Algebraic thinking is about recognizing, analyzing, and developing generalizations about patterns in numbers, number operations, and relationships among quantities and their representations. It doesn’t have to involve working with the x‘s and other stuff of algebra. In this post I propose a way of scaffolding learning of operations with integers and some properties of the set of integers by engaging students in algebraic thinking. I will focus on subtracting of integers because it difficult for students to learn and for teachers to teach conceptually. I hope you find this useful in your teaching.
The following subtraction table of operation can be generated by the students using the activity from my algebraic thinking and subtracting integers -part 1.
Now, what can you do with this? You can use the following questions and tasks to scaffold learning using the table as tool.
Q1. List down at least five observation you can make from this table.
Q2. Which of the generalizations you made with addition of table of operation of integers still hold true here?
Q3. Which of the statement that is true with whole numbers, still hold true in the set of integers under subtraction?
1. You make a number smaller if you take away a number from it.
2. You cannot take away a bigger number from a smaller number.
3. The smaller the number you take away, the bigger the result.
Make sure you ask students similar questions when you facilitate the lessons about the addition of integers. See also: Assessment tasks for addition and subtraction of integers.