# Rocking the Multiplication of Fractions Greater than 1

Yesterday I was in Ms. Lavallee’s Grade 8 class.  They were challenged to prove that 3 1/2 + 1 2/5 = 3 1/2 x 1 2/5.

Here is what one group found…

Hmmm…

How can that be??  We revisited to question – what did I ask you to do?  Prove that they were not the same??  Prove that they are the same????  THE SAME?????

When we reviewed how the students added the fractions, it was discovered that they added the whole numbers – 3 +1 to get 4; then they added the fractions – 1/2 + 2/5 to get 9/10.  They applied this same “rule” (process?) to the multiplication of the fractions – 3 x 1= 3  and 1/2 x 2/5 = 2/10.  Thus, the sum and the product are not equal.

Our conversation then turned to alternative ways of writing mixed fractions – we discussed converting the mixed numbers to improper fractions.  Once we tried that…

Students discovered that just because one method worked for the addition operation, it did not necessarily work for the multiplication operation.    The next challenge they faced was how to show this on grids????

Their first attempt was unsuccessful, so they tried it again.  After the second attempt, I assisted them with the model – hopefully they will be able to apply this information in future investigations in multiplying fractions greater than 1.

Awesome fun in Ms. Lavallee’s class – chi-miigwech!!