# The Library Problem – Fractions

Some of you who were involved in the EQAO Primary Assessment last year may remember this question.

There are 24 students in Mrs. Lowe’s class.  She divides the class into 4 equal groups.  Make a drawing to show the 24 students divided into 4 equal groups.  One of these groups goes to the library.  What fraction of the groups goes to the library.  Justify your answer.

A few of my Grade 3 educator friends commented on how challenging this was for many of their students.  I scribed for one child and observed first hand where the challenge was.

At a quick glance you might wonder why this is was so difficult as the participants were told how to begin – make a drawing and divide into 4 equal groups.  Once this is done the drawing reveals 4 groups with 6 students in each group.  Here lies the difficulty.  Students focus on the number in each group instead of the number of groups.  They are not unitizing (6 students =1 group and 1 group is one of the four groups in the class (one-fourth).  Unitizing is a key concept of proportional reasoning!  One-fourth of the students went to the library, but I have a feeling that a lot of “sixes” or “sixths” were in the final answers.

We spend a lot of time on multiplication and division in Grade 3.  What a perfect opportunity to make connections to the “set model” of fractions at the same time.  I love finding these curriculum connections!  Why not try this with your students and observe what happens.