If you prefer to read posts in order, here is the series of post on the theme of the middle.
In the Middle In the first post, we play with an approach for finding the middle of a pair of points. Our starting point is how kids actually approach this problem. The model they use corresponds to a metaphor of having a person on each endpoint walking towards each other, and then looking at where they meet. In this post we compare this with the teacher’s notion that the middle corresponds to the average of the two points.
In the Middle – Median In this post we explore how a variation of the approach for finding the middle will allow us to find the median. Kids find this completely easy and natural.
In the Middle – Weighted Average By taking two people walking towards each other but at different speeds, we arrive at a simple model for dealing with weighted averages.
In the Middle – Weighted Average, part II An exploration of different models for looking at weighted averages. Why would it be called “weighted” average?
In the Middle – Weighted Average, part III If we fix the points, but change the weights, what happens to the weighted average? A simple scale, a simple geometric model.
In the Middle – Weighted Average, part IV Just by bringing in coordinate systems, we can see that weighted averages connect naturally to a parametric equation for a straight line.