# Lesson 17

Annually, Quarterly, or Monthly?

These materials, when encountered before Algebra 1, Unit 5, Lesson 17 support success in that lesson.

### Lesson Narrative

The property of exponents, $$(a^b)^c$$ is equivalent to $$a^{bc}$$, might present an obstacle in the associated Algebra 1 lesson. The purpose of the warm-up is to revisit writing equivalent expressions using this property. When students notice that they can use properties to rewrite expressions, they are noticing and making use of structure (MP7). Additionally this lesson introduces terminology like “quarterly” means “four times per year,” which students will be expected to interpret correctly for the next several lessons. In the activity “How Many Times Per Year?”, students perform a few numerical computations and then generalize by writing an expression, which is an example of expressing regularity in repeated reasoning (MP8).

### Learning Goals

Teacher Facing

• Revisit the property of exponents: $(a^b)^c$ is equivalent to $a^{bc}$.
• Understand vocabulary associated with different compounding intervals.

### Student Facing

• Let’s use different time intervals to solve problems.