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
Identify and represent algebraic expressions and equations using algebra tiles.
Apply the concept of zero pairs to simplify expressions and equations.
Model one-step linear equations using a balance mat and algebra tiles.
Model and solve two-step linear equations using algebra tiles and the balance principle.
Model and solve linear equations with variables on both sides using algebra tiles.
Explain the algebraic steps corresponding to each manipulation of algebra tiles.
Ever wonder how to 'see' algebra in action? 🤔 Algebra tiles are like building blocks for equations, helping us visualize tricky math problems!
In this lesson, you'll learn how to use these colorful tiles to represent variables, constants, and entire equations. We'll e...
2
Key Concepts & Vocabulary
TermDefinitionExample
Algebra TilePhysical or virtual manipulatives used to represent variables and constants in algebraic expressions and equations. Typically, a large square represents $x^2$, a rectangle represents $x$, and a small square represents a constant (1).A green rectangle tile represents '+x', and a red rectangle tile represents '-x'.
Variable TileAn algebra tile (usually a rectangle for 'x' or a large square for 'x²') that represents an unknown value.A green rectangle tile represents 'x', and a red rectangle tile represents '-x'.
Constant TileAn algebra tile (usually a small square) that represents a specific numerical value, typically +1 or -1.A yellow small square tile represents '+1', and a red small squ...
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Core Formulas
The Balance Principle
Whatever operation (adding or removing tiles) you perform on one side of the balance mat, you must perform the exact same operation on the other side to keep the equation balanced.
This rule ensures that the equality of the equation is maintained throughout the solving process. If you add three '1' tiles to the left, you must add three '1' tiles to the right.
Forming Zero Pairs
Any positive tile and its corresponding negative tile (e.g., +x and -x, or +1 and -1) can be grouped together to form a 'zero pair' and then removed from the mat without changing the value of the expression or equation.
This rule is crucial for isolating the variable. By adding or removing zero pairs, you can eliminate unwanted terms from one side of...
5 more steps in this tutorial
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Challenging
How would you model the first step to solve the equation 6 - x = 2? (Note: '-x' is one negative 'x' tile).
A.Add one positive 'x' tile to both sides.
B.Remove one negative 'x' tile from both sides.
C.Remove six positive '1' tiles from both sides.
D.Add two negative '1' tiles to both sides.
Challenging
A student solves 2x + 5 = 4x - 1. They incorrectly remove four 'x' tiles from both sides, resulting in -2x + 5 = -1 on their mat. What was their conceptual error, and what should they have done instead?
A.Error: Violated balance. Should have only removed 'x' tiles from one side.
B.Error: Incorrect zero pair. Should have paired 'x' tiles with '1' tiles.
C.Error: Misinterpreted signs. The '-1' should have been a positive tile.
D.Error: Created unnecessary negative variables. Should have removed the smaller number of 'x' tiles (two) from both sides.
Challenging
After solving an equation, your mat shows that x = 4. You know that one of the steps you took was to add three positive '1' tiles to both sides. Which of the following could have been the original equation?
A.2x + 3 = 11
B.2x - 3 = 5
C.x + 3 = 1
D.x - 4 = 0
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