The algebraic expressions given by the three students which was derived using the tiles represented in the figure are all correct.
Patti's algebraic expression :
2 - 1 + 2x - 3 could be broken down as follows :
- 2 = two shaded tiles with each having a +1 value
- -1 = white tile which has a - 1 value
- 2x = two shaded tiles labeled x
- -3 = 3 shaded tiles in the negative portion of the rectangle, with each having a - 1 value.
Carla's Expression :
2x + 2 - 4 could be explained thus :
- Carla builds on Patti's expression by summing up the negative values of the tiles.
- 2x + 2 - 1 - 3 = 2x + 2 - 4
Emile's expression :
2x - 2 could be explained thus ;
- Emile simplified the expression further by adding all the constant values to produce a simplified expression
2x + 2 - 1 - 3
2x + 2 - 4
2x - 2
Therefore, all the algebraic representation of the tiles given by the students are all correct.
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