Overview and Rationale
"Shortcuts are the privilege of experts." This has been a recurring phrase in Roger Howe's seminar entitled "Place Value, Fractions, and Algebra: Improving Content Learning through the Practice Standards," and it rings especially true to me as I navigate guiding my students through the Common Core State Standards for Mathematics (CCSS-M). Beginning the CCSS-M as eighth graders puts my students at an immediate disadvantage, as they will have gaps in learning some key content that has now been relocated from eighth grade in our former state standards to lower grades in the CCSS-M. For students who have not felt much success in math, this can dampen their enthusiasm for learning. While it can be tempting to teach them "tricks" to quickly fill these gaps in order to get to the grade level content, the goal of this unit is to help build background knowledge that will deepen their understanding of foundational ideas in order to internalize it and apply it to new situations.
Developing algebraic thinking in students whose foundations in mathematics are limited presents a unique challenge in the middle school algebra I classroom. Students express frustration at learning this "new language" and grappling with representations of numbers they have never seen before; nor do they see the relevance of it in their lives. My goal in this unit is to build a strong foundation for students to explore and understand expressions and equations in a coherent progression based on their prior knowledge. It is also my goal for them to apply their understandings to investigate the mathematics behind topics that matter to them. The core of the unit will be devoted to developing strong, fearless problem solvers who become experts who have earned the privilege of applying shortcuts with understanding to real world problems that matter to them.
Through focused problem sets designed to gradually extend subtopics of expressions, students will construct meaning about the properties of numbers and variables as we discover how these things work together in algebra. By reordering topics to present a logical progression of ideas, I will scaffold my students' learning to prevent burnout and promote the Standards for Mathematical Practice in the CCSS-M. Sense-making, tinkering, and developing problem solving strategies and skills will provide the core of our class discussions. Students will work to define algebra within their own contexts to apply it in a culminating project where they investigate issues that are important to them and apply their algebraic reasoning and skills to come up with viable solutions to share with our school community.
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