
Relax. It's a math thing. I'm going to explain.
What number can you multiply by that won't change a quantity's value?
You know this--it's 1, of course.
But what if you need a quantity to stay the same but "look" different so that it will play nicely with its other little math counterparts? You need common denominators? Maybe like numerators? Rationalizing a radical expression?
You still must multiply by 1... but you choose that value of 1 to suit your needs. 10⁄10 or perhaps [3x(x+2)]⁄[3x(x+2)]. A carefully chosen value of one. Sneaky, isn't it? Math gives you the power over appearances. Choose wisely!
I suppose every math classroom develops some "language" of its own. I try to be very careful that my kids know when we're using universally accepted math language (which is most of the time) versus when we are creating our own semantics. I don't want my students leaving our cozy Ballard family to discover they've been misled for some time (like Matt and Socrates...but that should be a story in somebody else's blog and I digress from my main point).
'Adding the opposite' is universal; 'double slash' is Ballard math talk. The repeating bar, or vinculum is more or less universal (the delightful Oklahoma blogger, Sarah, at mathequalslove.blogspot.com prompted me to research vinculum); 'Jake bar' is definitely Ballard math talk. 'A carefully chosen value of one' is Dr. Debbie Bosch math talk. And I couldn't get too far into this writing adventure without giving credit where credit is due.
Dr. Debbie is a dear friend of mine. But first she was my math professor and degree advisor at Oklahoma Baptist University. Oh, the stories I could tell. Oh the stories SHE could tell! Debbie helped a sometimes-insecure, most-of-the-time-pain-in-the-backside, small-school farm girl learn that we are not created to try to shoulder everything on our own all the time (Galatians 6). She cared deeply and took the time to find out what I was about. She and college roomie Martie taught me to laugh at myself. Debbie was the paragon of support who knew when I needed a swift kick in the pants and when I needed a shoulder to cry on. She helped me temper excellence with practicality.
I love to pass on her "carefully chosen value of one" phrase because every time I do I am happy in my mind's eye to have Debbie visiting my classroom for just a moment.
There was, however, one thing that Debbie got wrong. She wanted me to go teach in a big school. Nope. God chose me for a little school. I am a department of one. "O Lord, you have searched me and known me!" (Psalm 139). I am a carefully chosen value of one.
I have the poster pictured above in my classroom. "One voice can make a song. One life can change the world." With God, all things are possible. (Matthew 19:26) I work hard to be His carefully chosen value of one for this moment in time, this spot wherever I happen to be in the world. And I often fail. Miserably. But grace and mercy are real and they keep me eager to see what's just beyond what I can see now. Come join me on the journey!