A Math Hack That Isn’t a Hack

Transcript

Welcome fellow Recovering Traditionalists to Episode 179: A Math Hack That Isn’t a Hack

I came across a video on Instagram this week sharing what they called a “mind-blowing math hack.”  Now I’ll be honest and say this idea wasn’t new to me but it was something I learned as an adult, not as a student.  So if you’ve never thought about this math concept in this way, it does seem ‘mind-blowing’ when you first learn it but it’s not a hack or trick.  It’s rooted in a property of mathematics and everyone should know about it and understand why it works.

So here’s the idea…

In a problem like 16% of 25 most of us learned that we turn that percentage to a decimal and that ‘of’ means to multiply.  So that problem is .16 x 25.  Or you might have learned to do 16 x 25 then divide by 100…either way works.  

However, did you also know that you could flip the numbers around and instead of doing 16% of 25 you can think about it as 25% of 16?  And 25% of 16 means you take a ¼ of 16…which is 4 and way easy to do in your head.

Two things to note:

1. This will ALWAYS work.  Because multiplication is commutative.  The order in which you multiply the numbers does not matter.  We all know that you can do 9 x 5 or 5 x 9, but many of us haven’t had experiences applying that no matter what types of numbers you are multiplying.  
2. Even though this always works, it doesn’t make sense to use it all the time.  There are some hacks or tricks that only mathematically work some of the time and so we discourage the use of them because they are just tricks that stop working.  For example, the multiplying by 9s trick where you teach students to use their fingers…yeah that only works for multiplying 9 by single digits.  It doesn’t work when you have to do 9 x17. With this ‘hack’, the idea will always work, you can always flip the numbers around and you will get the same answer…but you may not want to.

Let’s take a look at a couple of examples.  If the problem was 27% of 315, we would get the same answer if we flipped it and did 315% of 27…but should we?  Does that really help us out at all???  

How about if you needed to find 27% of 50?  Thinking about it as 50% of 27 would be more helpful.

I guess with this episode, I want you to think about the math hacks or tricks you see or maybe even teach your students and really dive in to see if it’s just a trick (i.e. if it stops working) or if it is based on solid mathematical ideas.  If it’s based on solid mathematical ideas, then spend time investigating it with your students.  Have them investigate and find out if it will always work. And then should we always use it?  If not, when does it make sense to use it?

And my final thought on this video was that it was a reminder of how often mathematical ideas do NOT get connected for students.  This hack seems mind-blowing because problems where you are finding Percent Of were not connected to the basic ideas of multiplication for you.  In every math concept we should be helping students see how it connects to the mathematical concepts they already know.  The more connections we can help students build, the more mathematics makes sense and isn’t seen as magical tricks and hacks.

Alright my fellow Recovering Traditionalists, until next week keep building math minds!