144
Hands-On Linear Algebra
Completed by 46 learners
Ages 11-16
Live Group Class
Live video meetings
1x per week, 5 weeks
2-8 learners per class
45 min
What’s included
5 live meetings
3 hrs 45 mins in-class hoursClass Experience
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.
Other Details
Parental Guidance
Learners should have a basic understanding of algebraic concepts. I recommend that learners take this class after taking Pre-Algebra and while studying 8th grade Algebra or Algebra 1. Depending on when learners take the class, it might be a hands-on introduction to core Algebra 1 concepts, or a review.
Learners may find it helpful to have taken my "Puzzling Into Algebra" workshops prior to this course, however they are not a pre-requisite.
Supply List
Learners will need an EAI Combination Algebra Tiles Set (54 pieces). This set can be purchased for about $8. These links are provided for your convenience and are not affiliate links. https://www.amazon.com/EAI-Education-Algebra-Tiles-Combination/dp/B079G82YGW/ref=sr_1_11keywords=algebra+tiles&qid=1561070859&s=gateway&sr=8-11 https://www.eaieducation.com/Product/520692/Algebra_Tiles_Combination_Set_-_54_pieces.aspx This set can also be used for my Hands-On Quadratic Equations course. Purchasing this set for the Linear Algebra course ensures that you have the materials for both courses. It is easiest if we all have the same set, however if you already own Algebra tiles or wish to purchase a different set, please make sure you have the following tiles: At least 20 units At least 10 "x" tiles At least 10 "y" tiles At least 5 "y-squared" tiles At least 5 "x-squared" tiles In a pinch, you can also print algebra tiles on cardstock and cut them out. In the initial materials I have included a PDF of some printable algebra tiles if you would like to do this. (If you plan to purchase the plastic Algebra tile set, you do not need to do anything with this file.) Cutting them out precisely is important, though, and would need to be done before class begins. Handouts will be provided as needed throughout the course. Learners will need the ability to download and print documents. Learners will also need a pencil!
1 file available upon enrollment
External Resources
Learners will not need to use any apps or websites beyond the standard Outschool tools.
Meet the teacher
Teacher expertise and credentials
Over the course of teaching math for over a decade, I have found that the most difficult aspect of transitioning to algebra is the fact that math becomes less concrete. Using algebra tiles is a fun and interesting way to represent abstract concepts (like variables and negative numbers) with concrete objects that can be physically manipulated. I love solving problems this way and seeing students grasp concepts that were previously too confusing or unfamiliar.
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