# We Got A Problem #7: Drawin’ on the Multiplication Table

August 31, 2012 2 Comments

Draw a rectangle on top of the multiplication table. The numbers in opposite corners of the rectangle form pairs.

What can you say about the products of the two numbers in each pair? Explain.

What can you say about the *sums* of the two numbers in each pair? Explain. Ooh, that’s a good one.

See if you can find anything similar in the addition table. Or, drop a comment with your favorite pattern from either table.

Create a rectangle on the table (with sides parallel to the axes). The sum of the values on the vertices is another entry in the table. Where?

Create a rectangle with two opposite vertices on the “main diagonal” (where the two factors are equal) The sum of the values on the vertices is also on the main diagonal. Where?

Any of these versions, and others (including variations with a hundreds chart) are infinitely more engaging for students than the “drill ‘n’ kill” practice worksheets often seen. I have personally seen dozens of students beaver away happily at these, trying to prove or disprove a point or pattern. Several times, I would tell students, “the pattern is [this] … am I right?” – with middle school students, especially, their desire to paint the teacher a fool overrides their disdain for skills practice as they attempt to find exceptions to prove the teacher wrong. Lots of fun, and they don’t usually realize they did more work, in more time, on these problems than they would have on “regular” practice worksheets.