“Nope.”
“We need to make a number line.”
“I stopped making number lines in sixth grade, Kath.”
“Well, humor me. Get some notebook paper and draw some vertical lines so we have graph paper.”
“Okay.” He complied. “Why are we doing this again?”
“Because I don’t know the answer to your question.”
“You don’t?”
“No.”
“How can you be so good at math, then?”
“Because I learn the rules. I follow them. I get the right answer. I don’t have to understand why.”
“Wow. I never would have thought…”
“Well, I never would have thought you’d care about why the rules of math are what they are. I’d have thought you just wanted to get your C and play baseball.”
“I do.”
“Don’t worry. You will, with me tutoring you.”
He smiled. “I know.”
“So you got your graph paper ready?”
“Yup.” He handed it to her. Kathryn quickly wrote out a number line starting in the middle with zero and going horizontally and vertically into positive and negative integers.
“Okay. Now, what is your exact question?”
“Well, positive numbers are numbers greater than zero, right?”
“Yeah.”
“And negative numbers are less than zero.”
“Right.”
“When you add two positives together, you get a positive.”
“Yup.”
“And when you add two negatives you get a negative.”
“You got it so far.”
“It makes sense so far. When you multiply two positives you get a positive. I don’t get why you wouldn’t get a negative when you multiply two negatives. I mean, when you think about it, multiplying is just adding, only adding more than once, you know? So if you get negative when you add two negatives, why don’t you get negative when you multiply two negatives?”
Wow. Impressive. He’d really thought this out. Determination gripped her. She’d find the answer for him. Clearly, he understood the concepts of addition and multiplication and how they were related. There had to be a reason for this stupid rule. There just had to be.
“Okay, let’s look at two times two.” Kathryn drew a line two blocks to the right horizontally from zero, and two blocks upward vertically from zero. “If we tie these together with coordinates, we get a volume of four on the graph, see?”
“Yeah.”