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Algebra Tiles can be used

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to physically model the linear factors of a trinomial.

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In this Virtual Manipulative,

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you can choose between three different levels.

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In levels 1 and 2, a trinomial is randomly generated for you.

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The tile representation of that trinomial

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sits inside of the given grid.

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To begin factoring the given trinomial,

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drag tiles from the Tile Bank to the outside of the grid

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to represent the factor of the inside tiles.

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Each tile along the outside of the grid

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should align with the length and sign

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of any tile on the inside of the grid.

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Continue dragging tiles to the outsides of the grid

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until all of the inside tiles lining the top and left edge

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have been factored

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and the tile representation of that factor

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is displayed outside of the grid.

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If you make a mistake while modeling the factors,

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you can drag tiles back to the Tile Bank to delete them,

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or click “Clear” to clear the grid.

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When completed, the factors along the outside of the grid

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should match the length and width of the given rectangle.

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Click “Check” to verify that the factors are modeled correctly.

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Remember, each tile should align with the lengths of any tiles

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on each of its sides.

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Once the modeled factors are correct,

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you will be prompted to enter

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the resulting binomial factors of the given trinomial.

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To input the factors,

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use the arrows above and below each value

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to numerically represent the number

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of the different types of tiles lining each side of the grid.

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Each side is one factor,

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and should be entered into one parentheses.

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Click “Check” again to proceed.

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Click “Try Another” to try another example.

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In level 2, the factors of the trinomial

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may contain negative values.

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These values will be represented by red negative tiles.

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To factor the trinomial

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drag tiles from the Tile Bank to the outside of the grid

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to represent the factor of the two inside tiles.

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Each tile along the outside of the grid

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should align with the length

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of any tile on the inside of the grid.

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The sign of the tile is determined

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by values of the factored trinomial.

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Continue dragging tiles to the outsides of the grid

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until all of the inside tiles lining the top and left edge

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have been factored

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and the tile representation of that factor

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is displayed outside of the grid.

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When completed, the factors along the outside of the grid

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should match the length and width of the given rectangle.

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Click “Check” to verify that the factors are modeled correctly.

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If you would like to clear all of the tiles

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lining the outside of the grid,

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you can click “Clear” to clear the grid.

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To input the binomial factors,

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use the arrows above and below each value

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to numerically represent

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the number of the different types of tiles

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lining each side of the grid.

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Click “Check” again to proceed.

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Click “Try Another” to try another example.

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In level 3, you must set up the tile representation

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of the given trinomial inside the grid

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before determining the factors outside of the grid.

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To build the tile representation of the trinomial,

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arrange them so that they form a rectangle

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starting with any x-squared or negative x-squared tiles

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in the top left.

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Then arrange the remaining tiles such that they form a rectangle.

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Consider adding the unit tiles after the x-squared tiles,

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starting at the lower-right corner of the rectangle

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formed by the x-squared tiles,

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so the possible locations of the x-tiles

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will be easier to visualize.

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If you make a mistake while modeling the trinomial,

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you can drag tiles back to the Tile Bank to delete them

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or click “Clear” to clear the inside of the grid.

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Click “Check” when you have finished

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representing the trinomial.

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When the trinomial is modeled correctly,

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you can proceed with factoring.