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Working with Algebra Tiles
In this example, a subtraction equation is solved using tiles.
Review of algebra tiles:
Algebra tiles can be used to model positive integers, negative integers, zero, x, and x-squared. Algebra tiles are a hands-on model that makes the symbolic nature of algebraic expressions with integers into a more readily understandable manipulative.
- Positive integers are modeled with yellow algebra tiles squares.
- Negative integers are modeled with red algebra tiles squares.
- The variable x is modeled with the green algebra tile rectangle.
- The variable -x is modeled with the red algebra tile rectangle.
- The variable x-squared is modeled with the green algebra tile large square.
- Zero is modeled with a pair of red and yellow small square algebra tiles.
Algebra tiles are used in our Math Tutorials to cover the following topics:
Addition of integers. This includes adding two positive integers, two negative integers, and a combination of positive integers and negative integers.
Subtraction of integers. This includes subtracting positive integers from positive integers, positive integers from negative integers, negative integers from positive integers, and negative integers from negative integers.
Modeling variable expressions. This includes using algebra tiles to model any combination of integers and variables, including square terms.
Combining algebraic expressions. This includes using algebra tiles to model the sum of two varaible expressions.
Solving equations. This includes using algebra tiles to solve linear and quadratic equations.
For each of the examples shown, we start with a mathematical expression written with numbers and variables. We then convert each term of the expression into the corresponding set of algebra tiles. In the process, we go from a purely symbolic representation of a mathematical expression to a concrete one that can be manipulated. This transition from a symbolic to a concrete representation provides for hands-on exploration of algebraic concepts that some students will find more comprehensible than a purely symbolic approach.
However, the goal is for students to read, understand, and write their own symbolic expressions. Algebra tiles are a transition to the symbolic, not a replacement of it. Once students find the solution to a math problem using algebra tiles, it is imperative for them to convert from the concrete back to the symbolic.
As students become proficient in the use of algebra tiles, they should also become proficient in converting their concrete models back to symbolic form. You should have the student transition out of using the algebra tile as their proficiency with symbolic manipulation increases.
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The library of Math Tutorials is a comprehensive collection of worked-out solutions to common math problems. This overcomes a common limitation of most textbooks: the handful of worked-out examples for a given concept. We provide the full array of examples and solutions, allowing students to identify patterns among the solutions, in order to aid concept retention. We also have quizzes for many of these topics.
Our current inventory of Math Examples include:
- Math Tutorial: Examples Using Algebra Tiles
- Math Tutorial: Solving Equations in One Variable
- Math Tutorial: Solving Equations with Fractions
- Math Tutorial: Solving Equations with Percents
- Math Tutorial: Slope formula
- Math Tutorial: Midpoint formula
- Math Tutorial: Distance formula
- Math Tutorial: Graphing linear functions, given m and b
- Math Tutorial: Graphing absolute value functions
- Math Tutorial: Graphing linear inequalities
- Math Tutorial: Using the Point-Slope form
- Math Tutorial: Finding the equation of a line given two points
- Math Tutorial: Graphing parallel and perpendicular lines
- Math Tutorial: Solving quadratics graphically
- Math Tutorial: Solving quadratics by completing the square
- Math Tutorial: Factoring Quadratics
- Math Tutorial: Polynomial Expansion
- Math Tutorial: Solving quadratics using the quadratic formula
- Math Tutorial: Using FOIL
- Math Tutorial: Graphs of Exponential Functions
- Math Tutorial: Laws of Exponents
- Math Tutorial: Graphs of Logarithmic Functions
- Math Tutorial: Graphs of Rational Functions
- Math Tutorial: Combining Rational Expressions
- Math Tutorial: Graphs of Conic Sections
