Algebra Tiles can be used
to physically model the linear factors of a trinomial.
In this Virtual Manipulative,
you can choose between three different levels.
In levels 1 and 2, a trinomial is randomly generated for you.
The tile representation of that trinomial
sits inside of the given grid.
To begin factoring the given trinomial,
drag tiles from the Tile Bank to the outside of the grid
to represent the factor of the inside tiles.
Each tile along the outside of the grid
should align with the length and sign
of any tile on the inside of the grid.
Continue dragging tiles to the outsides of the grid
until all of the inside tiles lining the top and left edge
have been factored
and the tile representation of that factor
is displayed outside of the grid.
If you make a mistake while modeling the factors,
you can drag tiles back to the Tile Bank to delete them,
or click “Clear” to clear the grid.
When completed, the factors along the outside of the grid
should match the length and width of the given rectangle.
Click “Check” to verify that the factors are modeled correctly.
Remember, each tile should align with the lengths of any tiles
on each of its sides.
Once the modeled factors are correct,
you will be prompted to enter
the resulting binomial factors of the given trinomial.
To input the factors,
use the arrows above and below each value
to numerically represent the number
of the different types of tiles lining each side of the grid.
Each side is one factor,
and should be entered into one parentheses.
Click “Check” again to proceed.
Click “Try Another” to try another example.
In level 2, the factors of the trinomial
may contain negative values.
These values will be represented by red negative tiles.
To factor the trinomial
drag tiles from the Tile Bank to the outside of the grid
to represent the factor of the two inside tiles.
Each tile along the outside of the grid
should align with the length
of any tile on the inside of the grid.
The sign of the tile is determined
by values of the factored trinomial.
Continue dragging tiles to the outsides of the grid
until all of the inside tiles lining the top and left edge
have been factored
and the tile representation of that factor
is displayed outside of the grid.
When completed, the factors along the outside of the grid
should match the length and width of the given rectangle.
Click “Check” to verify that the factors are modeled correctly.
If you would like to clear all of the tiles
lining the outside of the grid,
you can click “Clear” to clear the grid.
To input the binomial factors,
use the arrows above and below each value
to numerically represent
the number of the different types of tiles
lining each side of the grid.
Click “Check” again to proceed.
Click “Try Another” to try another example.
In level 3, you must set up the tile representation
of the given trinomial inside the grid
before determining the factors outside of the grid.
To build the tile representation of the trinomial,
arrange them so that they form a rectangle
starting with any x-squared or negative x-squared tiles
in the top left.
Then arrange the remaining tiles such that they form a rectangle.
Consider adding the unit tiles after the x-squared tiles,
starting at the lower-right corner of the rectangle
formed by the x-squared tiles,
so the possible locations of the x-tiles
will be easier to visualize.
If you make a mistake while modeling the trinomial,
you can drag tiles back to the Tile Bank to delete them
or click “Clear” to clear the inside of the grid.
Click “Check” when you have finished
representing the trinomial.
When the trinomial is modeled correctly,
you can proceed with factoring.