Which board geometrically represents 4×2 – 1 using algebra tiles?
The Correct Answer and Explanation is:
✅ Correct Board Representation:
A board that geometrically represents 4x² – 1 will contain:
- Four large square tiles, each labeled x² (representing the term 4x²).
- One small unit tile, colored red (or shaded differently to indicate negative 1), representing –1.
Explanation:
Algebra tiles are a powerful visual aid that helps students understand and manipulate algebraic expressions concretely. Each tile type corresponds to a part of an expression:
- A large square tile represents x².
- A rectangle represents x.
- A small square (unit tile) represents the number 1.
Positive values are usually represented with green or blue tiles, while negative values are represented with red tiles or a contrasting color.
In the expression 4x² – 1, we are combining two types of tiles:
- 4x²: This means placing four x² tiles on the board. These represent the total area of four identical x-by-x squares.
- –1: This indicates removing or subtracting one unit, so we place one red unit tile (to show negative 1).
No x-tiles (which represent linear terms like 4x) are needed, since the expression does not include an x term.
The key idea is that algebra tiles represent both magnitude and sign visually. The expression 4x² – 1 is geometric because:
- The area of each square corresponds to x².
- Subtracting 1 means removing a unit from the total area.
Thus, the correct board has:
- Four x² tiles placed together to represent 4x².
- One red unit tile nearby or slightly apart, showing that 1 is being subtracted.
This model supports a conceptual understanding of algebra, especially for visual learners
