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.

Thanks for sharing your experience! Every teacher has his/her teaching tactic. I think, that it’s important to change your approach according to your students’ needs and interests. I’m going to use online writing services UK to order a professional essay that will help me to become a teacher and I think that I need to learn a lot. Regarding to your article, I don’t really like mathematics because it’s a complicated subject but in any case, I’m sure that your students would appraise your help.

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