Looking for the best order for teaching multiplication facts? You’re in the right place!
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Why not teach the facts in order from 0-12?
We’re going for understanding, not just memorization. It makes sense to choose a particular order, because that will let us start with the simpler facts first and help our students build on the knowledge they already have as they learn each new set of facts.
Teach the foundational facts first
Start with x2.
I know, I know. Most people will tell you to start with x1 or x0, because they’re the easiest to memorize.
The reason I recommend starting with x2 is because we want to start with the concept of multiplication. Kids have experience with doubling and grouping in pairs, so it makes sense to start with x2.
Next, teach x10.
10 is a foundational number that students have a lot of experience with. They know how to skip count by 10, group in tens, and work with base ten blocks.
Continue with x5.
Students know how to skip count by 5. And now that they know how to multiply by 10, we can teach them that multiplying by 5 is half of multiplying by 10.
NOW teach x1 and x0.
Yes, it’s easy to memorize these facts, but they can be difficult to visualize. Now that your students have a conceptual understanding of multiplication, it’s a good time to teach x1 and x0.
Move on to the derived facts
Teach x11.
Multipying by 11 is the same as multiplying by 10 and adding one group. You can also teach the shortcut of writing the factor twice, but this only works for multiplying 11 by 1-9.
If students are multiplying 10 x 11, they can think of it as 10 x 10 (100) and then add one more group of 10. 10 x 11 = 110
Next comes x3.
Teach this fact by helping your learners understand that multiplying by 3 is like tripling a number. Teach them the shortcut of doubling the other factor and adding one more group.
For 4 x 3, they can double the 4 (to get 8) and then add one more group of 4. 8 + 4 = 12.
Move on to x4.
Multiplying by 4 is like doubling the product of a the x2 fact.
Teach x6.
I like the shortcut of multiplying by 5 and adding one more group.
If a child is doing 7 x 6, she can first think about 7 x 5, which equals 35. Add one more group of 7, and you get an answer of 42.
See how it helps to know those foundational facts first?
Now teach x9.
There are a lot of tricks for teaching the x9 facts. If you want to simply build on previously learned facts, just teach students to multiply by 10 and subtract one group.
If a learner is doing 8 x 9, he can think about 8 x 10, which equals 80, and subtract one group of 8 to get 8 x 9 = 72.
There’s a really cool trick to help students multiply by 9. Lead them to see that each two-digit answer to a x9 fact has two digits that add up to 9.
For example, 3 x 9 = 27 (2 + 7 = 9)
To use this trick when solving a fact, they need to take the factor that isn’t 9, decrease it by 1, and put that number at the start of the answer.
4 x 9 = 3_
For the second digit, they choose the number that, when added to the first digit, will equal 9.
So 4 x 9 = 36
(For all the tips for teaching x9, check out this post by Shelly Gray Teaching.)
Teach x8.
If your students know their 4’s facts, they just need to double multiplication by 4.
For 5 x 8, they can start with 5 x 4 = 20, and then double that answer to get 40.
Next comes x7.
These aren’t the simplest facts, but if your students have learned all the other facts in the order I recommend, they only have a couple left.
A great mental math strategy for x7 is to multiply by 5 and add a double.
For example, for 6 x 7 the students can multiply 6 x 5 to get 30. Adding a double (of 6) would mean that 30 +12 = 42, so 6 x 7 = 42.
Last is x12.
We’ve reached the end! Students only have one fact left to learn: 12 x 12 = 144.
Hurray!
But if they need a mental math strategy for the x12 facts, teach your students to multiply by 10 and add a double
With 8 x 12, they can multiply 8 x 10 first, to get 80. If they add a double of 8 to the answer, they will get 80 + 16 = 96. Therefore, 8 x 12 = 96.
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Jeff C Chalfant
I agree with ALMOST everything. But why even bother teaching the 11’s and 12’s? That is an outdated construct. Teaching through 10 makes sense (we have a base-10 number system), but other than that the utility of knowing all SINGLE-digit multiplication and division facts is the priority for future multi-digit multiplication/division. Maybe there is something I am not considering . . . let me know.
Anna G
I definitely don’t think it’s a must, but I think that knowing an extra set of facts by memory makes mental math (and thus, problem solving) easier.
Sarah
Haha. I JUST told my friend the same thing. If I went and quizzes all the adults in my neighborhood, I bet most would fail at reciting them.
V Dean
Always start with the number you are teaching. If you are teaching the 3s, you should start with 3 as in 3 x 4, 3 x 5, etc. as in 3 groups of 4, 3 groups of 5, etc. Then your method to double the 4 or 5 makes more sense. The same with other numbers. 6 x 7 is 6 groups of 7. 7 x 8 is 7 groups of 8. The order in which the fact is stated matters.