Real Life and Inequalities

I find it baffling that students don't see how simple linear inequalities are. The idea that they are so similar to a simple equation, just with a different symbol in the middle seems to pass all but my A grade students.

Perhaps that is the problem though, I see it as solving an equation but having a different sign in the middle. A student, who probably doesn't really get the point of algebra anyway, is not going to be won over on that weak vision of mine.

So I went about trying to relate inequalities to real life. It's actually quite easy. I often show them that we are doing something called inequalities (this works better with KS4 who have come across these symbols more often).
I then ask them to get into groups of less than four.  Most of the time you will get a question of "does that mean four as well?", to which you just repeat the same command.

Brilliant - you have them cornered - they all understand inequalities as they have just proved it. How big could the groups be? How small could they be?

Maybe go again with two parameters, maybe with an equals to, and you will get a pretty strong success rate. Suddenly the daunting topic of inequalities doesn't seem so bad.

The main activity

The Lift Problem

Next - my activity on real life inequalities. I give them a job at a company called U Raise Me Up. They produce lifts, and the job is to work out the safety parameters on each lift.

The powerpoint is fairly self explanatory, but essentially you are looking for them to consistently make links and explain the inequality that is formed when working in this real life context.

My favourite part of this activity is even before getting onto the forming and solving. Finding the average weight of humans by country is always an interesting debate, but by using Wikipedia as 'open knowledge' and spotting that there are blanks in the data, we had to do some extra maths to work out the weights of women in certain countries.

I explained that there is no wrong answer here, and I got some great independent thinking, including averaging women's weights, finding the average difference between male and female weights or comparing similar countries.

Anyway enough rambling - how could I make this activity better?