I was talking to a colleague recently about how we plan for a new school year, and the parable of rocks in a jar came up.

You’ve probably heard it – a professor holds up a jar with several large rocks in it. “Is it full?” the professor asks. Her students say sure. She then adds gravel, which fills in the space around the rocks. “Is it full?” she asks again. Her students, beginning to understand, say no. The professor then proceeds to pour in some sand, filling the spaces between the gravel. “Is it full?” she asks again. The students are uncertain, until the professor pours water into the jar, filling the jar to the top. “What is the moral of this lesson?” asks the professor. A student yells out, “You can always fit more in the jar!” The professor shakes her head. “No,” she says. “The moral is that if you don’t put the big rocks in first, they’ll never fit.”

Reflecting on this parable, I decided to select four big “rocks” – one for each quarter – that are the foundational ideas I want to cover this year. Building lessons while keeping the four big concepts in mind would help ensure that they wouldn’t get lost in the day-to-day gravel and sand of the school year.

This year I will be teaching Math 8 and Integrated Math 1. So, with the California Common Core State Standards for Mathematics in hand, I picked my four rocks.

For Math 8, I picked these four:

- Linear relationships, including their graphs and equations
- Exponential relationships, including roots
- Rates of change, including slope
- Right triangle congruence and similarity, including the Pythagorean Theorem

For Integrated Math 1, I picked these four:

- Arithmetic (linear) vs. Geometric (exponential) growth
- Systems of Equations
- Represent and interpret data sets, including bivariate data
- Rigid motion in the coordinate plane

What do you think? Do you agree with my “rocks”?