Mathematics
Grade 6
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 variables and constants using algebra tiles.
Set up a visual model of a one-variable equation using algebra tiles.
Apply the concept of zero pairs to simplify algebraic expressions within an equation.
Maintain the balance of an equation by performing inverse operations on both sides using algebra tiles.
Solve one-variable equations for the unknown variable using algebra tiles.
Explain the steps taken to solve an equation using algebra tiles.
Ever wonder how detectives solve mysteries? 🕵️♀️ They look for clues to find the unknown! In math, we'll be detectives using special tools called algebra tiles to find unknown numbers.
This lesson will teach you how to visually represent and solve one-variable equations using algebra tile...
2
Key Concepts & Vocabulary
TermDefinitionExample
Algebra TilesPhysical or virtual manipulatives used to represent variables (like 'x') and constants (numbers) in algebraic expressions and equations. They come in different sizes and colors to distinguish positive and negative values.A long green tile often represents '+x', a small yellow square represents '+1', and a small red square represents '-1'.
VariableA symbol, usually a letter (like 'x', 'y', or 'a'), that represents an unknown number or a quantity that can change.In the equation 'x + 3 = 7', 'x' is the variable.
ConstantA number in an equation or expression that has a fixed value and does not change.In the equation 'x + 3 = 7', '3' and '7'...
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Core Formulas
The Balance Principle
To keep an equation balanced, any operation (adding, subtracting, multiplying, dividing) performed on one side of the equation must also be performed on the other side.
This rule ensures that the equality between the two sides of the equation is always maintained, allowing you to find the correct value for the variable.
The Zero Pair Principle
$+1 + (-1) = 0$ and $+x + (-x) = 0$
A positive tile and a negative tile of the same type cancel each other out, forming a 'zero pair'. These pairs can be removed from the equation without changing its value, helping to simplify and isolate the variable.
Isolating the Variable
The goal when solving an equation is to get the variable tile(s) by itself on one side of the equation, with only constant t...
5 more steps in this tutorial
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Challenging
To solve the equation x + 6 = 2 using algebra tiles, you add six '-1' tiles to both sides. After removing all possible zero pairs, what is the final state of the model?
A.Left: one 'x' tile. Right: eight '+1' tiles.
B.Left: one 'x' tile. Right: four '-1' tiles.
C.Left: one 'x' tile. Right: four '+1' tiles.
D.Left: one 'x' tile, six '+1' tiles. Right: two '+1' tiles, six '-1' tiles.
Challenging
A student correctly models and solves an equation, leaving a final state of 3 'x' tiles on the left and 15 '-1' tiles on the right. If the student stops here and reports the answer as -15, which pitfall have they made?
A.Misinterpreting negative tiles
B.Incorrectly forming zero pairs
C.Not maintaining balance
D.Not isolating the variable completely
Challenging
A student is solving 2x - 3 = 5. They perform the following steps with tiles: (1) Add three '-1' tiles to both sides. (2) Remove zero pairs. (3) Divide the tiles on the right into two groups. Which step contains the error?
A.Step 1: They should have added three '+1' tiles.
B.Step 2: They should not have removed zero pairs.
C.Step 3: They should have divided into three groups.
D.There is no error in their process.
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