Math 1 · Unit 7 · Lesson 1
A New Family That Multiplies
Lines were the first family of graphs, and they grow by adding the same amount every step. The exponential family multiplies by the same number every step. Down a table, a line has a constant difference and an exponential has a constant ratio. Exponents are the short way to write the multiplying, and walking a table backward shows why anything to the zero power is 1.
The big idea
Lines add, exponentials multiply. A line adds the same amount every step, so its table has a constant difference: subtract to see it. An exponential multiplies by the same number every step, so its table has a constant ratio: divide to see it. That one idea separates the two families. An exponent is the short way to write the multiplying, with the base as the number multiplied and the exponent counting the copies, and walking the table backward shows why any base to the zero power is 1: it is the do-nothing number from Unit 1, the place where nothing has been multiplied yet. Keep walking left and the outputs become fractions, small but never zero.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the add-versus-multiply idea, the two tables, exponents, the zero power walk, and a worked check. Plus a worksheet with an answer key and a short lesson plan.