# Conceptual Understanding, Stategic Competence and Multiplication: Guided Math Group Work

Strategic Competence is extremely important to build in our students. When students have strategic competence they are flexible with numbers and can think about a variety of efficient solutions. Strategic competence requires conceptual understanding. Students have to know what they are doing, in order to think about it in a variety of efficient ways.

When I say efficient, I am referring to the fact that some strategies are slow and others are fast. So for example, let’s take 12 x 14. One strategy is to draw 12 groups of 14 and count them up. This is a strategy but it isn’t very efficient. There are much more efficient ways to solve this problem. One way is to multiply 10 by 14 and then add 2 by 14. This would be much more efficient than the previous method. Another way would be to multiply 12 by 12 and then add 12 x 2. The point is that when students can think of multiple ways to approach a problem they are exhibiting strategic competence. Below I have listed some examples of ways to think about teaching double digit multiplication, so that students build conceptual understanding and strategic competence.

*Double Digit Multiplication*

Base Ten

http://www.youtube.com/watch?v=4df1wyLgFaY

http://www.youtube.com/watch?v=mjYYbwuued0&feature=related

Partial Products

http://www.youtube.com/watch?v=zGXHaKmA4dE&feature=related

Lattice Multiplication

http://www.youtube.com/watch?v=1M2L0LJ6PFE&feature=related

Explanation of Lattice Multiplication

http://www.youtube.com/watch?v=S3z4XqC_YSc&feature=related

Cross Hatch Multiplication

http://www.youtube.com/watch?v=U5F7g2ZbKjA

Box Multiplication

http://www.youtube.com/watch?v=CIwxJIB43Co

Other Resources:

http://mason.gmu.edu/~jsuh4/teaching/resources/cards.pdf

I really need to connect with you because these are the ideas I presented at a PTA meeting for parents regarding math instruction just last week. Strategic competence is a pedological term for providing efficient strategies for students’ math thinking? I like it. I just knew it as looking at validating where students are, and then stretching their thinking to the next level. Of course, I printed the strategy icons because these can be used in small groups. Thank you.

Lisa PietrosimoneOctober 29, 2010