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Learning multiplication is one of the most important concepts that second and third grade students need to master. In order to become successful math students, they must not only memorize their multiplication facts, they must also understand the fundamental concept behind multiplication---it’s simply repeated addition. Back in my day (when there were nine planets!) I learned my times tables the old fashion way--good ole rote memorization and constant repetition. After failing a multiplication test at school, my dad made me sit down at the kitchen table everyday after school for a month and practice a set of multiplication facts. One day I would do my 2’s (2 x 0 = 2, 2 x 1 = 2, etc.), the next I would work the 3’s (3 x 0 = 3, 3 x 1 = 3, etc.). At the time I thought these activities were boring and useless but when I experienced the results, better test scores and faster recall of multiplication facts, I began to trust that constant practice of my multiplication facts would lead to better math grades.
Having overcome math challenges as a child, I can certainly relate to those that have a fear of math. On one occasion was teaching algebra to ninth graders and I had a student who was getting low test scores. At first I thought she did not understand the algebra concept I was teaching. But when I thoroughly evaluated her math skills I discovered that she did not know her multiplication facts past three! I was dumbfounded that a student could enter the ninth grade without being able to easily recall their times tables. Nonetheless, she was not successful in algebra and had to go back and learn basic multiplication concepts. This should not happen.
Although this extreme experience is not a reflection of most math students, it is critical that once students matriculate past third grade that they are comfortable with multiplication. Learning multiplication facts is the foundation for success in advanced arithmetic as well as algebra and beyond. According to Michael Priyev, founder of New Founder of New York City's Eureka Math Tutors, students who struggle with math in “later elementary school and beyond are often missing vital foundation elements.”
While this is true for a number of math topics (addition, subtraction, division, place value, fractions etc.), in this article I will focus on helping parents and teachers with tips for helping students improve their multiplication skills.
1) Understand the basic concept of Multiplication
At its core, multiplication is simply repeated addition. In practice two multiplied by four (2 x 4) with look like this: 2 + 2 + 2 and 4 multiplied by 5 (4 x 5) looks like this: 4 + 4 + 4 + 4 + 4. If students fail to understand the fundamental concepts behind multiplication, they may have difficulty memorizing the multiplication table. This could also lead to problems in higher level math (algebra) when they encounter multiplying exponents or square roots.
2) Practice Daily
Pele, one of the world’s greatest soccer players often said, “Everything is practice.” Practice is an important skill that kids must come to embrace in their journey as math students. Teachers and parents must be the key initiator in instilling the idea of practice as an essential skill that will yield positive results, not only in math, but in all subjects. Many students that struggle with math in general do not devote enough time to studying and often believe that those that are good at math are just smart. Practicing times tables on a daily basis will lead to faster recall and better math confidence as well as higher self-esteem.
3) Learn in Small Bits
“The journey of a thousand miles starts with a single step.”
For second and third grade students mastering the multiplication table can be a daunting task. So it is important that they use the “Small Bit Theory.” This means that they should learn their times tables in small chunks. Master one section and move on. As they master their 1’s multiplication facts, they move on to the 2’s, etc. Trying to memorize too many multiplication facts at one time may lead to frustration and an overall bad experience. In later years this leads to a fear of math.
4) Point to Patterns and Special Properties
Learning patterns and unique properties of the multiplication table will make learning the times table more fun. It will lead to better memorization and recall of multiplication facts. Michael Priyev describes this approach as being savvy about numbers, "Those who excel in math …. know that 6+9=15, but that the same result can be achieved by using friendlier numbers, such as 10+5."
Here are basic properties of multiplication:
• Property of Zero - Any number times zero is zero.
• Identity property - Any number times one is that same number.
• Commutative property - Changing the order of factors does not change the product. 3 x 5 = 15 (three groups of five) and 5 x 3 = 15 (five groups of three).
• Associative property - Grouping factors in different ways does not change the product.
• Multiplying by two - the special properties of the two multiplication facts (2 times any number is always even)
• Different numbers same product - Knowing that 1 times 12 (1 x 12), 2 times 6 (2 x 6), and 3 times 4 (3 x 4) are all equal to twelve.
• Division - Multiplication is the inverse of division. 3 x 4 = 12 and 12 ÷ 3 = 4 or 12 ÷ 4 = 3.
Bonus fact about multiplication facts:
• Multiplying by 6 - When multiplying an even number by 6, the result ends in the same digit as the even number. For example, 6 x 2 = 12, 6 x 4 = 24, 6 x 6 = 36, 6 x 8 = 48, 6 x 6 = 36. Pretty cool huh!
5) Use Different Tools to Learn Multiplication
We are fortunate to live in a word where second and third grade students have many different options for learning how to multiply. Gone are the days where there was only one approach for learning your times tables. Nowadays there are a number of math strategies teachers and parents can use including traditional pencil and paper, free and paid math games and apps for mobile and desktop devices, online games, and mental math games. Using multiple math tool to learn multiplication facts will keep math instruction fresh and fun.
6) Apply Real World concepts
Anton Chekhov, a Russian playwright once said, “Knowledge is of no value unless you put it into practice.” As a kid I remember that learning the five multiplication facts was easy to learn because my friends and I often counted by 5’s to 50 when we played hide and go seek in a rhythm. This was before I even knew of the concept of multiplication. Consequently, learning my five multiplication facts in school was easy because my friends and I had used the concept of multiplication in a real world setting. Teachers and parents must find ways to show how everyday routines relate to their times tables. This may include items at a store ($4.99 x 4), figuring out miles per hour, counting money, or viewing food recipes. Just as parents read to their kids on a daily basis they must also provide opportunities to apply multiplication skills.
7) Play Games and Math Apps
Math games and apps are perfect for second and third graders. In general, kids are instantly attracted to interactivity and feedback that math games offer. Games that include characters, animation, sound, and special effect can boost a child’s interest in practicing their times tables. Quackenworth in particular, is a big believer in this approach. We currently have two math apps in the Apple App Store, Bubbletime First Grade Math and Fruit Rockets Multiplication and Division. Both of these apps include highly engaging characters, instant feedback, and are all set in a gamified environment. Fruit Rockets Multiplication makes memorizing multiplication facts easier.
Check out some game play from our Fruit Rockets Multiplication app.
Quackenworth specializes in mobile games and educational web products. Our mission is to develop fun products that teachers and parents can use to educate and enrich the lives of children and young adults.
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