Growing up with Eureka: Multiplying by 9

In this video, 6-year-old Autumn shows how easy it is to multiply by 9. Watch her multiply 18x9 in her head and explain how she did it!

Parents and teachers may also want to watch our 3-part video series on learning how to multiply along with this video.

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 leaves the following products:

6x6, 6x7, 6x8, 6x9, 7x7, 7x8, 7x9, 8x8, 8x9, 9x9.

This list can be reduced to just 6 facts by learning how to multiply by 9, i.e., the content of this video. 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 a lot work learning "complements of 10," 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 (take a look!).

With multiplication by 9 understood, that only leaves the "tricky six" facts left: 6x6, 6x7, 6x8, 7x7, 7x8, 8x8. You see Autumn explain how to find some of these products just knowing that "6x7=42" in the video:

Finally, it should be said unequivocally that the goal is for your children to learn their multiplication table from 0x0 to 10x10 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. But, and this is important, the process also helps your children to think flexibly about numbers in general (while practicing their addition/subtraction facts). For example, Autumn was able to apply the same technique to 18x9 in the video where she had to find 180-18 in her head. That flexibility and number sense will help your children as they starting working with letters in Algebra, where that flexibility is required, even demanded.

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