rearrangement add/take with numbers

intuitive knowledge about rearrangement can be obtained from simple number sentences and their equivalent forms, probably assisted by diagrams

objectivity can be established over time - by participating in discussion about the allowable transformations

my preference is to let students develop their own notions about rearrangements by presenting them with several (judiciously chosen) examples

I don’t think it is helpful to simply tell students that e.g.  ‘changing sides changes the sign’ because, however instrumentally effective, it is better that students notice and interpret information and build their own structural sense of techniques

students can and do note that signs change when they ‘move’ from one side of an equals sign to the other

they can hopefully relate this understanding to an appreciation of using the the helpful notion of inverses

the powerpoint is here