The Secret of Learning the Multiplication Facts
This is a guest post written by Dr Lynne Gregorio who runs the Apex Learning Website and Learning Center.
Multiplication facts are essential for every student.
As students move forward in mathematics into high school and college math, they will rely heavily on their multiplication and division facts. Students start to learn these facts around the age of 7 and it can be a challenge for some. Many teachers simply suggest that students “memorize” all the facts. This is challenging and many children are unable to do this.
The multiplication facts strategy
Eventually we hope that students will just “know” their facts, but when first learning multiplication facts, it is best to teach students strategies for finding the facts, so that they always have a way to find the fact if they forget it.
It also makes them quicker to learn.
Teaching facts should be taught in a particular order, so that the student doesn’t get frustrated, and so that they can rely on their “partner fact” (3X4=4X3) for some of the harder facts.
Before multiplication facts
Before starting, let me stress a prerequisite that must be accomplished before starting multiplication. Students must be adept at addition without counting on their fingers prior to starting multiplication. Specifically, they need to know their doubles.
If you say, 8 + 8, they should immediately know the answer is 16. 9 + 9 = 18. If these doubles are not automatic, start drilling these and then come back to multiplication.
You will also want your child to be able to double twice for the X4 facts, so they should be able to do problems like 14 + 14 and 16 + 16 in their head. The 16 +16 is a harder one since it requires you to carry, I accomplished this one with a song that goes like this: “2 and 2 is 4, 4 and 4 is 8, 8 and 8 is 16; 16 and 16 is 32.”
Use a sing-song voice and the kids learn these doubles quickly including the hard one 16 + 16 = 32!
Some multiplication facts to get you started
Here are some methods for each fact:
X0 Fact: Anything X0 is 0. This is a very easy fact since students just need to learn that anything times 0 is 0. Remind them that 0 sets of something is 0.
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X1 Fact: Anything X1 is itself. Again, another very easy fact. For example, 1 X 7, this means 1 set of 7, which is just 7 items.
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X2 Fact: Circle the number that is not 2, double that number. Since the student is good at doubling, this is an easy fact.
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X4 Fact: Circle the number that is not 4, double the number and double again. The student should have doubling down well before starting, so X4 facts will come very easily to them. The only one that might be difficult is X9 – tell them that they can wait and use the “9’s trick” on that one instead of the 4’s trick if they don’t know 18 + 18 since we didn’t really drill that double.
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Find the complete list of multiplication facts at the Apex-Learning website.
The Multiplication Facts Chart
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | Double | Double | Double | Double | Double | Double | Double | Double | Add Zero |
| 3 | Double | Count by 3’s | Double Double Again | Count by 5’s | Double 6 + 6 | Double 7 + 7 | Double 3 times | Nines Trick | Add Zero |
| 4 | Double | Double Double Again | Double Double Again | Double Double Again | Double Double Again | Double Double Again | Double Double Again | Double Double Again | Add Zero |
| 5 | Double | Count by 5’s | Double Double Again | Count by 5’s | Count by 5’s | Count by 5’s | Count by 5’s | Nines Trick | Add Zero |
| 6 | Double | Double 6 + 6 | Double Double Again | Count by 5’s | Rhythm | Memorize | Rhythm | Nines Trick | Add Zero |
| 7 | Double | Double 7 + 7 | Double Double Again | Count by 5’s | Repeat | Memorize | 5678 | Nines Trick | Add Zero |
| 8 | Double | Double 3 times | Double Double Again | Count by 5’s | Rhythm | 5678 | Rhyme | Nines Trick | Add Zero |
| 9 | Double | Nines Trick | Double Double Again | Nines Trick | Nines Trick | Nines Trick | Nines Trick | Nines Trick | Add Zero |
| 10 | Double | Add Zero | Add Zero | Add Zero | Add Zero | Add Zero | Add Zero | Add Zero | Add Zero |
If you look at the above chart, the only one’s that requires total memorization with no help at all are 6 X 7 and 7 X 7.
Once students get a handle on multiplication facts they can start looking at the concepts of divisibility and division.
Dr. Lynne Gregorio’s Apex-Math website offers additional articles and great value workbooks, games, and practice for students to explore multiplication concepts in greater depth; in a progressive manner; and without being overwhelmed with too many concepts at one time. Visit the website and see how she can help!
Share your multiplication facts ideas in the comments below!
I agree that a working-out strategy is good to have. One I find that really works is to give “goal posts”, for lack of a better term.
Most kids have no problem learning their 2x, 5x, and 10x tables; to a degree, even 9x and 11x.
So, when stuck, I say use those and move either forward or backward by adding or subtracting. This drills them in addition and subtraction, too. For example, if you don’t know 7×8, you can start from 7×10 and -7 twice. Or, if the kid is struggling with subtraction then start with 7×5 and +7 three more times. Sometimes I even throw in the concept of range – it’ll be between the x5 and x10 result.
This strategy also reinforces the concept of multiplication as repeated addition – good mathematical foundation. Also, estimation.
Malyn,
I agree. It’s always good for kids to have back up strategies for when they forget facts and especially good for kids to have the concepts that link multiplication to repeated addition.
These are some great strategies. I wish they had these strategies when I was struggling to learn my multiplication facts 30 years ago. Having a strategy is very beneficial to the student and lessens the frustration. Thanks for sharing!