Solving for X
My daughter’s always done fine in school. Particularly in math. For years, we cruised smoothly through the basic playground of mathematics together, she and I. We hopscotched through the simple playground of Addition and Subtraction in those early elementary school years. We learned about borrowing, and understood when to carry the two. We didn’t freak out when we graduated to the grand ballroom of Multiplication and Division, which dressed numbers up in their fancier clothes and brought them together in new, swirling waltzes. Over the last couple of years, we tackled fractions, ratios, percentages, even flirted with quadratic equations. All with relative aplomb.
My level of involvement was clear: if she needed help, I would sit next to her and serve as support staff. I wouldn’t do the work for her, but sometimes I would help her figure out the first step in the equation, if needed. Just to help her get a sense of direction, or equilibrium. If she asked me some basic theoretical questions, I would provide answers that established a foundation for her process, but still enabled her to unravel the problem herself.
My skills were sufficient enough for this. I held my own. Years after the end of my own math education, I could still solve for “X” just fine, thank you very much.
But now, as we near the end of fifth grade, we find ourselves facing some challenges. Something is happening. Math is changing.
After getting home from school the other day we both sat down at the table, she with her work, me with some of my own. She pulled a sheet of paper out of her backpack, slapped it down between us and said, “I need help with math.”
“You haven’t even started yet.”
“I started them at school. They’re too hard and I need your help.”
“You’ll be fine,” I said, not looking up from my own stuff. I had student essays to grade. “Just remember to read the problem slowly. When you rush, you get frustrated. When you slow down, you usually figure it out, right?”
“I know. But these problems are different. I can’t do any of these.”
“Yes, you can.”
“Daddeeeeee, I neeeeed some help.”
“Sweetheart, you know I’m not allowed to help you with these,” I said. Which was true. Her teacher, The Diabolical Ms. V, had recently sent out a missive expressly forbidding parents to help their kids with the new sequence of math work.
“You don’t have to do them," my daughter cajoled, "just give me a hint on how to get started.”
“Just a hint?”
“Yea. Like, you tell me what the first step should be, and I’ll totally do the rest.”
She was wearing her frustrated face. Awww. She was looking to me for help. Of course she was: for for the past ten years I’ve gone to great lengths to make sure my daughter understood that I, her father, know everything. About everything.
Don’t give me that look. All dads do that.
“Ok,” I said, “let’s see what you got.”
She showed me the first problem:
The average of five numbers is 18. Let the first number be increased by 1, the second number by 2, the third number by 3, the fourth number by 4, and the fifth number by 5. What is the average of the set of increased numbers?
I read it carefully. Hmm. Ok. Averages. I remembered how to figure out averages. They don’t give the first number, but if they say if we keep adding one to each one, and… or maybe you’re supposed to start at the end and work backwards. If the average is 18, and you have five numbers, and they’re increasing by 1, and the two trains are moving towards each other at 30 miles per hour while John gives Sally 3 apples…Wait. Don't get distracted.
“Why don’t we skip the first one?” I said casually. She said ok, and we moved on to problem #2:
When a natural number is multiplied by itself, the result is a square number. Some examples of square numbers are 1, 4, 9, 16, and 25. How many square numbers are there between 1,000 and 2,000?
Huh. Is this normal for fifth grade? I don't see how... wait. What’s the deal with natural numbers? Are they just regular number numbers? So how do you figure out how many… Oh, hold on. This has something to do with square roots of things. There are 1,000 numbers between 1,000 and 2,000, if you want to pull out the square numbers you have to find the root of... No.
What the Hell was up with these math problems? I was starting to sweat.
“Just tell me the first thing to do, and I’ll take it from there,” my daughter prodded eagerly. Back off, kid, I thought.
“Let’s look at the next one,” I said weakly.
The owner of a bicycle store had a sale on bicycles (two-wheelers) and tricycles (three-wheelers). Each cycle had two pedals. When he counted the total number of pedals of the cycles, he got 50. When he counted the total number of wheels of the cycles, he got 64. How many tricycles were offered in the sale?
Ok, seriously? What the fuck is this? Whoa. Just chill, Dad. It's ok, just breathe. Breathe. This one can’t be that hard. I just have to draw a bunch of bicycles and start counting pedals. No, that's obviously not what you're supposed to do. Maybe I just have to use the total number of wheels, and divide by pi, apply the Pythagorean Bicycle Theorem and then…
“You know,” I said, sitting back, “if I help you get these started, you won’t learn how to do it yourself. You really need to figure these out on your own.”
She looked up at me with skeptical eyes. Did she suspect? Did she know what had just happened? That we’d just crossed the threshold that had been slowly approaching for years? Had we finally reached the event horizon, the day when my daughter had to solve math problems that her father was too simple-minded to do? Was it time to confess to my daughter that her dad is, in fact, nothing more than a Math Doofus? And would that mark the end of my role as authority figure, advice giver, sage, prophet, Guy With All the Answers To Everything?
She looked back down at her problem sheet, brow furrowed. A moment passed. Then another.
Then her face brightened. “Oh, wait. I totally know how to do the first one.” And she hunkered and started scrawling her answer with enthusiasm. “It’s so easy!”
Whew. I patted her on the back, knowing I'd just dodged a major bullet.
"Good job, kiddo," I said, feeling eight kinds of relief. "See? I knew you could do it. Aren't you glad I didn't help?"
She pushed her paper back over to me. "Will you check my answer?"