St. Michael's Orthodox School

The Patterns of the Times Tables

Everything that God has created is beautiful, even in its current fallen state. After each Day of Creation, we read that God “saw that it was good”, and finally after the last Day, we read that “God saw that it was very good”. This beauty is very easy is see in the language of mathematics.

However, it is also easy to be unaware of, or to overlook, the beauty of mathematics if it is presented as just one more thing to memorize. Within the world of mathematics there are patterns, and patterns within patterns. These can be seen in the way leaves grow on plants and in the way frost forms on window panes. It is available even to the young in the form of the simple times tables.

One way we have found to show the beauty and rhythm of the times tables is to show the patterns they make on a specially designed string board. This board is very easy to make and is an enjoyable woodworking project.

Start with a piece of “shelving pine” available at any hardware or home improvement store. Shelving pine comes in various widths - 11.5 in., 9 .25 in. 7.25 in. and , 5.5 in. , etc.  The smallest size may be a little too small, but the others sizes work well.

Whatever size you use, cut the board so it is a square, equal on all four sides. Then construct a circle which will fit easily inside the square piece of wood, with a margin of at least a ½ inch from the edge of the board. You can use a compass or a small plate of the right size to construct a circle.

With a protractor, carefully mark off ten angles of 36° each and make a small mark on the edge of the circle for each angle. When the circle with the ten 36° angles is complete, place it on the board so that the center of the circle is as close as possible to the center of the board. With a dark permanent marker, make a mark on the board for each mark made on the circle.

Use the same marker to number the marks made on the board, starting with zero (0) and ending with nine (9). It is best to put the number on the outside of the marks. At this point we sand the edges of the board so they are smooth and paint the board with watercolors. You could also put a simple finish on the board.

At each of the ten marks, use a hammer to pound in a finish nail (nails with very small heads) about 1 ½ long, leaving about an inch exposed. Then cut a piece of yarn or string (preferably colorful) about three feet long and tie one end to the nail at the zero (0) mark. Now you are ready to begin to see the patterns.
For the two times tables, wrap the yarn or string around the nail at the two, then around the nail at the four, then around the nail at the six, etc. Continue this process until you reach 24 (2 x 12). For the three times table, wrap the yarn or string around the three, the six, the nine, etc. until you reach 36, (3 x 12). You will see a different pattern. If you make all the patterns, you will notice that there are repetitions. What is the pattern of the repetitions? We will leave that discovery for you and your children.

If you would rather not gather all the materials for this project, we sell kits in The School Store which includes the board, the pre-marked circle, sandpaper, nails, and a piece of yarn. This is everything you need but the hammer and the paints.

The picture at the side is of the two times pattern. If you click on the picture, it will get larger.  We have each of the students make a set of patterns and tables in a book.  For each table there are two pages.  The first page has the title, for example, " The Two Times Tables".  On the back of the first page is the pattern of the table, similar to the top of the picture on the left.  On the second page, the student writes out the equations, similar to the bottom of the picture on the left.  A sample of the pages for the four times table is available here.  A blank form that can be used for each of the times tables in this book is available as a PDF file - here.

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