Powers, Roots, and Logs are Related Facts

This year, in my Algebra 2 class, I prefaced our individual function units with a overview of functions in general. One thing that happened is that before we studied exponential functions, we had a decent understanding of inverses and how several functions are related in this way. Several weeks before I ever needed to hint at the existence of logarithms, the students saw the need for an inverse to an exponential function and also were stymied by the relationships that are already comfortable to them: namely, the existing inverse relationships between powers and roots.

So this month, when we got to the middle of our exponential function unit, I decided to present logarithms as a group of THREE related facts in a fact family.

We listened to a fabulous Radiolab program that presents numbers and logarithmic thinking as a human interest story. I am so grateful for programs like this that do my hard work for me!

Then we talked about how powers, roots, and logarithms are all different ways to say equivalent things, while each highlighting a different feature.

Fact families are something that students are familiar with. No one batted an eye.
When I asked them what is meant by logarithmic thinking, I was happy with how their explanations centered around exponents and thinking about 'how many times a number is doubled or tripled,' etc.


We concluded with some fact practice by using fact triangles and naming the three related facts. I made these awesome octahedral dice with fact triangles in base 2, base 3, base 4, and base 5. Their job? Roll a die and record the three facts that can be written from the trio of values.

The students whipped through it, never complained, and had 100% accuracy on our quiz the following day. I'll count it as a worthy addition to my filing cabinet.