February 02, 2017
Please remember that the steps in the Pythagorean are important components to the ‘proof’ of understanding when it comes to the difference between 1 dimension (the length of a line) and 2 dimensions (area of a shape). This difference will become even more important as we move into volume which is 3 dimensions.
Also, please ensure that you leave your variables on the side the original question places them. This will become more important as we move on to equations involving variables and maintaining the structure of the question as you progress through it.
January 18, 2017
In anticipation of the inevitable question: “why do we have to learn this?” I have identified the reflections of another person asking the same question… sorry, no you are not the first.
In his blog Dan Pearcy identifies that the reasoning behind teaching an abstract concept is indeed something to consider, and references David Wee’s blog, which questions the need to teach this theorem (perhaps the most convincing reason/s are discussed in the comments to this post).
These are all great discussions to have regarding the need,real or imagined on the why’s we teach something. However, they do not detract from the fact that we are teaching this concept. Perhaps the most pressing argument, as noted by Dan Pearcy, for me is the fact that any learning we do provides us with greater intellectual power, and isn’t that what learning is all about? Are we not here to become proficient mathematical thinkers? We learn things through the exploration of ideas, not avoiding or discarding them.
Besides Pythagoras was a pretty weird cat and if his math isn’t interesting to you maybe his life will be :)…so there is that.
- Unknown Line Segments (textbook 1.3)
- handout-for-1-5 (total marks here = 16. Question 3 should have all work shown however the mark is for the correct final answer rounded to one decimal place…including units)