The main goal in education today is to teach algebra to all students. The XY Chart™ provides a tremendous headstart to achieving this objective. Students in the primary grades are provided with a preview of the important concept of graphing while learning their multiplication facts. When I share the chart with teachers of elementary mathematics they react with enthusiasm and are eager to use it in their classrooms. The question they ask most often is: “Why didn’t someone think of this before?”

In my opinion, as a teacher of math methods, I believe The XY Chart™ is far superior to any multiplication chart and is the only one that should be used in the elementary classroom.

**~ Charles Sonenshein**

Teacher and Educational Consultant

In 25 years of teaching mathematics, I have not seen as powerful or as elegantly simple a way to help students learn the multiplication tables as the XY Chart™. While using the chart, students not only learn these critical arithmetic facts, but they are brought in contact with some of the most important concepts of mathematics including the meaning of area and a method of evaluating it, as well as the relationship between space and numerical quantities underlying the Cartesian Coordinate System. It would be interesting to measure the difference that such an early exposure to these profound ideas might cause in students studying calculus twelve years later.

**~Mr. Joseph Hofmeister**

Director of Technology

Cincinnati Country Day School .

I found the the XY Chart™ in my search for an alternate approach for teaching multiplication to students who were struggling with math. My students began to master their math facts with more enjoyment and understanding than with “drill and practice” worksheets or flash cards. It’s a joy to see how quickly they apply their math skills to learning division, fractions, decimals and graphing. Now I include an XY Chart™ with the materials for all my teacher training workshops.

**~Marilyn Wardrop**

Math Teacher and Trainer

Multi-sensory Math Workshops Vancouver, B.C.

I find it useful to teach mulltiplication and division facts, especially for visual learners and those who need kinesthetic reinforcement. They can see and hear the facts as they run their fingers over the XY Chart™. This multi-sensory approach helps them learn more effectively. The chart also provides an easy way to see patterns in multiplication and division, and students can “see” the square numbers, giving concrete meaning to the term- important for students who are not yet thinking abstractly. I also love the way I can introduce the concepts of ordered pair coordinates. Activities like Descartes and the fly are engaging and fun for the students and they provide important language arts and social studies links, helping to integrate curriculum ideas. I like to show how math sentences can be graphed. This is an important introduction to algebra.

**~Barbara Marin**

4th Grade Teacher, NCTM Member

For the past two years, Joe Speier has visited my classroom to introduce my fourth grade students to the XY Chart™. Although reading from bottom to top is initially new to them, they take to it very quickly. The story of Descartes and the fly draws them in, and the logic and fun of the the chart itself is immediately engaging. The connection to multiplication rectangles and area becomes clear to them very quickly; the connection to coordinate graphing is just as clear to me. The chart helps them learn what they need to know now and lays a firm foundation for what they will need to learn later. I am excited about finding more ways to connect the chart to our math program.

**~M. E. Hager**

4th Grade Teacher