I did not create the following information, but it is important so I have copied the text from Math Resources website.
The basic number facts are among the tools that students need to be successful in their mathematics program. In the past, students memorized the facts once they had been introduced to Multiplication as a faster method of addition.
Now it is recommended that students learn patterns and strategies for as many facts as possible so that they strengthen their understanding of the relationships between numbers and the patterns in mathematics. Then they begin to memorize. There are many strategies out there. Here are some that have been successful with many students.
Before these strategies are taught, students must gain a complete understanding of the concept of multiplication. They should actually make groups of things and relate these groups to the number facts. They should skip count and make arrays to gain a complete understanding of multiplication.
Multiply by zero
If you have zero groups of anything you have nothing. It is fun to teach this by offering several different groups of zero to students.
“Here, you can have zero Smarties. How many did you get? zero
Work through several examples. The idea is that it doesn’t matter how many numbers are in a set or group, if you have zero sets you have nothing. So 1 x 0 is 0 one group of zero and 0 x 1 = 0 zero groups of one = zero
Once students understand this they will never have to practice it.
Commutative Property (Turn around facts)
Students may as well learn this right away. If you have 2 groups of zero or zero groups of two, you have the same amount. Work through several examples with zero to be sure that students understand. Then, review this with all the other strategies as all facts have a turn around fact.
Multiplying by one
Again this is a concept that students need only to understand and then they will always know the one times facts. One times any number means one group of that number which is the same number.
1 x 6 is one group of six = six
Turn around fact; 6 groups of one = 6 x 1 = 6
If students do lots of examples to gain this understanding, they will not have to practice this.
Multiply by Two
This is just double numbers, which they should already be familiar with.
For example: 2 x 8 = 8 + 8 = 16
It would take a couple of lessons to work through examples where you relate the two ideas and give students a chance to practice. Then they should be able to use this strategy.
Multiply by Ten
A hundreds board works great for this as do base ten rods. Students need to make groups of tens. They will see the pattern fairly quickly but they need to see the number pattern of increasing by ten as well as the “adding zero” factor. Once they explore with groups of ten then they can use the rule of adding zero to multiply 10 by any number. Again, they should review the turn around fact as well.
Two groups of ten = 20 10 groups of 2 = 20
Multiply by five
Counting by fives is a common factor in our society so multiplying by fives can fit right in here. Use a clock to introduce the five times table.
We talk about 5 after, ten after, fifteen after – so this is one group of five, two groups of five, etc.
Have students count by fives and review the zero – five pattern 5, 10, 15, 20 (ends in zero, ends in five).
Work with examples like these to help children find patterns in the five times table and then remind them of the turn around facts.
Multiplying by 9
There are several ways to help students with this but the neatest one is that there is a nifty pattern to the nines. If students look at some examples: one group of nine is 9. Two groups of nine is 18, three groups of nine is 27 they can see that the answer adds up to nine and the tens digit is one less than the factor the nine is being multiplied by. Correspondingly the last digit, when added to the factor makes ten.
For example:
4 x 9 – the first digit is one less than 4 (the factor) and the
last digit will add up to 9 if added to the first digit. Also, the factor 4 and the last digit will add up to ten.
It is confusing until you try it out several times and then the pattern appears much more simple.
Those are some basic strategies that along with the turn around strategies help give students a solid base on which to build their multiplication facts. The Nelson program also teaches students to build new facts from known facts.
For example: If a child knows 5 x 3 = 15 they can figure out 6 x 3 = 18 (one more group of 3)
If a child knows 6 x 7 = 42 then 7 x 7 = one more group of seven = 49
Halving strategies
This can be used on facts with 5’s and 10’s.
If a child knows 8 x 5 = 40 she can halve and double to find 4 x 10 = 40. (half of 4 and double 5)
Another example; 4 x 5 = 20 half and double 2 x 10 = 20.
Multiplying by eleven
It quickly becomes very obvious that multiplying by 11 follows an easy pattern. If students do some examples 2 x 11 = 22, 8 x 11 = 88 etc. they soon see that it is taking the original number and multiplying it by ten and then itself. Make sure they understand the p
attern and then let them practice with other numbers. Again this pattern never changes.
Number Neighbours
A child who doesn’t know 7 x 6 = might know 6 x 6 = If so they can just add one more 6.
A child may not know 5 x 6 but they might know 5 x 5 so they can just add one more five.
Multiplication Table (lines crossed out represent use of strategies instead of memorization) The strategies we have discussed should have eliminated the need to memorize most of the facts.
On the chart above, all the facts that can be taught using a strategy, are covered, leaving only the facts that need to be drilled highlighted in blue.
Taken from http://olc.spsd.sk.ca/de/math1-3/p-mentalmath.html#basicmult