Mathematics
Grade 8
15 min
Model and solve equations using algebra tiles
Model and solve equations using algebra tiles
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Represent algebraic equations using algebra tiles.
Identify and create 'zero pairs' with algebra tiles to simplify expressions.
Apply the concept of balance to manipulate algebra tiles on both sides of an equation.
Use algebra tiles to isolate the variable in one-step and two-step linear equations.
Solve linear equations by interpreting the final algebra tile model.
Connect the concrete manipulation of algebra tiles to the abstract steps of solving algebraic equations.
Ever wonder how to make abstract algebra problems feel more like a game? 🎮 Algebra tiles let you 'see' and 'touch' equations to find their solutions!
In this tutorial, you'll learn how to use these colorful tiles to model algebraic equations and systemat...
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Key Concepts & Vocabulary
TermDefinitionExample
Algebra TilesPhysical or virtual manipulatives used to represent variables and constants in algebraic expressions and equations. They come in different shapes and colors to distinguish between positive/negative values and variables/constants.A long green rectangle represents 'x', a small yellow square represents '+1', and a small red square represents '-1'.
Variable TileA tile (usually a rectangle) that represents an unknown value, typically 'x'. Its value can change depending on the equation.A green 'x' tile represents the variable 'x'. Two green 'x' tiles represent '2x'.
Constant TileA tile (usually a small square) that represents a specific numerical value, typically '+1' or...
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Core Formulas
Zero Pair Rule (Additive Inverse Property)
$$ (+1) + (-1) = 0 $$ $$ (+x) + (-x) = 0 $$
Any positive tile combined with its corresponding negative tile creates a 'zero pair' which has a value of zero. You can add or remove zero pairs from either side of an equation without changing its overall value. This is crucial for simplifying expressions and isolating variables.
Balance Rule (Properties of Equality)
$$ \text{If } A = B \text{, then } A \pm C = B \pm C \text{ and } kA = kB \text{ (for } k \neq 0) $$
To maintain the equality of an equation, any operation (adding, subtracting, multiplying, or dividing) performed on one side of the equation must also be performed on the other side. With algebra tiles, this means adding/removing the same tiles from both sides, or d...
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Challenging
An algebra tile model is manipulated. The first step was adding 4 red (-1) unit tiles to both sides. After this step, the model shows 3 green x-tiles on the left and 6 yellow (+1) unit tiles on the right. What was the original equation?
A.3x + 4 = 10
B.3x - 4 = 2
C.3x = 2
D.3x + 4 = 6
Challenging
To solve the equation -2x - 3 = 5, a student first adds three +1 tiles to both sides, resulting in -2x = 8. What is the most effective next step using algebra tiles to find the value of a positive x?
A.Add two +x tiles to both sides to create zero pairs on the left.
B.Divide the 8 positive tiles into two groups, concluding x = 4.
C.Flip all the tiles on both sides to their opposite color.
D.Remove two tiles from each side to maintain balance.
Challenging
The equation is (1/3)x = 2. Since there are no 'third' tiles, how could you use standard algebra tiles to model and solve this?
A.Model x = 2, then cut the x-tile into three pieces.
B.Represent the equation as x = 2 + 2 + 2, so you can model x = 6.
C.Place one x-tile on one side and two unit tiles on the other, then add two more x-tiles and two more groups of two unit tiles.
D.This equation cannot be modeled with algebra tiles.
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