How to Subtract!

This week in class we learned about the importance of different algorithms and why it is important to promote several approaches to answering a question. With the EQAO assignment in mind, I have tried to not only see the importance of different algorithms but also attempted to answer math-based questions using different methods. We got to play around with some simple math expressions in class using different approaches. It was surprising to see that many students take different approaches that may have seemed confusing to me before this class, but now appear to be useful and easy ways to approach math. Understanding this will help me to become an effective teacher as I plan to implement several algorithms throughout my math courses.

387-146=241

Having developed my math skills over the years, it didn't take me long to figure out that
387-146=241. My approach to answering this question, however, is a way that can be extremely confusing to students who have a different learning process. I learned that it can be extremely effective to start with a number line, even if some students don't find it as useful as others.


By breaking up the equation into steps, students can understand the role of numbers and how they can be broken up into smaller numbers in order to make math easier. By starting on the right side with 387, students can move to the left (addition would move to the right) by blocks of numbers that they understand. In the picture to the right, 146 is broken up into three parts: 100, 40, and 6.  As students subtract the numbers and move along the line to the left, they arrive at 241. This method is known as the Partial Subtraction, which is subtracting from the greatest to the least place value.

Compensation Subtraction
Another method of approaching this problem is known as the Compensation Subtraction method. This method involves making a friendly number. By adding 4 to 146, students might have an easier way of solving the problem. 387-150 may appear less daunting than 387-150 and students may prefer this method. It is important to note that the 4 added to 146 needs to be subtracted at the end to balance the equation; when you borrow, you must return.

Constant Difference Subtraction
Much like the compensation method, the Constant Different Subtraction method involves making a friendly number. Unlike the compensation method, however, the equation isn't balance out at the end. If you add 4 to 146, you need to minus 4 from 387. The equation will read 383-150, but the answer will still be the same. Some students may prefer this over the compensation method, but both are equally acceptable.

During my placement I have been given the opportunity to watch students during their math class to see how they answer questions. While I helped students get to the right answer, I was surprised to see many using methods that I was never taught. The class I have been placed in is a grade eight elementary class and they are just beginning to learn the basics of algebra. Understanding the role of symbols within math can be challenging to many students. I was surprised to see that visual manipulatives formed the basis for many students' understanding. Breaking down the problem in front of the students is an extremely effective method and can be used at any grade. Another thing I noticed is that while my teaching associate promoted several approaches, he made it necessary for students to understand more than one method and use several on tests and quizzes.