7.) Number Flow (Addition/Subtraction)
Many mental math strategies involve breaking a problem into smaller parts. While this can be effective, it also requires working memory to keep track of multiple intermediate steps.
An alternative approach is to think of numbers as flowing between each other in order to simplify the problem.
For example:
532 + 966
Instead of adding directly, you can let part of one number “flow” into the other. Move 34 from 532 into 966 to make 1000.
Now the problem becomes:
(532 − 34) + (966 + 34) = 498 + 1000 = 1498
By shifting value between the numbers, you create a round number and reduce the difficulty of the calculation.
This idea also works for subtraction:
704 − 298
Instead of subtracting directly, move 2 from 704 into 298 to make a round number:
(704 − 2) − (298 − 2) = 702 − 296 = 406
Or more simply, you can think of it as adjusting both numbers:
704 − 298 = 706 − 300 = 406
By shifting both numbers together, you turn an awkward subtraction into a much cleaner one.
This idea extends naturally into multiplication.
When multiplying, you can think of numbers as collections of factors that can be rearranged. These factors can “flow” between numbers to make the calculation easier.
For example:
24 × 24
Instead of using the standard algorithm, break one 24 into factors:
24 = 2 × 2 × 2 × 3
Now let those factors flow into the other 24:
24 × 24 = (2 × 2 × 2 × 3) × 24 → 24 × 8 × 3 → 192 × 3 = 576
By redistributing the factors, you turn a harder multiplication into a sequence of simpler steps.
Over time, this way of thinking reduces the need to track multiple pieces at once. Instead of managing complexity, you reshape the problem into something easier before solving it.