Learning Multiplication Tables: Help for Struggling Students

Making Multiplication Clear to Struggling Students

Why Students Have Trouble with Multiplication

Other than not paying attention in class, not doing the work and otherwise not trying, there's often another reason why students have difficulty with multiplication. Somewhere along the line they didn't learn some basic facts or processes, which can lead to inattention or not completing assignments. Because math is cumulative, the first step in helping these students is discovering where they got stuck. Ask yourself:

• Do they understand what addition is?
• Do they know their addition facts?
• Do they understand what subtraction is?
• Do they know their subtraction facts?

Back up as necessary to be sure your students fully comprehend addition and subtraction concepts. Re-teach any facts that haven't been learned. Then be sure they grasp the basics of multiplication.

Understanding Multiplication Basics

The basics of multiplication might be summed up in two concepts:

1. Multiplication is a shortcut for adding a number to itself a specified number of times. Demonstrate this concept on the board until it's clear to the students.
2. Multiplication can be understood as 'groups of.' Use manipulatives (e.g., buttons and an egg carton) to demonstrate this idea until you're sure the students understand it thoroughly.

Once students have a handle on these two basics, they're ready to learn the facts. Here are some suggested activities for teaching the multiplication tables.

Learning the Facts

Make It Fun

Learning the multiplication tables can be difficult for some students. They may feel overwhelmed when they see that learning the table from 0-10 or 0-12 involves memorizing 121 or 169 math facts. Enjoyable ways to present the tables, or to reinforce the facts as they're learned include:

Reading books, such as Amanda Bean's Amazing Dream by Cindy Neuschwander or Barrington and the Math Princess by Roxanne Eckenrode.

Singing along with CDs, such as Hap Palmer's Multiplication Mountain or Disney's well-known Schoolhouse Rock: Multiplication.

Making manipulatives in class using Fun-flap Facts: Multiplication by Danielle Blood or Scholastic's Monster Multiplication Wheels: Reproducible Patterns for 20 Interactive Wheels That Help Students Memorize the Multiplication Facts from 1 to 12.

Memorize the Multiplication Tables

No matter how many fun ways there are to learn multiplication facts, children still must learn them well and be able to recall them quickly. Shortcuts help learning the multiplication tables and reduce the daunting task of learning so many facts to learning a few rules and facts.

Let's look at a way to memorize the table from 0-10. There are 121 possible facts. When we learn the first rule, 'any number times 0 is always 0,' it reduces the 121 facts to 100 (highlighted in yellow).

The commutative property, 'syrup x pancakes = pancakes x syrup,' decreases the total number we need to memorize further to 55. We can memorize 3 x 5 = 15 and 5 x 3 = 15 together.

The next rule, any number multiplied by 1 equals that number, removes a whole row, bringing the total down to 45. The rule that any number multiplied by 10 is that number followed by a 0 reduces the total down to 36.

Summary:

Rule 1: any number times 0 is always 0

Rule 2: commutative property

Rule 3: any number times 1 equals that number

Rule 4: any number times 10 is that number followed by a 0

With only 36 facts now left to go, divide the table into four sections by drawing lines between the columns and the rows for 5 and 6 both horizontally and vertically. You can cross out the columns and rows for 0, 1 and 10 because they were covered by rules 1, 3 and 4.

Have your students memorize the table from 2 x 2 to 5 x 5. Because of the commutative property, there are only ten facts to learn.

When that's mastered, work on 2 x 6 to 5 x 9. The 16 facts here also cover the next section (6 x 2 to 9 x 5), so when these are learned, more than 3/4 of the table has been covered. Finish with ten facts from 6 x 6 to 9 x 9.

Patterns may help to learn many of the facts. These patterns are:

1. Multiply by 2: Double the number (i.e., add it to itself). Example: 2 x 5 = 5 + 5 = 10
2. Multiply by 4: Double the number, then double the answer. Example: 4 x 5 = (5 + 5 = 10) and (10 + 10 = 20)
3. Multiply by 5: The answer always ends in either 0 or 5.
4. Multiply by 9: Multiply by 10, then subtract the number. Example: 9 x 4 = (10 x 4) - 4 = 40 - 4 = 36