The division algorithm is by far the most complicated of all the written algorithms taught in primary/elementary school. It involves processes of division with remainders, multiplication, subtraction and regrouping, making lots of potential chances to make a mistake. It is no surprise, then, that some adults say this is one algorithm we should no longer teach at school, but instead students should be taught to use a calculator.
I don’t want to cause offence here, but those adults are wrong. If students reach for a calculator to do division instead of exercising their thinking abilities, they will never truly understand what division is, nor be able to estimate answers or apply division in other flexible ways. Doing the algorithm is tough, like doing pushups is tough: not all that enjoyable at the time, but really important for building fitness and strength.
Here are some recommendations, which I also go over in the video:
As with the previous two weeks’ videos, use base ten blocks to illustrate the algorithm
DON’T talk about a number “going into” another (such as “4 goes into 15 3 times”). This simply is a nonsense statement, and does nothing to build students’ understanding of what division is about. In its place, talk about sharing a quantity among a number of groups (eg, “15 shared among 4: each gets 3, and 3 are left over”).
Always refer to the amounts being shared, such as “23 tens shared among 5 is 4 tens”
Avoid also saying “bring down the …“, but instead talk about putting the “left-overs” with the next place to the right for the next division phase
Save short division until students have got long division and can do it successfully
Stop at dividing by one digit, unless students want an extra challenge; there is little point dividing by a two-digit number except for the exercise