## Introduction to the World of Diamonds

What is Diamond Math?

## Let us get Started

It seems that one of the big issues in Algebra is working with quadratic equations.  It seems that working through the factoring of the quadratic would be nice if we could find an easy way to approach the problems.  This essay addresses this issue and attempts to work the students through the factoring process in perhaps a simple method.

Set up your students into groups of two – four. Assign these teams the following

DIAMOND PROBLEMS,

see if the teams can discover what is going on and how the numbers are related. # Into Discovery

Notice the Diamond Math works like this:

(left)x (right)  =  AC

(left) + (right)  = B Patterns and pattern recognition are important skills that are helpful for future work in Algebra.

These skills are developed and honed through a variety of pattern activities.  This particular activity is used in a number of different processes throughout Algebra.

It is particularly important that the students recognize the relationships the numbers have with each other in the

Diamond

problems.  It may be necessary to provide several more completed examples in order for the students to see the connections.

Initially, the combinations used can be helpful in the development in the usage of Integer Operations (adding & subtracting, multiplication & division).

The use of signs both positive and negative provides much needed practice.   Worksheet #2 should help the students work through adding positive and negatives as well as the multiplication rules associated with the positive and negative sign.

Now it is time to change the challenge.

The following group allows the students to either solve the problems using algebra or through the guess and check method.

## Let the Students Build the Diamonds

Now that you have worked several Diamond Problems, it is time to let the students make up their own combinations.

What Can We Do With All This Knowledge?

Let us use the Diamond Math to help us learn to factor polynomials.

How can this be used?

### When introducing students to the

#### “Art of Factoring”

it is interesting to see if there are tools that may help the students see the number combinations a little easier than the guess and check method.

The Diamond Math lets the students play with number facts and eventually they can with a little more ease perform polynomial factoring.

Given the quadratic equation in the form of:

ax2 + bx + c The students then use the diamond math in their efforts to factor trinomials.

Let us try an example:

Early Conclusion:

This method is proving to be very useful with both the Algebra I class and the Applied Algebra class.  It was introduced as a game with just the diamonds and none of the connections to factoring.  Later in the class instruction when it was time to introduce factoring the Diamonds reappeared. The students either actually use the Diamond Math or it becomes a crutch (a signal of what to do) that aids them in further factoring efforts.