Do Your Numbers Break?

It occurred again today. I was working with a group of kids and one of them stopped me for help with his math. The problem was:

The student was stumped. He did not understand what the arrows were for, or why the 7 was suddenly a 5. I quickly explained to him that it is far easier to take 5 away from 15 than it is to take away 7. He agreed with me, but then he became stuck when I asked him how much more still needed to be taken away. He wanted to tell me that 3 and 4 make 7, but he had no reference for what would make 7 with a 5 involved. Fingers became involved, and we discovered that he still needed to take away 2 more. Thus, he eventually got to the answer of 8.

For many parents, this kind of problem causes an anxiety attack. “Why can’t it just be 15 – 7 like when we were kids? The answer is 8. Let’s move on!” After all, this is borderline “new” math, and the “old” math worked just fine. The problem is, old math did not work for many children because old math relied on memorization. What do you do when you cannot remember what 15 – 7 is? With old math, you stared into space, pretended to not care, or you did it quickly on your fingers under your desk. The best math programs move students beyond rote memorization and make sure they understand the hows and whys of math. They help kids break numbers.

How many ways can you make 8? Did you know the possibilities were endless? 8 can be 4 + 4, 1 + 7, 15 – 7, or -3 + 11. Do you see the beauty? Numbers that “break” can be made to do all kinds of things. What if I am at the store and I have to add $2.53 and $4.76 to make sure I have enough cash? Oh! The fun! I can take a quarter from $2.53 so that I have $2.28 because I like working with quarters in money. I can add it to the $4.76, and I realize that I have $5.01. I do not like that penny there, so I quickly stick it back on the $2.28 so that I now have $2.29 and $5. Just like that, I know that I have $7.29 worth of stuff to buy. I did not have to solve it that way, though. There are countless other mental possibilities that would have got me to the answer. Sometimes it is fun just to see how many you and your children can come up with!

Now I could have used the algorithm. I could have pulled out a sheet of paper, written the problem out and ended up with this:

But what if I did not have paper? Or what if the paper actually slowed me down? We lose a lot of our math brain’s flexibility when we use the algorithm.

Hear me clearly: the algorithm is important! The algorithm exists because it is the simplest, most direct way to get the right answer every time. But do you understand it? Do your kids? Do they know why that little 1 got put above the 2? Can they explain to you that it is because the 5 tens and the 7 tens gave them so many tens that they ended up with a whole new hundred? Do they have the math language?

Mastery, which is memory, is actually the lowest level of learning. Let’s take a step up the ladder to the level of understanding, and let’s play with numbers. In the process of breaking numbers, you will be amazed at the amount of memorization that naturally occurs!

(The most important part of breaking numbers is being able to make 10. I tend to chant things that I really want the kids to remember. Check out the video for my short chant on what makes 10.)

### Rachel

...a self-avowed "Wander Woman," homeschools her three children while traipsing the globe with her Army Chaplain husband. Her third greatest passion, falling below her love for God and family, is empowering other parents to teach their children.