4 circles).