What is Diamond Math?

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 Ð four. Assign these teams the following

**DIAMOND PROBLEMS**,

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

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.

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**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.

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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?**

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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:

** ax ^{2}
+ bx + c**

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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.