Summer of Math Exposition

I am a bit confused about your target audience. You encourage them to teach the trick to their kids or siblings, but the structure feels more like you already target young learners. In any case, I don’t recall you ever calling the binomial formulae you use by that name (might be my mistake), which might have helped to make some connections with prior knowledge. Further, I get the impression that the video could have been more focused by including fewer chapters; while all of them are relevant, the message may come across more clearly if you stick to fewer examples and motivate these more deeply. I get the impression the video does well what it sets out to do, but stays too close to already available material. Apart from that, it is clear that the lesson was well planned and prepared and I was glad when you derived the formula in the last section.

In a nutshell, I really appreciated the core of the video, but wanting to put too many examples makes it a bit long and repetitive. I would have scored higher a shorter version of the same content with less examples.

• The first 5min that introduce the core idea are well-thought and realized.
• The examples to use it for mental calculus are neat and interesting.
• There are too many examples on the a^2 - b^2 = (a+b)(a-b), especially as this special case is more commonly known I guess.

This was a nice demo of benefits of understanding the difference of squares. I think the only thing it lacks is a sense of discovery. So, if I were to use it in class, I would leave it up to students to discover that you can benefit from it in different scenarios (like the one with the Pythagorean theorem).

Clarity was a bit foggy at times, when not explicitly writing down things (like just saying 7 * 9 = 63 = 8 * 8 - 1^2).

Novelty is there in the assembly of different examples.

Motivation and Memorability are somewhat low. Why should one want to know these things when we have calculators? Now we need to look for these patterns and if we don’t notice them… we’re stuck to the basic approach, so, we even loose time in some cases… These questions can come to mind and aren’t addressed.

When you write numbers by hand, they are hard to read. Try not to overcrowd the screen. The video is rather long, considering the average attention deficit of students. I had the impression that the video presents some topics in a complicated way that could be approached more simply.

A bit lengthy for what it’s doing but I watched it at 1.5x speed and it was a good video.

Great set of examples uniting the difference of squares topic. Really liked the opening exposition of “discovering” the pattern through a nice concrete optimization problem. (Maybe showing that parabola in the very first example and mentioning the “it’s maximized by the square case” would have been nice, before then after showing the intuitive answer discovering how the visual difference of squares proof was hiding in this problem all along).

Algebra turned into geometry was how I first started getting interested in maths. I was able to see some familiar shapes rather than x, y and stuff. I really loved this video.

A very underutilized perspective on a common topic. The things presented should be in every algebra textbook. The series of applications presented in the video worked very well. Some possible extensions include digging into why terms of a Pythagorean triple are adjacent numbers two apart or expanding on how FOIL relies on a double distribution. It will help with viewers’ understanding.