Understanding and Mastering Multiplication

Many children struggle to memorize their multiplication tables, and many adults have bad memories of trying to learn them.

Why should children learn the multiplication facts? Because children without either sound knowledge of their facts or a way of figuring them out are at a profound disadvantage in their subsequent mathematics achievement. Students without multiplication-fact fluency spend more time determining routine answers and less time on more meaningful applications. Students who know their facts build on these fundamental concepts which ultimately benefits their later mathematical development.

For years, learning to compute has been viewed as a matter of following the teacher’s directions and practicing until speedy execution is achieved. There has been little or no emphasis on understanding the concept. Memorize 7×6=42, and so on.

When skills such as multiplication facts are taught for conceptual understanding and connected to other mathematics concepts and real-world meaning, however, students actually perform better on standardized tests and in more complex mathematics applications.

Numbers and equations are far more interesting when they represent real-life specifics. For example, the problem “What is 3 x 4?” can be posed as “If there are 3 pods with 4 whales in each, how many whales are there altogether?” As kids begin to visualize whales swimming through the ocean, the math becomes much more specific, rich, and understandable.

When my granddaughter was in the 3rd grade, we would use travel time in the car to practice our multiplication facts. First, I would make up a problem (7 tricycles, how many wheels?), and she would have to give me the complete equation (7×3=21). And then I would ask, “Why isn’t this a 3×7 problem?” Too many times all we say is 7×3 is the same as 3×7. That can be very confusing.

Then it would be her turn to make up a question (5 cars, how many rear-view mirrors?), and I would have to come up with the entire equation, plus justify why it wasn’t a 3×5 question.

Sometimes we would discuss what might make a good 4×7 question, or a 9×6 question, etc.

Keeping with the idea of making multiplication facts understandable, you might try a math game such as Bubbles and Stars.

Bubbles and Stars (Beginning Multiplication)

What you need:
2 players
1 die
paper and a pencil for each player (fold it in quarters)

Player #1 rolls the die and draws that many bubbles (as big as he/she can in one of the quarters).
Example: Player #1 rolls a 5 and draws 5 bubbles.

Player #2 rolls the die and draws that many bubbles.
Example: Player #2 rolls a 1 and draws 1 bubble.

Player #1 rolls the die and puts that many stars inside each bubble.
Example: Player #1 rolls a 3 and draws 3 stars inside each of his/her 5 bubbles

Player #2 rolls the die and puts that many stars inside each bubble.
Example: Player #2 rolls a 6 and draws 6 stars inside his/her 1 bubble.

Both players record how many bubbles and stars they drew and then record how many stars they have altogether.
Example: Player #1 – 5 bubbles x 3 stars = 15 stars
Player #2 – 1 bubble x 6 stars = 6 stars

Player #1 rolls the die one last time.
If the roll is odd – 1,3,5 the player with the most stars wins.
If the roll is even – 2,4,6 the player with the least stars wins.

Parents and teachers who use these kinds of activities with their children, will help them master their multiplication facts. Resultingly, these students will have a more positive attitude about their mathematics abilities and further mathematics experiences. Teaching for understanding equals a formula for success.