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The multiplication table is the familiar grid that contains an x quadrant, ranging from 0-12, 0-10, or 0-9, and a y quadrant with numbers of the same range. The product of any two numbers can be found by looking at the intersection between x and y. For example, if you wanted to find 8 X 2, you would merely look at the 8, and move down to the 2 space, to find the number 16. Alternately, since order does not affect simple multiplication, you could find the number 2 and count over to reach its intersection with the number 8.
The products of the intersection of numbers would be listed in several spots on the table. In a simple 0-9 multiplication table, the number 16 would be listed 3 times. You would find it at the intersection of 8,2, 2,8 and 4,4.
Many primary grade math programs insist on memorization of the multiplication table, or knowing your “times tables.” Actually, though the reference is to the multiplication table, students may never use the real multiplication table. They may instead simply memorize multiplication facts in order. The multiplication table is sometimes seen as a crutch, because students can use it without memorizing the facts, or alternately, they can use a calculator. Early grades may display large multiplication tables in a classroom, but from grade 3 and up, most classes no longer display them, or teachers cover them during tests so students don’t use them for multiplication problems.
There has been decline in use of the multiplication table since 1989, when the US National Council of Teachers of Mathematics (NCTM) suggested that students should evolve their own methods for figuring out multiplication problems. This suggestion didn't entirely solve the problem of memorizing multiplication, since some students appear not to evolve their own methods. Some students appear better served by actual memorization, while others might be able to make observations about numbers that help them keep in mind how to solve each problem.
In truth, knowing your multiplication facts often makes more advanced math simpler. There is a direct correlation between declining grades in mathematics and failure to memorize the multiplication facts, especially from 1-9 X 1-9. Failure to understand such facts often makes advanced concepts like long division extremely challenging. Some teachers now try to employ some of the suggestions made by the NCTM and also reinforce memorization. The NCTM revised their own statements to stress the importance of memorization of basic math facts, after a large body of evidence suggested de-emphasis had led to greater problems with math.
If your child is having difficulty memorizing math facts, it doesn’t hurt to have a few examples of the multiplication table posted at home. The ceiling over a child’s bed may be an excellent place to put one, and kid’s bathrooms also are good places. This may help the child find patterns and become better at learning math facts, simply because they have greater exposure to the multiplication table. You can purchase inexpensive large tables at teacher supply stores, in bookstores and on the Internet. You can also make your own with a child, to reinforce learning math facts.
We used to have a multiplication table poster in my house when I was younger. It went up to 13X13, and I am proud to say I know my math multiplication tables really well even though that is pretty close to the limit of my math abilities.