once some ideas of (and a language for) allowable transformations of statements has been fairly firmly established for arithmetic these same techniques can be used in rearrangement of symbolic statements (formulas or relationships)
for a sequence of rearrangement lessons,
a transition, or progression
might start with simple number statements that can be easily checked;
then rearrange number statements with bigger numbers (less easy to check - but you still can, maybe with a calculator)
then to simple letter statements (e.g. h - d = k, so h = k + d)
to more complex (looking) symbolic statements
for example,
5 + 7 = 12 (e.g. to make 7 the subject, 7 = 12 - 5) and 9 - 4 = 5 to 9 = 5 + 4
a transition, or progression
might start with simple number statements that can be easily checked;
then rearrange number statements with bigger numbers (less easy to check - but you still can, maybe with a calculator)
then to simple letter statements (e.g. h - d = k, so h = k + d)
to more complex (looking) symbolic statements
for example,
5 + 7 = 12 (e.g. to make 7 the subject, 7 = 12 - 5) and 9 - 4 = 5 to 9 = 5 + 4
to: 37 + 28 = 65 [37] and 46 - 29 = 17 [46]
to: a + c = b [a] and m - t = k [m]
to: a2b + c = fg3
[c]
a powerpoint is here
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