Matemáticas, lógica y resolución de problemas en la escuela secundaria: decimales, división y fracciones

This is the third 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 which 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 lead 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.
Course C is a five week long study of decimals, divisions, and fractions which reinforces rates, percentages, ratios, and area as previous topic and extends upon the skills previously taught. Students work out strategies for multiplying and dividing fractions and decimals through real-world problems using previously taught strategies. They will understand the link between fractions and decimals and be able to use them as tools to solve and think about problems. 
In week 1, learners review the vocabulary and meaning associated with division including “divisor”, “dividend”, and “quotient”. Then they will work on the connection between division and groups to begin work dividing fractions. 
In week 2, we will continue dividing fractions progressing from concrete methods using drawings and diagrams towards developing the algorithm from a holistic standpoint. We will practice using this algorithm to work with ratios and rates with fractions to spiral in knowledge from course two. 
In week 3, we will work with fractions in lengths, areas, and volume to continue solidifying our geometry knowledge. We will also practice solving word problems involving fractions from a variety of contexts. We will also take a mid-course check-in to see which skills need further support as we transition to our next topic. We will also introduce decimals through to shopping as it is a common real-life experience and use diagrams to practice adding and subtracting decimals in that context
In week 4, we will begin multiplying decimals. We will discuss several methods based on strategies for multiplication students are likely familiar with including partial products and area models. We will focus on conceptual understanding before moving towards efficiency. We will also work on dividing decimals and how decimals can simplify the long division process. We will also discuss the importance of place value. 
In week five, we will work on using decimals to solve real-world problems including a hands-on STEAM activity on making a set of nesting boxes. This will emphasize the importance of decimals to many trades, activities, and careers students may be interested in. We will also take our end of unit assessment to demonstrate mastery and provide detailed feedback and recommendations for students next math experience.