The tasks below are for deepening students’ understanding about the absolute value of a number and provide a context for creating a need for learning operations with integers. You may give the problems after you have introduced the students the idea of absolute value of an integer and before the lesson on operations with integers.
Tasks (Set 1)
1) Find pairs of integers whose absolute values add up to 12.
2) Find pairs of integers whose absolute values differ by 12.
3) Find pairs of integers whose absolute values gives a product of 12.
4) Find pairs of integers whose absolute values gives a quotient of 12.
These may look like simple problems to you but note that these questions involve equations with more than one pair of solutions. The problems are similar to solving algebraic equations involving absolute values. Problem 1) for example is the same as “Find the solutions to the equation /x/ + /y/ = 12. Of course we wouldn’t want to burden our pupils with x’s and y’s at this point so the we don’t give them the equation yet but we can already engage them in algebraic thinking while doing the problems. The aim is to make the pupils be comfortable and confident with the concept of absolute values as they would be using it to derive and articulate the algorithm for operations with integers later in the next few lessons.
Tasks (Set 2)
1) Find pairs of integers, the sum of absolute values of which is less than 12.
2) Find pairs of integers the difference of absolute values of which is greater than 12.