Matemáticas y lógica de secundaria: relaciones proporcionales, círculos y gráficos

This is the fifth 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 provides 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 four week study of pre-algebra and middle school math skills centered around proportional relationships. Students will learn to identify constants of proportionality and display this information using tables and graphs. Students will work on the coordinate plane and understand the importance of the origin. Students will begin working with circles including circumference, diameter, radius, area, and building an understanding of pi through hands-on activities and digital interactives.
Week One: Students will learn about proportional relationships and equations using tables and identify the constant of proportionality. They will identify and use reciprocal thinking about proportionality to generate multiple equations and manipulate equations to solve problems. They will be able to compare relationships using tables, graphs and equations. They will be able to determine whether relationships are proportional. 
Week Two: Students will use critical thinking to determine the best way to represent proportional relationships and identify information needed to solve problems. They will solve problems about realistic situations involving proportional relationships. They will generate graphs of proportional relationships, identify the constant of proportionality from graphs, and explain the significance of points on the line. They will use graphs to compare two relationships of the same variables. They will generate graphs and constants from a singular point. 
Week Three: They will review measurements of squares and represent relationships between these measurements on graphs. They will learn how measurement error can impact graphing. They will compare different ways to measure a circle and generalize relationships between these measurements. They will learn the terms "diameter" "radius" and "circumference". They will learn about pi and common representations of pi and how they can impact calculations. They will derive an understanding of pi and the area of circles through a hands on activity deconstructing a circle.They will use their knowledge of area to estimate area of complex shapes and decompose irregular shapes. 
Week Four: Students will apply their knowledge to a variety of real-world problems and calculate the area of shapes including circular and semicircular parts. They will represent the proportional relationships in shapes and other settings using a variety of strategies. They will complete two projects using their knowledge to understand household water usage and understand the creation and pricing of stained glass windows incorporating art. We will also finish the unit with a one-day assessment.