Fractions / Fractions and Unit Squares

Understanding

This lesson helps to illustrate the need to clearly specify the unit of a fraction in order for it to be interpreted or used with any meaning.

What to look for

Some of the wording in the problems might need to be adjusted slightly depending on the background of the students. The language of tiling is one possible instance—a region is tiled by a shape if it is completely covered by the shape with no gaps or overlaps.

Sample Assessment

Identify three fractions equivalent to (4/12). 

Answer:  (1/3), (2/6), (3/9), …

The Big Idea

A unit on a number line can be related to a unit square with sides the same length as the unit on a corresponding number line.

What are the students doing?

As students work with or observe the manipulation of the unit square, help them to relate the total number of rectangles to the denominator of a fraction and the number of shaded rectangles to the numerator.

What is the teacher doing?

Help students make the connection between the size of the rectangles in the unit squares and the denominator in the fraction.