How do we do this "new" way of dividing?

You’re a star in the mathematics education world

This is how I teach students who can’t grasp traditional division. It isn’t new, it is called repeated subtraction.

I high key love this tbh

Partial quotients was a strategy the UK tried to introduce many years back but math teachers pretty much refused to teach it. Also, it can extend to decimals.

Looks like distributive property of multiplication over addition, kind of "distributive property of division (multiplication by inverse) over addition (& subtraction)" In your examples divisor d≠0 is left of Dividend D, but we could D÷d= [A+B-C]÷d =A/d + B/d - C/d, where D=A+B-C

another way to divide! with prior estimation and decomposition into multiples! 🌐

This is how I taught it to grade 4s.

I find this far more intuitive than the standard long division algorithm, and I like the fact that it allows some room for creativity instead of being an entirely rote algorithm.

Wait. Say that all again but slower please.

The "Big 7" was a big hit with my last class. However, I saw a few students who struggled because they had problems with subtraction and in some cases regrouping. Also, some would only multiply by 10 even if 25 was an option . It turned into too many steps.