Hands-On Quadratic Expressions

In this course, learners will use algebra tiles to explore key concepts in Algebra 1. Our agenda will look like this: 

Session 1: Representing Expressions
Learners will be introduced to the use of algebra tiles, including different ways to represent both positive and negative values. They will become familiar with translating between written expressions and equations and those represented with algebra tiles. We will also show how multiplication of integers can be represented with the algebra tiles. 

Session 2:  Multiplying Polynomials
Learners will learn how to multiply polynomials using the algebra tiles. We will draw connections between using algebra tiles and both the area and FOIL pencil and paper methods. 

Session 3: Factoring Polynomials -- Part I
Learners will "reverse engineer" the process of multiplying polynomials in order to factor polynomials. This lesson will involve some challenging problem-solving and experimentation.

Session 4: Factoring Polynomials -- Part II
 Learners will expand on the skills learned in Session 3 in order to deal with some particularly tricky polynomials in which the leading coefficient is not 1. Learners will wrap up this unit with a mixed review of different types of problems that they can solve with the algebra tiles, or with pencil-and-paper methods. 

This unit addresses the following Common Core Math Standards: 

CCSS.MATH.CONTENT.HSA.SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.*

--> CCSS.MATH.CONTENT.HSA.SSE.B.3.A
Factor a quadratic expression to reveal the zeros of the function it defines.

CCSS.MATH.CONTENT.HSA.REI.A.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.