The mathematical purpose of this lesson is for students to revisit their understanding of negative exponents, first encountered in grade 8. To do so, they extend the rules they have developed for working with numbers with positive exponents to include numbers with negative exponents. They make sense of what negative exponents mean through explaining their reasoning as they complete a table of values. In the associated Algebra 1 lesson, students will encounter exponential functions that take negative values as inputs. They don’t need to evaluate expressions involving negative exponents, but they do need to recognize that negative exponents have meaning and are consistent with the properties they have developed to work with positive exponents. Students use tables to explore expressions with negative exponents, they are noticing and making use of structure (MP7). As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).
- Revisit the meaning of a negative exponent.
- Let’s explore numbers with negative exponents.