Wow, I had some tired students this morning, but everyone had a great Halloween so it is back to the grind.
We are still plugging away at two digit multiplication and I thought that I would share the strategies that we use in our class and see if anyone else had any others they would be willing to share. I believe in showing students many different ways to solve each problem and letting them choose which way works best for them.
Now with that being said, we spend a lot of time talking about efficiency. While you may have used loops and groups to solve 7x3=21 pretty efficiently, 74x21 isn't going to be so easy with loops and groups.
Okay, on to the strategies.
The first strategy is the good old algorithm. When I was in school this was the one and only way that we were taught. To go along with the algorithm there is a cute rhyme to help students remember the process.
Ones to the ones, ones to the tens. Drop the zero and do it again. Tens to the ones, tens to the tens. Add it all up and that's the end.
The second strategy that we use is the open array. For visual students this strategy seems to work really well. It breaks down the multiplication into easier facts that they can use the power of ten to solve.
To start, you break down the numbers into their tens and ones. For example, 74 would be broken down into 70 and 4. While 21 would be broken down into 20 and 1. Then draw yourself a four part open array. You then place one set of numbers across the top of the array and the second set down the left side of the array as shown in the picture below.
Then, you multiply the width and height of each part of the array. Finally, you add all the products of the array together to get your final product.
This strategy works really well for some students and is too cluttered for others.
The third strategy that we work on is partial products. Partial products is basically the same as the open array, but without the picture. After breaking down each number you make sure that all the numbers get multiplied by one another. For a two digit by two digit problem there should be four partial products. Finally, you add all the products together to get your final product.
The fourth strategy, that I just learned this week, is lattice. Now, a few of my students call it lettuce, but I will take what I can get. This strategy seems to work really well for students who don't understand the other strategies. I think that they feel like it is less work, it is certainly less writing.
To perform the lattice strategy you start by drawing a four square array. Then you draw diagonal lines from the upper right hand corner of each box through the bottom left corners and extend them slightly past the outside of the box.
After you have completed your box and diagonal lines you write one number across the top, with one digit above each column and the other number down the right hand side.
Then, you multiply each width and length. When writing the product the tens place goes above the diagonal line, and the ones place below the diagonal line.
Finally, using the diagonal lines you add each number together and write the sum on the outside of the box. If you read the number from the top of the left hand side and across the bottom you have your product.
Sounds confusing right, that's what I thought until someone actually showed me and it is actually really simple.
In case my explanation didn't make sense. Which I think is pretty likely, here is a YouTube Video explaining it.
I hope that one of these strategies can help you. If you have another strategy for my class and I to try PLEASE share in the comments below!