Team Tim Harford's [multiprev] BBC R4 programme More or Less is back on air. Dau.II is a slightly bigger groupie for this Polish Your Crap-detector prog than me: insofar as she told me about the new season rather than the other way around. I gave her The Undercover Economist for her b.day last year and she returned How to Make the World Add Up for Christmas. Both books are excellent: they make you think. For us, this extrapolates; from the quirky examples that float through Harford's mind to think critically about the numbers that surface in ours. That's important, if you have a feeling for numbers [Landmark Numbers for example] then you are less likely to get flim-flammed or bamboozled by the black hats lurking out there to take advantage or innumeracy.
Calculators came on the scene in the mid-70s before that adding numbers had to be done with pencil and paper. But it could be done in your head if your pencil broke. In 1983, my colleague Rob Harper could accurately tally up long columns of figures quicker than they could be keyed in to a calculator. I think he'd worked as a child in the family corner-shop. It would a rare student from The Institute in the 2010s who do that; their instinct, even for simple sums like (28 + 47) would be to reach for a calculator - or their phone. And absolutely believe the answer generated, even if bonkers.
In the 02Jun21 episode of More or Less they summarized the results of a crowd-sourced problem: "How do you add 28 + 47?". There is no correct way but you might pause and reflect on how you do this task in your head.
- The brute force as if I had a pencil and paper approach is to add the units 8 + 7 =15; then add the tens 20 + 40 = 60; then add 60 + 15 to get 75. If your method didn't get that answer, then you might try this.
- A number of people rounded up 28 to 30 and/or 47 to 50 and then subtracted the surplus from 30 + 50 = 80
- Harford stripped the 7 from 47 and added that to 28 to make 35 and added that to the stripped 40. He was delighted to be told by the elementary math teacher that this was called partitioning.
- Teacher also mentioned the idea of Number Bonds To Ten which are still taught in primary school. If you can internalise these pairs of numbers (3 + 7) (4 + 6) etc. which sum to ten, it will greatly help your mental arith. If you have small children this can be trained in by playing Tens Solitaire where you lay out 12 cards on the table and are allowed, by dealing from the remaining cards, to cover pairs of cards which bond to 10. You finish with only face [JQK or even VDR] cards visible.