# Archive for October 27th, 2010

## 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

Partial Products

Lattice Multiplication

Explanation of Lattice Multiplication

Cross Hatch Multiplication