High School: Number and Quantity
Vector and Matrix Quantities HSN-VM.C.7
7. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
Students should understand that sometimes, the planets align and the cosmos paves the way to their happiness. They might find $5 in the pocket of their jeans or get asked out by the person they've been crushing on for months. Or sometimes, the math lesson for that day is incredibly easy.
Tell your students to check their back pockets, because this may turn out to be one of those days.
Students should understand that when a matrix is multiplied by a constant (called a "scalar"), each entry in the matrix is multiplied by that constant. Sounds like the distributive property… again. At this rate, we'll run out of things to distribute.
To use a concrete example, let's pretend you own a fleet of cars. We might as well dream big, right? You make a matrix to illustrate the price of keeping them all gassed up (no fart jokes, please).
Much to your dismay (and everyone else's, for that matter), you find that the price of gas has gone up 23% over the past few months. What do you suppose happens to the price of gassing up each of those cars? They're all multiplied by 1.23 (1.00 to keep the price the same, and the 0.23 because of the price increase).
Easiest math lesson ever, right? Now, they'll have to wait until class is over, but you can tell your students to check their texts because there may be a message from that special someone waiting for them.