If we understand the theory first and then rework it into slogans for children to learn, then we give them a path to understanding. If we invent slogans first and they don’t line up exactly with theory, then there are logical gaps and misdirections. These confuse the student and hinder an understanding of logical structure.
When logical structure is not developed this way, even without their knowing it, they are not ready for fractions or algebra.
It is very hard to work out rules of counting and understanding the counting of small sets. If we count a herd of cows in a different order do we get the same number? This is a hard thing to work out correctly why we do. One tends to assume the result in naive explanations.
To work out why we get the same number if we count a set in a different order requires theoretical understanding. This has to be written down exactly correct, or as best as possible.
Once this is done, we can then work the correct logic into slogans, chants, puzzles, games, etc. that teach this logical structure.
If we just invent the slogans and chants without understanding the actual logical structure, then we will create gaps and confusions. These accumulate and show up in walls that can’t be scaled at fractions and algebra.