In my earlier post on this topic, I discussed why teaching subtraction using the numberline is not helping most students to learn the concept. In this post I describe an alternative way to teaching operations with integers that would help students develop a conceptual understanding of the operation and engage their mind in algebraic thinking at the same time.
The table of operation is one of the most powerful tool for showing number patterns and relationships among numbers, two important components of algebraic thinking. It is a pity that most of the time it is only used for giving students drill on operation of numbers. Some teachers use it to teach operation of integers but more for mastery of skills and to show some beautiful patterns created by the numbers. Below are some ideas you can use to teach operation of integers conceptually as well as engage students in algebraic thinking. I promote teaching mathematics via problem solving in this blog so this post is no different from the rest. Use the task below to teach subtraction and not after they already know how to do it. Of course it is assumed that students can already do addition.
The question “Which part of the table will you fill-in first?” draws the student attention to consider the relationships among the numbers and to be conscious of the way they work with them. It tells the students that the task is not just about getting the correct answer. It is about being systematic and logical. Engage the students in discussion why they will fill-in particular parts of the table first.
Students will either subtract first the same number and this will fill the spaces of zeroes or they can subtract the positive integers. They will of course have to define beforehand which will be the first number (minuend) and which will be the second number (subtrahend).
Surely most students will get stuck when they get to the negatives except with the equal ones which results to zero. You may then ask them to investigate the correctly filled up parts of the table that could be of use to them to fill-in the rest of the table. Students will discover that the numbers are increasing/decreasing regularly and can continue filling-in the rest of the spaces. This is not a difficult task especially if the process for teaching addition was done in the same way. Encourage the class to justify why they think the patterns they discovered makes sense.
The discussion of this topic in continued in Algebraic thinking and subtracting integers – Part 2