After the students have solved many problems in a variety of their own ways we move onto the algorithms (procedure for calculating).
Break-apart strategies use the distributive property of multiplication. Don’t worry, I hadn’t heard of that before I started teaching math either. I wish I had because it’s really important to understand (even if you don’t know the term). It is critical for algebra and it is also handy for mental math. I talked about it in my post about math talks here because we can use it for our times table facts too. This video does a really good job explaining it with visuals.
I find that some of the students can find the break-apart method of multiplying a 2 digit number by a 1 digit number on their own and when they share their strategy with the class! Wow! The other kids eyes open wide with a Eureka moment! What is the break apart method? You break one or more of the numbers into parts to make the multiplication easier. It also demonstrates why you would “carry” a number over to the next column.
When I go on to teach the students the traditional way of multiplying they will be able to see why they are “carrying” the 2 (it’s really 2 tens in 25 and needs to be in the tens column). The grade 4 students are working on this right now. The grade five students have already done this with 2 digit by 2 digit numbers.
In grade five we have been working on division. We started with problems and pairs solving the division any way they wanted to. Then we moved on to the alternate long division algorithm. I like this method because it reinforces that division is the inverse operation to multiplication (they undo each other) and that it is repeated subtraction. Here is an example:
I started with 10 groups first because 10 is a nice easy number to multiply by but many kids quickly see that it is easier and faster if you multiply by larger “friendly” numbers).
I like this video explaining the method except that it does not have sound and the reading could be a problem for some kids – but we can read it to them.
Multiplication and division take a long time to learn well. Students need time to solve problems, learn different ways to solve problems, practice their times tables, practice algorithms. I think all students would benefit from doing one subtraction problem a day (and check their answer with addition) and one division problem a day (check their answer with multiplication) until they are fluent.