Most of us learned a short cut in school to help us multiply multi digit numbers known as the standard algorithm or traditional algorithm. One thing we as teachers need to be careful of is not teaching short cuts first. Short cuts are so much more meaningful when you discover it on your own.
Multiplying Multi-Digit Numbers
Traditional Algorithm / Standard Algorithm
If students have a great understanding of place value and are quick with addition and multiplication, this method is easy for them.
As an intervention teacher, I don’t get to choose what students learn first. A lot of them come to me trying to remember how to do this standard algorithm. Students that don’t have their multiplication fact memorized sometimes forgetter where they are or what they are doing because they have to pause so much between each step. They also tend to forget to add in the number they carried.
Multiplying Multi-Digit Numbers
Partial Products Algorithm
The Partial Products algorithm is the first strategy I would teach in a homeroom. This allows students to go through one simple step at a time. They do all their multiplication and then add. This method also allows you to reinforce place value. It is important to emphasize at first the they are multiplying 6 time 80 rather than the short cut of 6 times 8. After a few problems you can have them look for a pattern. They will notice that there is always a zero there and they can feel like they discovered their own short cut.
Sometimes my intervention students know they are supposed to put a zero somewhere but they don’t know why or where. I tell them to forget about that for a little bit and I walk them through multiplying using place value.
Once the students have an understand of the place value of multiplying multi-digit numbers, expanding the number of digits is easy for them. The intervention students I get, often know the short cut but have no idea how it applies when there are more digits. They make mistakes like putting one zero when they are multiplying a number in the hundreds or thousands place.
Multiplying Multi-Digit Numbers: Box Method
The box method is great for students that get overwhelmed and lack confidence in math. I teach them to say the number slowly to put it in the top box. When you say 83 as “eighty…. three” you can hear how to separate the numbers. Some of these students are ones that use multiplication charts often so the box method is comforting to them because it feels familiar. The beauty is that they can multiply in any order. It doesn’t matter whether they multiply 80 x 6 first or 6 times 3 first.
Which Should I Teach?
Personally, I like to teach Partial Products first. Then I teach the box method side by side. I make the students do a few problems with me for the strategy I teach, then I have them pick one strategy to stick with for the day. When students tell me they learned another way, I say, “Great! There are so many ways to find the same answer. Let’s try this strategy today.”
When I do problems all together, I’ll ask for one volunteer per strategy. They’ll come up and do it on the board. Students see that the similarities and reinforce the mathematical concepts happening in the problem. Eventually volunteers ask if they can show another strategy. When they do, I make sure to compare the traditional to the partial products and it becomes clear that they are the same thing written a different way and done in a slightly different order.
Looking for Resources?
|2 Digit times 1 Digit: Introducing 3 Strategies for Multi-digit Multiplication Featuring Beat the Clock|
|3 Digit Times 1 Digit Introducing 3 Strategies for MultiDigit Multiplication Featuring a Beat the Clock Challenge|
You can find all of my multiplication products here.
If you are ready for resources in Google Slides, I have these two. Just click the pictures below to find them.
Check out these 5th grade blog posts.