Fractions / Units Other Than a Unit Square

Understanding

A fraction makes sense only if it refers to a particular scale or unit. One half of a unit square can represent different areas depending on the size of the unit. If two unit squares do not have the same scale, a unit fraction will not have the same size area.

What to look for

Students should reflect on what they know about equivalent fractions, comparing fractions, and adding and subtracting fractions, noting that these operations only make sense if the fractions represent the same whole.

Sample Assessment

A box of granola bars contains 18 bars. How many bars will be in (2/3) of the box?

Answer: 12 bars

The Big Idea

If two unit squares do not have the same scale, a unit fraction will not have the same size area.

What are the students doing?

Students tile rectangles to compare fractions of different units.

What is the teacher doing?

As students work with or observe you working with the tiling activity, help them to relate the parts of the fractions to the defined area and the shaded area.