Yesterday he reminded me that I owe him $100 for rent. We help him with his rent while he’s in college and he was able to sub-let his room for the summer for a fraction of what he usually pays.
“Just add it to what I already owe you,” I told him. About five seconds later he said, “Okay, that’s 6 hours and 40 minutes of work.”
Now, I do not subscribe to the idea that the faster someone can do math, the smarter they are. Math is not about speed. It’s about thinking. But that said, I was pretty impressed with how quickly he came up with the number of hours and minutes he needed to earn $100. So I asked him how he figured it out so quickly.
“I get $15 an hour. So $15 times 6 hours is $90. I had $10 left so I had to figure out how many minutes $10 of $15 per hour is so I thought how long it would take to make $10. 10 divided by 15 simplified is 2/3. And 2/3 of 60 minutes is 40 minutes. So, $100 is 6 hours and 40 minutes of work.”
I so badly wanted to be in a classroom and have him explain to the group how he solved the problem. This is exactly the type of thinking and sharing out that is encouraged in the Common Core and NCTM* Standards.
But that’s not what this newsletter is about. It’s about what happened next.
My son continued, “I found this really cool app called Math Tricks. I have to solve problems in a certain amount of time. But what I really like about it is that it shows me tricks that can help.”
He pulled it up on his cell phone and solved a problem within seconds. 111 x 105 = 11655. “Look, here’s how it works. Subtract 100 from 111 and add the 11 to 105 to get 116. Add two zeros after 116 to get 11600. Then multiply the 11 by the 5 and add the result to get the final answer of 11655.” He then showed me how he learned the “trick” by accessing the training mode where the trick is described.
So this started an argument, uh, discussion on math “tricks”. I insisted they not be called tricks. These tricks, I told him, are not tricks. A trick is intended to create mystery and that’s exactly what we don’t want to do in math. These are strategies based on mathematical structure (MP7). Some of them may be pretty complicated and difficult to understand but, regardless, they’re not tricks.
“Well, it doesn’t make sense but it works. It’s not like I really know what I’m doing but I know how to get the answer,” he argued.
So to illustrate my point I showed him how he could find the answer to 5 + 7 by simply finding the number in between 5 and 7 and doubling it. In other words, 6 – the number in between 5 and 7 – doubled is 12 so the answer to 5 + 7 is 12. A young child may call this a trick because they simply haven’t had the experience yet in working with numbers. But it can be easily modeled by taking 5 beans on one side and 7 beans on the other side, moving one bean from the 7 over to the 5 side so both sides have 6. So now it’s easy to see how this “trick” works.
He seemed impressed but I wasn’t done. “Let’s take 8 times 6,” I told him. “If you can’t remember 8 x 6, but you do know 4 x 6 then how about breaking it up into (4 x 6) + (4 x 6). Is that a trick or a strategy?” I was about to gather my inch tiles so I could create an array to prove that it would work when he acquiesced.
What I find so exciting about the Common Core State Standards in Mathematics is the push towards getting our students to understand – really understand – the math they are doing. When this happens, math will no longer be full of tricks. Students will begin to develop confidence in their ability to do math and we’ll move away from generations of I’m not good at math to generations of I can do math. And part of that comes from taking away the math tricks and replacing them with the math strategies they are.
I am happy to say that none of our Family Math Night kits include tricks. Just lots of fun. So if you haven’t calendared your Family Math Night event, there’s still time. As you know, our number one priority is to help you host the best event of the school year!