Proportional Reasoning Decluttered: Part 1

Okay ... I have an opinion here. I believe the curriculum has lost sight of the simple and powerful idea of "scaling in tandem" on the topic of proportional reasoning, and so is missing a wonderful opportunity: To provide our fabulous students an opportunity to practice their common sense, their powerful wits, and be confident problem solvers for the current age. This video is about that. In subsequent videos I'll go through all the usual expected ramifications of the one simple idea here - even though I actually question the need to even mention these details, let alone give everything names.

[guntmar]

Sir, i have been watching your videos over the past few weeks, and i wish i would have had you as a teacher way back when. i think you are one of the gems of youtube, tucked away with low viewer and subscriber numbers, when you really should be having 1 million view per video ! keep up this amazing work !

[scottekim]

Great point. Let's discuss. Proportional reasoning is the #1 piece of mathematics that adults actually use day to day that is harder than simple arithmetic (rates also fall in this category). Focusing too much on terminology and formulas makes people worry about formulas they don't understand, instead of relying on common sense. The moral of the story is that you can reconstruct the formulas from common sense. But even more importantly that we should have students in math class always start from common sense, not formulas. In practice this is exactly what I do when presented with a rate problem...I may in fact use a formula if it's faster, but I won't recall it from memory...I'll reconstruct it on the fly to make sure I'm doing it correctly and that it makes sense to me. A good intermediate concept for students to learn is that close by any mathematical statements there is a cloud of closely related statements that are easy to derive, like scaling two quantities in tandem by multiplying by 2. Oh, and there's a great animation the visualizes scaling in tandem. Worth animating. Very memorable once you see it once.

[moshenazarathy]

fabulous! (and not exploding dots based, ha, ha)
have it extended to the dreaded d = v*t problems. 3 hrs<-> 270km, 1hr<->90km, ..., 24hrs<-> ? km
move those hours and kms in tandem . Then choose another driver with 1hr <->150km
and for intermediate level skiers, introduce quantities which "move inversely in tandem".... one doubles, the other one halves itself, one triples the other one cuts itself in 3 .... ("inversely proportional",
they call them)

[jessieshirley]

This was really well done - need to share this with teachers because...it simplifies a concept in the curriculum that is often presented in a complicated manner,  brings common sense and number sense to the forefront, and is presented in a joyful and engaging manner.  Thank you!

[AnonimityAssured]

A good attempt at "omelettes". I love your (mirror-image) presentation and enthusiasm. Have you ever wondered why 1 inch is exactly 2.54 cm and not a tiny bit more or less? I ask because of the way the metre/meter was derived as a measurement based on the size of the Earth, whereas imperial measurements had very different and wholly unrelated origins. I suspect that one or other of the measures (probably the metre) was deliberately rounded to line up exactly with the other every so often.

[marcusaurelius]

This was absolutely brilliant, James.