I remember learning multiplication in third grade and the memories of that time are stressful ones. We were taught only one way to solve multiplication,
Recently in a math education class we talked about multiplication and this was the only method I could remember learning. What makes that even worse is that when asked why do you solve the problem the way you do? What’s the reason behind the steps? I could only answer with “because that’s how I learned it thirteen years ago.” Before we discussed this method in class I did not remember the reasoning behind solving problems with this method. Now I realize that it is all about place value multiplying throughout the top number by one place value at a time, then using a zero in the answer row as a place holder when you move up to the next place value.
Within class discussions, I learned of a few new ways to solve a multiplication problems, such as using an array to break down the problem and make it more visual, such as this example,
When using an array to solve the problem, students (and myself) can visually see the reasoning behind what they are doing. They can break the larger numbers 13 and 16 into smaller numbers that they are more comfortable with. They can then solve the smaller problems, 10×10 can be solved by a memorized fact or the student can physically draw ten rows and ten columns and then count the squares to reach the same answer. Once the student has solved each of the smaller problems they add the answers together to reach their final answer. This method makes sense to me because you can break up the numbers into combinations that make more sense to you and that you are more comfortable with. You can also see the layout and the grid, if needed you can count out the squares to double check your answer.
Another way to solve a multiplication problem is by grouping.
Since the problem is 3×2, you make three groups and then place two stars, dots, tallies, etc. in each group. When you have done that for every group you count the total number of objects in all the circles.
A method that shows the very definition of multiplication, repeated addition.
If you are using larger numbers (or smaller ones), you can break them down into smaller pieces. For example, 15×7 can be broken down by replacing 15 with 10 and 5, and 7 with 5 and 2. So 15×7 turns into 10×2+10×5+5×2+5×5.
I am a proponent of teaching various ways of solving problems and having my students choose the way that they understand the most and are the most comfortable and competent with. I would rather give myself more work in teaching the methods and grading assignments and assessments and have my students actually learn than assume they will learn with cookie cutter methods.