Multiplying by 25

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

Autumn is now 7 years old! Thank you to everyone out there who has been watching her grow up.  We have many more great videos planned for this year, so please like us on Facebook (www.fb.com/ScottJBaldridge) or follow us @ScottBaldridge, or follow this blog for updates.

In this video, 7-year-old Autumn shows how to quickly and easily it is to multiply by 25.  The idea is simple.  To multiply $36 \times 25$,

1. Divide $36$ by $4$ to rewrite it as the product $36=9\times 4$.

2. Use the Associative Property to group the product of 4 and 25 to get 100,

$36 \times 25 = (9\times 4) \times 25 = 9 \times (4\times 25) = 9 \times 100$.

3. The answer is 9 hundreds, or 900!

The key to using this method, of course, is to understand the Associate Property:

$(a \times b) \times c = a \times (b \times c)$ for any three numbers $a, b, c$.

I am often asked, “Why do we need to teach our children `multiple ways’ to solve a problem?  We should just teach them the column multiplication algorithm like I learned when I was a child.”

There is so much packed into a question like this—it would take several articles to fully explain my position on this question, including why it is so important for students to be fluent with the column multiplication algorithm that we remember from our childhood (cf. the article Fluency without Equivocation for example).

Here’s the short answer:  I designed Eureka/EngageNY Math to cover a different method or strategy primarily when that strategy was important preparation for later topics in mathematics and science.  So while I strongly want all children to be fluent in the column multiplication algorithm (and designed Eureka Math to facilitate that fluency), I also want them to see many numerical examples of the Associative Property because it plays a quintessential role in learning algebra.

We can handicap our students if they don’t see interesting (and amazing) numerical examples of the Associative Property before they see it in it’s “letters only” version in their Algebra courses.  In fact, this may be one of the reasons so many of us adults had trouble with mathematics in middle and high school where algebra is taught.  Let’s try not to make the same mistake with our children that our teachers (unknowingly) made with us.

CHANNEL: Growing up with Eureka
© 2015 Autumn Baldridge and Scott Baldridge
Partially supported by NSF CAREER grant DMS-0748636