중학교 수학, 논리 및 문제 해결: 방정식 및 표현식

Please Note : Time Change after Winter Break from 9 am PST to 12 PM PST. 

This is the fourth course in a series of micro-classes for middle school math. These micro classes are a hybrid of individualized learning and traditional classes. Each section has no more than five learners which provide a foundation for strong relationships, social-emotional learning, and truly individualized instruction. 
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 beginning middle school and students who need to catch up. 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. Students will complete a math notebook In the style of a “Main Lesson” book found in Waldorf and Steiner education philosophies to help with recall and long-term retention.
This unit is a five-week study of pre-algebra in which students develop a fundamental understanding of independent and dependent variables, coefficients, expressions, equivalent expressions, and exponents. They learn more efficient strategies for writing equations and work with positive whole number exponents and whole number, fraction, and variable bases. They will learn to solve linear equations with a single variable and simple equations with exponents. They will use these as tools to reason about the real world and geometrical situations and learn to represent and share this information in graphs and tables. 
Week 1: Students will learn to represent and solve equations with one variable beginning with tape diagrams, learning to understand whether equations are true or false, and balancing simple equations using the "mobile" strategy, they will also reconnect the knowledge of fractions and division. 
Week 2: Students begin writing expressions where letters stand for numbers and develop a logical system for explaining these choices. They revisit percentages in the context of simple equations and began working with equivalent equations. They will also apply their knowledge of the distributive property to problems. 
Week 3: Students will review what they've learned so far and take a mid-unit check-in to guide their practice and prepare for the second half of the class. They will also apply what they've learned to area, volume, and surface area to begin understanding the meaning of exponents. 
Week 4: Students work with exponents in expressions beginning with representing them, than evaluating simple expressions with exponents, and then working with equivalent exponential expressions. 
Week 5: Students learn to create equations and visual representations for systems involving two related quantities including identifying independent and dependent variables. They will work with tables, equations, and graphs in a project-based lesson. They will take an end-of-unit assessment.