I came up with three primary types of Betweeness problems. While not every problems fits nearly into one of these three categories, most do. And, by teaching my students and classifying the different kinds of geometric relationships that could exist helped them to build a firmer geometric reasoning foundation almost immediately. The difference between this lesson and lessons in prior years was quite large.

The three primary types were differentiated in the slides I gave in class. A PDF of those slides is included below:

I introduced these types over the course of two days. On the first day, we only did Type I and then quite a bit of practice. On the second day, we did Type II and III problems and practice. Then, on day three, the types were combined. Students had to classify the problems by type and then solve them. The practice sheet for their notebooks was the following:

I will definitely continue to teach the Betweeness postulates like this, simply because it helps kids catch onto the geometric reasoning layer so quickly.

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