Graphs help us understand the real world. My granddaughter Anna was doing her seventh grade science homework. At the same time she was fielding calls and texts about her 13th birthday party this weekend. For the first time, over half the friends she has invited are BOYS. In between the interruptions, I asked her if she understood the terms independent variable and dependent variable.
I did my best to explain that the independent variable is the quantity that YOU select--or that exists regardless of whatever else is going on (for example, TIME). The dependent variable is a quantity that changes IN RELATIONSHIP TO the independent variable. "Given X [independent] then Y [dependent] will occur." The independent variable is written across the horizontal (X) axis, and the resulting dependent values are measured up or down the vertical (Y) axis. I gave Anna several examples, such as the time it took to heat an object and the resulting temperature. They all drew blank stares.
Then Anna said, with a mischievous grin, "Explain it to me in terms of boys, and then I might understand." After a moment's thought, I suggested that if there were one boy in the room, Anna would be happy. I could see from her look that that idea didn't work. (After all, the look said, it would depend the boy.) OK, then--TWO boys? Alright (I got an instant smile), immediate happiness. Three boys, you would be giggling. Four boys you would be overjoyed. (Her smile was getting bigger.) "How about 30?" she asked. OK, suggested Grandpa, euphoric, ecstatic. Your degree of happiness is dependent on the number of boys in the room. It is the dependent variable. Anna marched forward through her homework with the concept of dependent variables firmly in her mind.Graphs help us understand the real world.
