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I am here with a historical question about maths education. I hope I have chosen the right SE as there are confusingly three that pertain to historical research into mathematics.

Any quantitative relationships where one quantity is the product of other two can be expressed by placing the symbol for the first quantity on top of the symbols of other two: $$ \genfrac{}{}{0pt}{}{M}{D \space\space V} $$ In the above $M$ stands for mass, $D$ for density, and $V$ for volume. If you cover $V$ with your finger, for example, the remaining part can be seen as $\frac{M}{D}$ and you will know that the volume of a given substance can be obtained by dividing its mass by its density. Cheat sheets of this type are many (not knowing the term, I'd tentatively call them quantities triangles): There are triangles for percentage, speed-distance-time, and capacitance.

All quantities triangles go back to that of Ohm's law proposed by Herbert M. Pilkington in 1892: $$ \genfrac{}{}{0pt}{}{E}{C \space\space R} $$

My question is: When did they start using quantities triangles for teaching arithmetic topics, especially speed and percent? I know T. Teahan proposed a percent triangle in 1979, but this may not be the earliest attestation. If there are pre-Teahan examples in other languages, they would be good to know too.

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    $\begingroup$ Honestly, I've never seen such a thing in my life. But that is not surprising, as this appears to be something that one would see in physics, and not mathematics. I'm not sure that this is really on-topic here. It might be on-topic at Physics. $\endgroup$
    – Xander Henderson ♦
    Commented Jul 12 at 13:27
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    $\begingroup$ It is a maths education topic. A mnemonic developed by electricians was appropriated by primary education teachers to give children cheat sheets for percentage and speed (see for the latter; thirdspacelearning.com/gcse-maths/ratio-and-proportion/…). $\endgroup$
    – Shacharit
    Commented Jul 12 at 13:42
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    $\begingroup$ Also never seen or heard of that. Skeptical it's very widespread. $\endgroup$
    – Daniel R. Collins
    Commented Jul 12 at 15:37
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    $\begingroup$ I beg for a little more patience. HSM doesn't even have a tag for primary education. Primary school maths questions may be rare in MESE but they'd be rarer in HSM. Quantities triangles are one of ways how teaching maths went wrong at primary school. Remember the outrage higher education people had for x.com/CarstenPaul1982/status/1384734904869703681 ? $\endgroup$
    – Shacharit
    Commented Jul 12 at 23:06
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    $\begingroup$ Widespread enough that it's seen in multiple places around the world down to at least early high school, this is very definitely a mathematics education question and topic. $\endgroup$
    – Nij
    Commented Jul 15 at 5:32

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