I have been at a stand still in finding activities/resources for introducing inequalities that both perplex students and transition naturally into the concept. Last year I started by putting x>3 up on the board and scaffoled my way up to multi-step inequalities. I wasn’t happy with the results; students had a very small base of conceptual understanding, which did not transition smoothly into linear inequalities.
I took a risk today and developed my own introduction. I really wanted to focus on letting students ask the question and approach the concept from a different direction.
I threw this up on the board;
Then asked students if they had ever heard of the half-your-age-plus-seven rule. Not a single student had. They calculated half Brad Pitt’s age plus seven; 32. I asked them if this had any meaning? A lot of students didn’t believe he was 50, so we Googled it.
After I told them he is married to Angelina Jolee;
“Brad Pitt is all good according to our rule” I told them.
At this point things started falling into place, we talked about what the rule might mean and decided that it would be creepy if Brad Pitt dated anyone younger then 32.
Professor Xavier they shouted out. Well our rule says 43.5 is the cut off. We talked about possible ways to work around the decimal; round up, round down, keep it. I let the students decide.
We went through who he is married to and finished up with the one:
I had students write a sentence about what our rule meant, it took a while for it to evolve but they eventually came up with:
It is creepy for Mila Kunis to date anyone under the age of 22.5.
We have been working to translating between words and math so I asked students to translate this into an expression.
If z is Mila,
then z > 22.5
After we talked a little more about if we should include 22.5 in the range of ages then moved into a few notes about inequalities and how to graph them.
Each period I taught the lesson it improved and I tweaked things around. I know there is still plenty to change and the tons of potential to further develop the lesson. What is just as important for me though is I was excited about the lesson. I was not excited about lecturing on how to interpret x > 3. Students feed off that excitement and it becomes a better experience for everyone involved.