Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 9-4)
Factoring Trinomials
Objective Factoring trinomials using algebra tiles.
Materials
• polynomial models transparency*
• algebra tiles*
• transparency pen*
• blank transparencies
* available in Overhead Manipulative Resources
Demonstration
Factoring 2x 2 3x 1
• Ask students how to model the polynomial 2x 2 3x 1.
2 yellow x 2 tiles, 3 yellow x tiles, and 1 yellow 1 tile
Display the polynomial models transparency and place the
tiles at the top of the screen.
x x x
1
x 2 x 2 x
• Ask students to suggest ways to arrange the tiles into a
rectangle. Try each suggestion until they arrive at the
rectangle shown to the right.
x 1
2x 1
x 2 x 2
x x 1
• Ask students to state the factors of 2x 2 3x 1.
x 1, 2x 1
• Remind students that when you demonstrated how to factor
x 2 5x 6 and x 2 3x 4, you first placed the x 2 tile(s)
and the 1 tile(s). Then you looked for ways to fit the x tile(s)
to make a rectangle. Ask students why this is similar to
making an organized list of factors and their sum, as in the
textbook. When you arrange the x 2 tiles, you indicate the
factor of the coefficient of the first term; when you arrange
the 1 tiles, you indicate the factors of the last term. To fit the
x tile(s), you are looking for a sum of those factors that
matches the number of x tiles.
© Glencoe/McGraw-Hill 162 Teaching Algebra with Manipulatives