Teaching Algebra with Manipulatives

Using Overhead Manipulatives
(Use with Algebra 1, Lesson 9-5)
Factoring Differences of Squares
Objective Factoring the differences of squares using algebra tiles.
Materials
• algebra tiles*
• transparency pens*
• straightedge
• blank transparencies
• colored acetate, if available
* available in Overhead Manipulative Resources
Algebra 1—Chapter 9
Demonstration
Factoring the Difference of Squares
• On a blank transparency, draw a line segment 4 inches long.
Label this segment a. Construct an a by a square. Ask
students to find the area of the square. a 2
a
a
• Draw another line segment 1.5 inches long. Label this
segment b. Construct a b by b square. Have students find the
area of the smaller square. b 2
b
b
• Place the small square inside the large square and shade the
L-shaped part of the square as shown. Ask students to state
an algebraic expression for the area of the shaded part.
a 2 b 2 Point out that this expression is called the
difference of squares.
a
b
b
a
• Ask students what the length of the top of the L is. a b
Ask what the length of the right side of L is. a b Erase
the unshaded portion of the figure, and label the edges with
length b as shown. Then draw a dashed line to separate the
L into two regions as shown.
a
a b
b
b
ab
a
• Place a blank transparency on top of the figure. Trace the
figure and the dashed line. Cut out the figure and cut along
the dashed line to form two trapezoids. Rearrange the
trapezoids to form the rectangle shown. Label the edges.
ab
b
a
a
b
ab
© Glencoe/McGraw-Hill 165 Teaching Algebra with Manipulatives