The method by which one learns the multiplication facts might be the topic of a debate, but the importance of the mastery of these facts for reliable and enjoyable mental math is beyond dispute. The XY Chart™ was designed to imprint the 10 by 10 multiplication facts and their arrangement within the first quadrant of the Cartesian coordinate system into the mind of the viewer. This will happen by its simply “being there”, through the unplanned activity of everyday observation.

Since the mathematical education of the next generation is a challenge to parents as well as teachers this guide is directed to both. Although The XY Chart™ is intended for the eyes of the math learner and will work without the intervention of outside authorities, teachers and parents can stimulate the natural process by following some of the suggestions below. It all begins by acquiring and displaying the chart.

Posters have been used for ages to educate the observer. Today major companies spend billions of dollars to visually advertise their products on billboards and the pages of magazines. These ads come without a user manual. They work by being seen – – being seen over and over and over again! Rational companies would not invest money in this process unless it worked. Consider the shoe company logo, the fast food chains, the beer and cigarette images. Why can’t worthwhile information be acquired in the same visual manner?

The XY Chart can work in the same way – by being seen.

**The following steps are suggestions:**

- Install The XY Chart™ in a very prominent place on a classroom, bedroom, or other visible wall. It is not only filled with critical mathematical information but it is compelling art. Its primary colors, clean lines, and literal meaning make it a delightful addition to any scene.
- Refer to it often. Point out patterns. The line of squares. The arithmetic sequences contained in each row and column. Ask the viewers to find new patterns.
- Practice skip counting for the 1 through 10 numbers. Let the counting continue beyond the 10 terms that appear in the chart. Point out that the value of each number counted is the product of the occurrence number of the term and the skip number.
- Explain how the index numbers on the X and Y axes combine in the multiplication operation to equal the product found at the point of intersection of the perpendicular lines leading from those points. Show how to work backwards from the product to the factors on the axes.
- Explain how the numeral found at the point of intersection represents or stands for the number of unit squares of the rectangle found between the X and Y axes and the perpendicular lines that intersect at that point. Note too that these unit squares might stand for any group of items outside The XY Chart™ such as the square yards on a playing field or the number of days in 5 weeks or the number of cents in 4 quarters. The numeral and the squares represent two distinct levels of abstraction. This is a very valuable insight into the nature of mathematical language.
- Tell stories about Rene Descartes. This French mathematician introduced the use of the rectangular coordinate system. It has becomes the primary visual tool of higher math. The story of his sleepless night’s attempt to describe the exact position of a fly on the ceiling is an entertaining anecdote.
- Display the art of Piet Mondrian. His compositions in the primary colors served as a model in the design of The XY Chart™.
- Continue to teach multiplication in your usual manner. Have students visit www.xycharts.com to find other materials and programs to reinforce what they see in The XY Chart™.
- Expect that the information in the chart be mastered and test for this.