Teach integers, quadratics and polynomials using hands-on experiences

Many students struggle with the leap from working with known quantities in elementary school math, to working with variables and solving equations for unknowns in middle school. Teachers can help bridge this gap by using concrete representations of integers, variables, squares and polynomial expressions to help students arrive at an intuitive understanding of algebraic concepts. We will demonstrate how to make algebraic concepts concrete and visual by giving them geometric meaning. The workshop will show teachers how to use concrete materials to guide students to discover for themselves the rules for adding, subtracting, multiplying and dividing integers; adding, subtracting, multiplying and dividing variables; how to extend the place value system to algebraic polynomials; the geometric meaning of squares and square roots; the geometric meaning of expanding and factoring quadratic equations; and using the additive inverse, multiplicative inverse and distributive property to solve algebraic equations. This work can be used to enhance conceptual understanding alongside any curriculum being used.