I’d like to understand your thinking but I’m not sure I get your approach. Could you try again?
Oops, left out the decimal point.
The diving at the Olympics is from the 10-meter platform. How much is that in feet?
1 meter = 39.37 inches
12 inches = 1 foot
\begin{equation}
10 m \times\frac{39.37 in.}{1 m}\times\frac{1 ft.}{12 in.}\\
\end{equation}
meters and inches cancel out:
\begin{equation}
10 \cancel{m} \times\frac{39.37 \cancel{in.}}{1 \cancel{m}}\times\frac{1 ft.}{12 \cancel{in.}} = 32.81 ft.\\
\end{equation}
The “Commutative Property” of multiplication: ab=ba
Handy when questions like “what’s 38% of 50”. So that’s .38*50. But using the Commutative thingy, “50% of 38” (.5*38) is easier to calculate.
Lol. In grad school one of my dissertation chapters revolved around a specific population biology problem. After putting together all the dynamics and equations, the problem ended up having a quadratic solution, so I’m one of the few people I know that has used the quadratic equation EXTENSIVELY in my adult life.
I almost had the equation tattooed on my arm at one point 
For converting between metric and imperial units, it is simpler and more accurate (in fact, exact) to remember 25.4 mm = 1 inch.
I’ve had the need to convert acceleration from knots per second into an angle (the angle wrt gravity required to cause the acceleration) in arc minutes - lots of multiplying by 1 there.
If you like.
\begin{equation}
10m\times\frac{1000mm}{1m}\times\frac{1 in}{25.4mm}\times\frac{1 ft}{12 in} = 32.81 ft
\end{equation}
All you need to do is remember one equivalence between English and metric, and you can do any conversion between the two.
While we’re at it with unit conversions, a lot of people screw up multi-dimensional unit conversions. Like, a cubic yard isn’t 3 cubic feet; it’s 27.
I agree, and that’s coming from working with people with disabilities, as well as normal preschoolers-- standard deviation is SO important. So are concepts like “net loss” and “net gain.”
“Since [child] started a particular therapy, he has gained 8 months of development in 6 months.”
“He’s 8 months ahead?”
“Well, his net gain is 2 months.”
Another I would add is regression to the mean. Teachers reward good performance, and the next day, the student does worse. I can’t believe how many people with master’s degrees don’t understand regression to the mean.
“I rewarded him, and it didn’t help.”
Track his progress over several weeks, and check his average. But notice that any time he hits the pinnacle, he will probably go down the next day-- there’s no where else to go, and “pinnacle” isn’t his mean performance.
Or, if it is, he’s probably in the wrong class, and not actually learning anything. Watch out for him getting bored and becoming a behavior problem. Especially when you start expecting perfection from him and stop praising and rewarding it.
I think you also need the associative property of multiplication to justify “x% of y = y% of x.”
38% of 50 = (38 \times \frac{1}{100}) \times 50 = 38 \times (\frac{1}{100} \times 50).
I remember learning that when I was quite small. My father had to demonstrate (with playing cards, I think), but then I got it (we may have been working on a carpentry project where square measure came up.
Or people scream at the student who does poorly and the next day he does well - so obviously screaming helped. Grr…
“it only kills 1% of people, it’s harmless!”
I did the math once on a bunch of scenarios to show how ridiculous that statement is. 1% plane crash rate would be 12-13 plane crashesper day…out of Toronto Pearson International airport alone. Imagine the death count worldwide!
I forget what other examples I used. One kid out of every 100 kindergarteners (lots of schools are that big), stuff like that.
The other math skill that’s useful every day is, fundamentally, multiplication and division but it’s basically the ability to determine unit costs. Our grocery stores post the unit cost on the price labels, but I know that’s not true everywhere. Sometimes it’s a better value to get two smaller boxes than a large one (looking at you, Bear Paws; box of 6 for CAD 3.99ea, box of 12 for 9.99…).
As to this, the adjacent skill to render stats to be easily visualized. In a job talk I once gave, I was arguing against the reduction in types of intervention services offered to people with substance abuse based on measured outcomes. I used the example of an intervention with a 66% positive outcome rate, which my audience agreed was pretty good. It’s not bad, but a graphic of two parents holding hands with a child showing one of the adults shaded out showed that duh, a 66% rate still leaves 1 in 3 people ineffectively assisted.
My idiot oncologist, whom I fired, told us (knowing we both had doctorates in a social science field), “Now, with just surgery, there’s a 63% 5-year survival rate. That may sound pretty good” and we both said, “No, it absolutely doesn’t.”
I’m pretty sure “pretty good” is meaningless without comparison to another intervention.
Or for that matter, understanding relative quantities in general. “Such-and-such airline removed the olive from the salad they serve in first class. It might not seem like much, but it saved them $10,000 a year!”. Sure, but $10,000 a year is… basically nothing. If they had increased the price of every first-class ticket by the price of one olive, nobody at all would have noticed that price increase, but they probably did notice the missing olive in their salad.
Relatedly, comparing big numbers to each other. “It would take ten thousand years to reach the nearest star, and millions of years to spread throughout the Galaxy! No human or alien race could possibly ever manage that!”. Except that the relevant comparison is the billions of years life on a planet would last.
Or knowing the audience. If it’s a cancer that mostly strikes people over 75, whose life expectancy may not be much longer without a cancer diagnosis, then “pretty good,” might be a fair descriptor. But if it’s a cancer of children, it’s an insult.
Scaling things up or down can also be interesting. A bow and arrow is an interesting example. About 10 years ago I was trying to raise some interest in building an 80 ft long cross bow similar to Daviinci design. Not everything simply scales up, the load changes, the density of the materials used comes into play. I finally abandon the idea of building it from wood.
Indeed. With additional interventions, it was 87%, a nice number in this context.
So what are you going to build it from ?