Form II: Arithmetic: Multiplication with Crossed Lines

I have found it very helpful for students who are just learning multiplication facts to have methods at their disposal for determining the facts they need.

One of these methods is using crossed lines. For example, if I student needs to figure out what 3 x 7 is, they can make three lines going down on a piece of paper and then cross those lines with seven lines going across. They are to count the places in which these lines intersect. If they make dots at each of the intersections, then they are less likely to get misplaced or skip one. By doing this, it reinforces the concept of what 3 x 7 means, and is not just rote memorization.

You can even play games with these crossed line matrices. Once they have made up a few of these, you can take them and cover up where they cross with a piece of paper, only leaving the lines sticking out at the top and left hand side. Then they have to visualize the dot matrix that is now under the paper. This is like flashcards, and yet you are encouraging the student to visualize the meaning behind these multiplication facts.

source: Mathematics; a Way of Thinking, Bob Baratta-Lorton