October 2, 2014

Teaching Multiplication Facts

Teaching Multiplication Facts

Multiplication facts are part of the North Carolina Standard Course of Study curriculum for the third grade.   Eventually we hope that students will just "know" their facts - in other words, they are memorized but when first learning facts, it is best to teach students strategies for finding facts.  This allows students to always have a fall back plan in case they "forget" the fact and it makes them quicker to learn. The order in which facts should be taught is given below.  The reason for this is that the easier ones get learned first and then they can rely on their "partner fact" (3X4=4X3) for some of the harder facts.

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 very 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 easy 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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X10 Fact: Add 0 to the number that is multiplied by 10.

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X5 Fact: There are two strategies that work here.  Lots of kids like to just count by 5’s because they are good at it.  That takes longer when they are counting by 5 eight times for numbers like 5 X 8.  For these bigger numbers (especially the even ones) they can try this other strategy:   multiply the number times 10 (see 10 fact) and then take half of that number:  so for 5 X 8 we would do 10 X 8 = 80 then take half = 40.

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X11 Fact: Circle the number that is not 11, write the number twice – 11 X 3 = 33.

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X9 Fact: Use the finger trick – hold up all ten fingers, count from the left and bend down the finger of the number you are multiplying by 9. For example, for 9X3, bend down your third finger. Now count the number of fingers on the left side of the bent finger, write that number down – then count the number of fingers on the right side of the bent finger, that is your second digit. With the 9X3 example, you have 2 fingers to the left of the bent finger and 7 fingers on the right side of the bent finger, the answer is therefore 27.  Also show your child all the different patterns in the 9’s.  The sum of the digits of all the 9 facts add to be 9.  The tens place of the 9’s facts is always 1 less than the number you are multiplying by:  if you multiply 9 X 6 then you know that your answer is going to be Fifty – something since 5 is one less than 6.

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X3 Fact: This is where we get the harder ones – students should know the commutative property and therefore only need to learn: 3X3, 3X6, 3X7 and 3X8. There is no good trick for these, tell the child to double the number and add one more. 3X3 = (double 3) + 3 = 6 + 3; 3X7 = (double 7) + 7 = 14 + 7 = 21.  They can also learn to count by 3′s.

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X6 Fact: With the commutative property, you will only need to learn 6X6, 6X7, and 6X8. 6X6=36 and 6X8 can be taught using rhythm (tap them out on the table as you say them).

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X7 Fact: For this group, you will need to learn 7X7 and 7X8. To memorize 7 X 8, I use the visual:  5 6 7 8 these numbers go in order of counting and you can just put = and x in the middle and get your fact 56 = 7 x 8. Help your child see this visual and use it as a cue to help them to remember the fact.  7 X 7 = 49 – sorry, just got to memorize that one.

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X8 Fact: You only need to learn 8X8=64. You can use “bend down touch the floor, eight times eight is 64” or “Skate X Skate = Sticky Floor.”  You can also do “double, double, double if the student can double 3X.  This triple double works really well for 8 X 3 as it is a harder 8 fact but is easy to double 3X.  Double 3 gets to 6, double 6 gets to 12, double 12 gets to 24.

You will want to work on 1 fact at a time, do lots of practice with that fact before moving to the next one. Once you move to the second fact, you should work on that alone and then provide a mix of that with all previously learned facts, and so on.

TABLE of FACTS - shows strategies for each of the different facts:

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
    ANY CHARACTER HERE

You will want to work on 1 fact at a time, do lots of practice with that fact before moving to the next one. Once you move to the second fact, you should work on that alone and then provide a mix of that with all previously learned facts, and so on.  Note that the facts above are written in the order in which they should be taught.  Don't teach them in numerical order but instead from easiest to hardest so that students can use the commutative property to their advantage and have a feeling of accomplishment.

We are getting ready to launch our Online Multiplication Curriculum. This online program will be interactive and affordable. It will teach your child each strategy mentioned and give them practice with instant feedback using the strategies. We hope to post it on our site soon but for those who can't wait, feel free to contact us about our pre-release version.

About lynne

Apex-Math was started by Dr. Lynne Gregorio. Lynne has been working in the field of mathematics education since 1989. She received a Ph.D. in Mathematics Education from North Carolina State University in 1998. She has taught everyone from Pre-K students to doctoral students. She runs the Apex Learning Center in North Carolina where she tutors students in reading, spelling, writing, and mathematics. She has recently started developing curriculum so that she can reach a broader range of students across the nation. She is married and has 4 children. She is currently homeschooling her oldest son for his senior year of high school.

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