Hands-On Linear Algebra

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. 

Sessions 2 and 3: Solving Equations and Inequalities
Learners will begin solving linear equations. They will solve one and two step equations in which they find the numerical value of a variable. They will extend and adapt these skills as they use algebra tiles to solve linear inequalities. Then we will learn to solve literal equations in preparation for Session 4. 

Session 4: Solving Systems of Equations by Substitution
They will solve literal equations in which they manipulate a multi-variable equation to find an expression representing an individual variable. Learners will then apply concepts from the previous two lessons to solve systems of linear equations by substitution. We will use the algebra tiles to model both the substitution and elimination methods of solving linear equations. 

Session 5: Solving Systems of Equations by Elimination
We will use the algebra tiles to model the elimination method of solving linear equations. 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.8.EE.C.7
Solve linear equations in one variable.

--> CCSS.MATH.CONTENT.8.EE.C.7.B
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

CCSS.MATH.CONTENT.8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.

--> CCSS.MATH.CONTENT.8.EE.C.8.A
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

--> CCSS.MATH.CONTENT.8.EE.C.8.B
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. 

CCSS.MATH.CONTENT.HSA.REI.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

CCSS.MATH.CONTENT.HSA.CED.A.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. 

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.

CCSS.MATH.CONTENT.HSA.REI.C.5
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

CCSS.MATH.CONTENT.HSA.REI.C.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.