Why Students Struggle
Students that are interested and willing participants in their own educations sometimes struggle with Algebra 1. We have observed three major reasons why. The resources here are designed with these in mind.
Number Sense
Many students fail to recognize that math describes real things. They think of it as a puzzle with steps to follow, and answers are right if they match the key.
Translation of Procedure
Many students fail to translate past procedures with numbers to algebraic expressions, or even to new numeric applications.
Conceptual Understanding
Not only do many students lack conceptual understanding, they fail to recognize exploration and discussion of concepts as mathematics.
Design Elements to Combat These Struggles
Each lesson explores the concepts and fundamental ideas, from which procedures are developed. When students struggle it is best to revert back to the concept, not find the inappropriate step. So, as you’re using these resources, when students stumble, find why the step was inappropriate, why it didn’t align the fundamental idea. If it something as simple as a sign or arithmetic error, there’s little to be learned. But, if a student fails to factor the radicand of a square root to find the largest square number, there’s a learning opportunity!
There is a time and a place for Skill & Drill resources, and many companies providing those types of resources. You will not find those types of resources here. Every lesson, assignment, activity and assessment is carefully designed to challenge student thinking, to promote problem solving and develop conceptual understanding. It is our experience that in the absence of these components, retention is nearly impossible to instill in students.
We do not just want students to pass this class, we want them to be well prepared for future courses, too.
Units
Number Unit
Serving this topic well is worth the investment in time. It is often rushed, but students need this knowledge!
Foundations of Algebra
Exploring Algebra as a branch of mathematics, not a class. Algebra roughly means to resolve through regression.
Functions
Understanding the fundamentals of functions is key for a lot of future mathematics. The foundation is laid here.
Linear Equations
Linear equations include writing equations, applications, graphing, reading graphs and creating and exploring models.
Polynomials
This is the foundation for understanding non-linear equations, especially quadratic equations. We introduce a lot of key concepts here.
Quadratic Equations
This is where Algebra 1 gets "next - level" for students. We learn completing the square and the quadratic formula.
Number Unit
Fundamentals