Division of fractions is one of the most challenging topics for upper elementary/early middle school mathematics. It (and multiplication of fractions) is also one of my favorite topics to discuss a…

The standards for mathematical practice in the Common Core State Standards describes “varieties of expertise that mathematics educators at all levels should seek to develop in their students.…

As I have discussed, in the Common Core State Standards, division of fractions by fractions is a grade 6 standard. Specifically, 6.NS.1 states: Interpret and compute quotients of fractions, and sol…

In the previous post, I discussed how the common denominator algorithm for dividing fractions can be derived. In one example, I shared that 7 1/2 ÷ 3/4 can be calculated as follows: 7 1/2 ÷ 3/4 = 1…

In a previous post, I mentioned that interpreting division as quotitive leads naturally to a division algorithm often called common denominator algorithm. I have written a post about that algorithm…

When discussing division of fractions, some mathematics educators suggest that we start with quotitive division problems. So, they may ask students to solve a problem like this: There are 12 pounds…

As I mentioned in my previous post, multiplication and division are typically introduced in equal group situations. Thus, if 3 quantities, A (number of groups), B (group size), and C (total), are i…

I observed 2 Grade 5 lessons that were on division of decimals recently, and they made me think a lot about division. In particular, I was wondering why we teach multiplication and division of deci…