Section	Teacher-facing learning goals
Exponent Review	Lesson 1 Comprehend that repeated division by 2 is equivalent to repeated multiplication by one-half. Create an expression that represents repeated multiplication, and explain (orally) how the structure of the expression helps compare quantities.
Exponent Rules	Lesson 2 Generalize a process for multiplying exponential expressions with the same base, and justify (orally and in writing) that \(10^n \cdot 10^m = 10^{n+m}\). Lesson 3 Generalize a process for finding a power raised to a power, and justify (orally and in writing) that \((10^n)^m = 10^{n \cdot m}\). Lesson 4 Generalize a process for dividing powers of 10, and justify (orally and in writing) that \(\frac{10^n}{10^m} = 10^{n−m}\). Use exponent rules to multiply and divide with \(10^0\), and justify (orally) that \(10^0\) is 1. Lesson 5 Describe (orally and in writing) how exponent rules extend to expressions involving negative exponents. Describe patterns in repeated multiplication and division with 10 and \(\frac{1}{10}\), and justify (orally and in writing) that \(10^{\text-n}=\frac{1}{10^n}\). Lesson 6 Generalize exponent rules for nonzero bases, including bases other than 10. Use exponent rules to identify (in writing) equivalent exponential expressions, and explain (orally) the reasoning. Lesson 7 Identify (orally) misapplications of exponent rules to expressions with multiple bases (orally and in writing). Use exponent rules to rewrite exponential equations involving negative exponents to have a single positive exponent, and explain (orally) the strategy. Lesson 8 Generalize a process for multiplying expressions with different bases having the same exponent, and justify (orally and in writing) that \((ab)^n = a^n \cdot b^n\).
Scientific Notation	Lesson 9 Describe (orally and in writing) large and small numbers as multiples of powers of 10. Interpret a diagram for base-ten units, and explain (orally) how the small squares, long rectangles, and large squares relate to each other. Lesson 10 Compare large numbers using powers of 10, and explain (orally) the solution method. Use number lines to represent (orally and in writing) large numbers as multiples of powers of 10. Lesson 11 Coordinate (orally and in writing) decimals and multiples of powers of 10 representing the same small number. Use number lines to represent (orally and in writing) small numbers as multiples of powers of 10 with negative exponents. Lesson 12 Determine what information is needed to answer a question about large numbers, and explain (orally) how that information would help solve the problem. Use exponent rules and powers of 10 to solve problems in context, and explain (orally) the steps used to organize thinking. Lesson 13 Identify (in writing) numbers written in scientific notation, and describe (orally) the features of an expression in scientific notation. Lesson 14 Generalize (orally and in writing) a process of multiplying and dividing numbers in scientific notation. Use scientific notation and estimation to compare quantities and interpret (orally and in writing) results in context. Lesson 15 Generalize (orally and in writing) a process of adding and subtracting numbers in scientific notation and interpret results in context.
Let’s Put It to Work	Lesson 16 Use scientific notation to compare quantities in context, and describe (orally) how using scientific notation helps with making comparisons between very large and very small quantities.

8.7 Exponents and Scientific Notation