One way to teach and assess students understanding of math concepts and procedures is to create a cognitive conflict. Here is one way you can create cognitive conflict in solving inequalities:
To solve the inequality x – 7 > 5, the process usually involve adding 7 to both sides of the inequality.
This process uses the principle a > b then a + c > b + c. There is no change in the inequality sign since the same number is added to both side.
Now, what if we add 7 to the left side of the inequality and 6 to the right side?
The process uses this principle: If a > b, c > d then a + c > b + d. Should this create a change in the inequality sign? Certainly not. There should be no change in the inequality sign when a bigger (smaller) number is added to the bigger (smaller) number side. Both of these processes create a cognitive conflict and will be a good opportunity for your class to discuss what solving inequality means and, compare the processes of solving equations and inequalities. Comparing and contrasting procedures is also a good strategy to developing conceptual understanding.
For those interested to learn more about inequalities I recommend this book:Introduction to Inequalities (New Mathematical Library)