When it comes time to introduce multiplication facts to your children do you have a plan? In What Order Should We Teach Addition Facts In?, I laid out a four step plan for introducing the addition facts. It is helpful to have a similar system for teaching multiplication facts to your children!
There are different ways you can go about teaching the multiplication facts, but the following order can be particularly useful.
Multiplying by 0 and 1, then 10 and 11
Start with the rules. Any number times 0 is 0 and any number times 1 is itself. Once your child shows understanding of that, then it is easy to teach multiples of 10 and 11. You could also teach multiples of 100, 111, 1000, 1111, etc. at this point, too.
Multiplying by 2, then 3 and 4
Next you can teach multiplying by 2 and relate this back to the doubles addition facts. If 3 + 3 is 6, then we know 3 x 2 is 6. Once your child is quick at these, you can teach him to use these facts to derive or ‘figure out’ the 3s and 4s. So if we know 4 x 2 = 8, then 4 x 3 would be just 4 more than that or 12. If we know 3 x 2 = 6, then we know 3 x 4 is going to be double that or 12. When we multiply by 4, we are really doubling a number two times. We eventually want children to memorize and recall these facts quickly and not rely on deriving them from other facts each time, but this is a great way for them to learn and practice a new set of facts.
Look how many facts you have already covered!
Using 10 to Multiply by 8 and 9
So using this plan, our children already know multiples of 10 so now let’s use those facts to derive multiples of 8 and 9. I know these tend to be the hardest in our homeschool! Ten is a “friendly number” so whenever we have a 9 fact, let’s make it 10 and then subtract the multiple from the answer. So 6 x 9 is really 6 x 10 minus 6 or 54. 3 x 9 is really 3 x 10 minus 3 or 27.
Once your child is quickly deriving the 9 facts, you could introduce the 8 facts in the same way. So if 6 x 8 can be turned into 6 x 10 minus double 6 or 6 x 8 minus 12 or 6 x 8 minus 6 and then minus 6 again.
Or you could teach the 8 facts by building off of the 4 facts if your child is really good at doubling. If 4 x 3 =12 then 8 x 3 is the same as doubling 12. The goal again is to teach your child a way to derive the facts and then practice enough to where she has the facts memorized and can recall them when needed.
Using 10 to Multiply by 5, then 6 and 7
So for 5, let’s head back to our friendly 10 as our starting place. 5 is half of 10 so all of our even 5 facts will be half of our 10 facts. 5 x 4 is half of 10 x 5 or 20. 5 x 8 is half of 10 x 8 or 40. Then for the odd 5 facts such as 5 x 3 and 5 x 5, children can be shown how these fall between the even five facts on a number line. Children are usually quick at counting by 5s to figure out their five facts, but showing some of these relationships on a number line and how they relate to 10 facts builds their number sense and moves them away from having to count.
Once your child has her five facts down, you can move on to 6 and 7 facts by relating them back to the fives. If 5 x 4 = 20, then 6 x 4 is just 4 more than that and 7 x 4 is just 4 more than that or it is 5 x 4 plus double 4 or 28. If you have a child that is into football, the 7 facts usually come pretty quickly. 5 x 7 becomes ‘if your team scores 5 touchdowns (assuming they make the extra point!) how many points do they have?’.
Now we have filled in all the facts, but a few 12 facts!
Multiplying by 12
I go back and forth as to whether I think it is important to have memorized 12 facts. My current philosophy is that they are good to memorize through 12 x 6. It is common to convert back and forth between inches and feet when figuring out someone’s height. It is also comes up when talking about a dozen of something. But unless you are a chef or party planner, I am not sure how often you will need to quickly know how many are in more than say 6 dozen! So you decide if you want to teach these or not!
This is just one system for teaching the multiplication facts. The important take away is that you should have a method to your madness. Teaching children how to derive facts from other facts leads them away from counting to determine answers and moves them closer to quick recall of their multiplication facts!
If you have any tips or tricks to the order you teach multiplication facts, I would love to hear them!