中学校の数学と論理：指数と科学的記法

This is the seventh course in year two of a series of middle school mathematics courses. These courses are taught in small-groups to provide individual instruction and social-learning opportunities aligned with a social constructionist or situated cognition view of learning. This series is based on an accelerated math curriculum that covers three years of content, aligned to Common Core Math Standards, over the course of two school years. It is perfect for students preparing to begin Algebra ahead of time, or those who need review and remedial support. 
The curriculum is problem-based this means instead of lectures or videos students work together as a small group to solve problems to discover principles and strategies with teacher guidance, as necessary. Therefore, we will spend approximately 90% of each class period working on problems and discussing them as a group. The use of discussion and problem-solving leads to generalized mathematics or proofs. This process prepares students well who may seek advanced mathematics in high-school or beyond. 
In this unit, we build upon work from year one with exponent notation and positive whole number exponents to uncover the rules for using exponents and combine this with their knowledge of powers of tens to understand what happens when we add, subtract, multiply and divide with exponents as well as what happens when things are raised to the zero power. Then, they expand to other bases. This will provide a foundation for working with scientific notation. 
Week 1: We will begin with a unit readiness assessment. Then we will complete an exponent review including fractional exponents and connecting this to the idea of repeated multiplication and division. We will use this repeated reasoning to understand what happens when we multiply powers of ten as a foundation for understanding multiplying exponents with the same base. Then we will use this to understand what happens when an exponent is the base for another exponent. 
Week 2: We will build off of what we learned in week one to understand what happens when we divide exponents beginning with powers of ten. This will also allow students to understand why 10^0 =1 and critique faulty reasoning. Students will then extend the rules they have developed so far in the unit to negative exponents and bases other than ten and prove their rules work. They will practice all of the exponent rules and work with expressions with multiple bases to practice their conceptual understanding before understanding how to treat exponents with different bases that are being raised to the same power. 
Week 3:  Students will prepare to work with scientific notation by using base ten diagrams to represent different powers of ten and understanding how multiplying and dividing by ten affect the decimal representation of numbers. Then they will use this to express very large and small numbers as exponents. We will visualize this skill with number lines to compare numbers using multiples of powers of ten including non-integer multiples and negative exponents. We will apply what we've learned to solve rich real world problems using scientific notation. 
Week 4: We will practice solving problems using standard scientific notation including multiplication, division, and estimation and expressing our results in context. Then we will practice with addition and subtraction. We will apply our skills to a project-based learning activity about space and computing power before taking our end of unit assessment.