Learning Division Facts: Numbers that are Products of Two 1-digit Numbers

Intended Audience: Teachers, prospective teachers, and parents (public, private, homeschool).

In this video, 7-year-old Autumn tells whether a number from 1-100 is the product of two 1-digit numbers. This is an important step along the way of using the multiplication table to learn the division facts.

So your students know their 1-digit multiplication facts, i.e., they know the complete multiplication table. This should mean that all you need to do is teach them that division is the inverse of multiplication and then they will know all their 1-digit division facts. Not so fast!

It is true that multiplication and division should be learned in tandem: As students are asked, “What are 5 sixes?” ( $5\times 6 =30$ ), they should also be asked, “How many sixes are there in 30?” ( $30\div 6 = 5$ ). This back-and-forth between multiplication and division is important for linking the two concepts together. And what an important link! Division is not a separate coin from multiplication but just the other side of the same coin. Building this relationship will make it far easier to learn fraction division later as well as smooth the way to learning algebra in middle school.

An immediate benefit of this link is that it greatly reduces the “memorization” that your students have to do to learn the 1-digit division facts. (It’s like throwing out all of the division cards out of the deck of multiplication and division flashcards, which effectively halves the amount of fluency work your students need to do.)

But knowing the multiplication table AND the relationship between multiplication and division does not necessarily mean your students will automatically know the division table. Just because they know that $6\times 7 = 42$ doesn’t mean they can “undo” this fact to get $42\div 7 = 6.$ The problem appears to be in recognizing which numbers between 1 and 100 are products of 1-digit numbers: Given $6$ and $7$ , students learn different strategies to combine them to get a result, namely $42$ . But recognizing that $42$ is an important number that can be factored into the product of $6$ and $7$ is a different process. It can be practiced as a separate skill, as Autumn and I show in the video above (when we factor $63$ ).

One of the goals of the activity in the video is for students to recognize the important integers between 1 and 100 that are products of two 1-digit numbers:

$1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27,$
$28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63, 64, 72, 81$

It should also be noted that it is important for children to recognize which integers between 1 and 100 are NOT products of two 1-digit numbers (like $43$ or even $39$ , which factors into $3$ and $13$ ). We cover this in the video as well. This is similar to how important it is to teach young children to “identify the spaces” between words in a sentence in order to identify the words in the sentence. I learned this learning-to-read fact from Melanie Gutierrez, who is an awesome Kindergarten master teacher who worked on Eureka Math’s Kindergarten year with Robin Ramos, Ben McCarty, and me. You can see some of the same type of thinking in Eureka’s early grades when teachers ask students to say the number of blank spaces in a 10 frame—not just the number of black dots—like the $3$ blanks in the 10 frame below:

If you just found my website and this is the first article you have read, you may be wondering, “How did 7-year old Autumn get to this point already?” I encourage and invite you to watch the following videos in this order:

Learning to Multiply, Part I
Learning to Multiply, Part II
Learning to Multiply, Part III
Multiplying by 9
Autumn Multiplying 6×7, 7×7, 8×7, etc.
But Honey, You do know the Multiplication Table!
And the video above, of course.

These videos will get you started with the basics of teaching multiplication using Eureka Math with your students. If you are parents, they also provide some great activities you can try at home. Parents–these videos show ways to cut out all those flash cards and get to a point where you and your child can have a tear-free discussion about mathematics. Here is a nice video that shows what that interaction can look like.

Hey, by the way, I’m wearing another female superhero T-shirt in this video! This T-shirt is the black widow from the Avengers. If you have another great female superhero T-shirt to share with us, go to our Woman Superhero T-Shirt Challenge page and leave your idea in the comment section. Thank you!

As always, comments are welcomed.

CHANNEL: Growing up with Eureka
© 2016 Autumn Baldridge and Scott Baldridge
Partially supported by NSF CAREER grant DMS-0748636