Having looked at the Lower school extension work, it seems to me that some of this moves steadily into work that sixth formers might find a challenge. In particular, there are points in work I have set for a bright Y8 top set that rather require a grasp of logs. Before the invention of the pocket calculator (in Britain, the first affordable ones were from Clive Sinclair, who I saw many times at lunch in Cambridge). Though Texas Instruments had a handheld calculator in 1967, it was 1975 before the price dropped to a point where it could reasonably appear in a classroom. Look up the Sinclair Oxford, £13. In 1974 the Sinclair Cambridge was £20. By 1976 there were arithmetic (four function) calculators for £5; By 1980 one could expect calculators to appear in classrooms.
http://www.vintagecalculators.com/html/the_pocket_calculator_race.html is a fairly good description of the early history. http://hackeducation.com/2015/03/12/calculators applies to US classrooms.
https://en.wikipedia.org/wiki/Mathematics_education_in_the_United_Kingdom
I have been surprised how difficult it is to establish when the first O-level paper permitted calculators. Perhaps the test to apply ought to be to ask when the first non-calculator paper was issued.
My point here is that logs were required when I was in early secondary school. I used a slide rule from Y8 onwards and kept one in a long pocket until leaving for university. So everyday experience with number required familiarity with logs and with the many tables in our slim book of 'log tables', which amounts to much of the information found in a school-level calculator today. But without the calculation function. These days logs are introduced in Y12 and I suspect are often not well understood.
DJS, 20220121
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I am hopeful that I will come across other content that falls above Y10 and below university. All GCSE material will continue to be within the Lower School extension content. But, just because you may be Y12, that does not mean that you will find that Lower School material trivial, though you may well work through it considerably faster than at the earlier age. A typical example of that occurs every time there is a region around a value, what I'd usually refer to as precision. Where a Y8 will find an exact answer and often declare the problem complete, a Y12 ought to be recognising that there is an implied precision and that therefore there will be testable precision in an answer. Further, it would be correct to show the region in which the 'answer' can fall, much as one would declare error margins in Physics experiments. Being mathematicians, we might well reverse this, requiring a particular result precision to tell us how precise the original figures ought to be.
