Subtracting Mixed Numbers - Borrow or Use Improper Fractions

 

Due to the Christmas holiday travel, our school has gone red for the second week in a row.  It had to do with the number of positive cases discovered.  As part of sending packets home, I'm including lots of detailed instructions.  One of the topics I am covering this way is subtraction of a fraction from a mixed number such as 5 1/3 - 2/3.  I realize the usual way to teach this topic is by teaching them to borrow before subtracting but it is extremely hard to teach by distance.

In addition, my students automatically rewrite it as 5 2/3 - 1/3 in their heads so they don't have to borrow.  With this in mind, I decided to teach this type of subtraction using improper fractions because there is no misunderstanding about which fraction is larger.  Furthermore,  they find changing mixed numbers into improper fractions much easier than borrowing.

The school sends home packets since most of the students in the village do not have internet access and limited data on their phones.  In fact, most students do not have computers at home so any computer work is done at school or when they are allowed to check out a digital device.  So I've been creating packets of work with lots of in-depth information and examples.  As I wrote out the instructions for borrowing a whole to rewrite the fraction, I realized it was just too hard to assemble a clear explanation so I switched.  I switched to  showing subtraction of mixed numbers using improper fractions.

When I wrote up the explanation, it was so much easier.  It made sense and students could "see" what was happening.  Even if they have to find common denominators first before they convert the mixed number to an improper fraction, they won't be readjusting numbers in their heads so they can subtract without borrowing.

In addition, it gives them practice for when we start multiplying mixed numbers later on.  It won't be the first time they are converting to improper fractions, nor is it the first time they've performed a mathematical operation using improper fractions.  Furthermore, learning to subtract, multiply, and divide using improper fractions shows students the need for learning how to convert between the two forms and for learning to use improper fractions.

In the past, I've never thought about using improper fractions for subtraction because I'd only learned to borrow before subtracting and I was teaching the concept in person but the situation caused by COVID has shown me that perhaps I need to teach both ways but focus on using improper fractions since it makes more sense.

I guess this means that an old dog can learn new tricks.  Let me know what you think, I'd love to hear.  Have a great day.