Here is a set of videos that covers Quadratics, Triangles and Squares with Pythagoras and a little bit more. Caution advised this is not a normal lesson nor is it the way you should present mathematics to younger students or even students this age, but because we have deadlines to meet I stuffed a lot more into the hour than usual. This might be good for some teachers/parents and students to see where we are going with all this...we seem to lose track of the destination sometimes when we get caught up in computation. This post should answer some WHY questions that may have been lurking out there.
Here is one of the graphs we made while we played around with factoring polynomials...the idea behind it all is problem solving, rational and critical thinking NOT memorizing rules. Note we don't even begin to cover application which means I am still being tricked into teaching backwards.
This is the crash course where we cover many concepts all in one hour. When you are teaching little kids you only cover one concept at a time and add more understanding in layers over time. For example you can spend quite a bit of time just playing and building squares. When they are used to factoring, then we can set it equal to zero and find "roots." What do we mean by roots?
So we start off with a simple one as a refresher and to make it non-threatening...and then we can start graphing and get more information.
Note how the symbols bring up some memories of linear functions for him...and you can see the blending of symbols, blocks, pictures and graphing.
We add more information and math terms like "axis of symmetry." Once we understand that we can add the "vertex", and now with those concepts and the concepts of "roots" we can start adding the "y-intercept" and the other points that make up a five point sketch of functions. YOU may want to take a break and make your own sketch...before watching the next one:
We stayed positive in this lesson and this is more than enough info to absorb for one lesson. Note a crash course with me still contains each rung in the ladder...
Then we change gears and play with triangles, radicals and Pythagoras:
And we also played a bit with fractions and covered the 5 concepts and how they related to everything we just did. You can hear him yawning which tells me we are stressing his attention threshold...good time to quit. No need for drugs or labels like ADD. The lesson went for a solid hour and we covered a lot of ground, MUCH more than you normally would. Stay tuned for more lessons.