Multiplying by 9

Intended Audience: Teachers and Parents of K-5 students.

In this video, 6-year-old Autumn shows how easy it is to multiply by 9. Watch her multiply 18×9 in her head and explain how she did it!

Parents and teachers may also want to watch Autumn’s and my 3-part video series on learning how to multiply along with this video (Part I, Part II, Part III). In the 3-part series, Autumn shows the basics of learning to skip count while keeping track of the number of skip counts on her fingers. This method helps young children learn what multiplication means and gives them a way to confidently find products of two numbers where one of the numbers is 2, 3, 4, 5, and 10. That, together with the commutative property (i.e., 6×7 is the same as 7×6), leaves the following products:

6×6, 6×7, 6×8, 6×9, 7×7, 7×8, 7×9, 8×8, 8×9, 9×9.

This list can be reduced to just 6 facts by learning how to multiply by 9, i.e., the content of this video. The multiplication by 9 method in this video can be easily seen using unit math: 9×7 means finding “9 sevens.” But just as “9 apples = 10 apples – 1 apple,” the same holds for sevens:

9 sevens = 10 sevens – 1 seven.

Of course, 10 sevens = 70 is easy, so 9×7 = 70 – 7.

As you watch Autumn, note that an important prerequisite to this technique is how to take away a 1-digit number from a multiple of 10, for example, 70-7, 80-8, 90-9, etc. This skill in turn comes out of learning to work with “10 combinations,” i.e., 2 and 8 make 10, 3 and 7 make 10, 4 and 6 make 10, etc. All of these prerequisite skills are learned and practiced in the Eureka Math/EngageNY math curriculum in grades K-2 using joyful mental math/counting activities and number bonds (take a look!).

With multiplication by 9 understood, that only leaves the six “most troublesome” facts:

6×6, 6×7, 6×8, 7×7, 7×8, 8×8.

You can watch Autumn explain in another video how to find some of these products just knowing that “6×7=42” by following this link.

Finally, it should be said unequivocally that the goal is for children to learn their multiplication table from 0x0 to 10×10 so that they no longer need to think about how to derive the answer each time–that they fluently recall each fact from memory without thinking. The process outlined in these videos, if practiced regularly, will lead to that instant recall over time (be patient). But, and this is important, the process also helps children to think flexibly about numbers in general (while practicing addition/subtraction). For example, Autumn was able to apply the same technique to 18×9 in the video where she had to find 180-18 in her head—just finding 180-18 is a sizable task for a first grader. That flexibility and number sense will help your children as they starting working with letters in Algebra just a few years later, where that flexibility is required, even demanded.

As always, comments are welcomed. Also, please share on twitter/Facebook/etc.