Teaching Algebra with Manipulatives

Chapter 9 Teaching Notes and Overview
3. factors of the product of the area
4. (2x y) by (x y); (x 2y) by (x y)
5. The dimensions of the rectangle represent
the two factors of the trinomial, which is the
area of the rectangle.
Using Overhead
Manipulatives
Factoring Differences of Squares
(pp. 165–166 of this booklet)
Use With Lesson 9-5.
Objective Model and factor differences of
squares using algebra tiles.
Answers
Answers appear on the teacher demonstration
instructions on pages 165–166.
Algebra Activity
Recording Sheet
Difference of Squares
(p. 167 of this booklet)
Use With the activity on page 501 in Lesson
9-5 of the Student Edition.
Objective Model and illustrate the difference
of squares by constructing a rectangle from two
congruent parts of a square and finding its
area.
Materials
algebra tiles*
transparency pens*
straightedge
blank transparencies
colored acetate, if available
* available in Overhead Manipulative Resources
This demonstration consists of an activity and
an extension.
• The demonstration features using one large
square and a smaller square to illustrate
factoring the differences of squares. The area
of the large square is a 2 and the smaller is b 2 .
Students are asked to place the small square
in the upper right corner of the large square
and to shade the remaining part of the large
square. Then students find the area of the
shaded part by cutting it into two trapezoids.
Next, the two trapezoids are rearranged to
form a rectangle. The length is a b and the
width is a b. The area is a 2 b 2 .
Thus, a 2 b 2 (a b)(a b). Then students
are asked to generalize about factoring
differences of squares.
• The Extension deals with using algebra tiles
to find the differences of squares. Students
are lead to see that to make a square with
the tiles, a zero pair of xy tiles are needed to
complete the square. Once again, students are
reminded that adding a zero pair of tiles does
not change the value.
Materials
straightedge
scissors
This activity deals with using the area of
squares and rectangles to model the difference
of squares. Students will draw one square
inside and similar to another square. The
smaller square is removed, and the remaining
portion is cut into two congruent pieces. These
pieces then fit together to make a rectangle.
Answers
See Teacher Wraparound Edition p. 501.
Using Overhead
Manipulatives
Factoring Perfect Square Trinomials
(pp. 168–169 of this booklet)
Use With Lesson 9-6.
Objective Model and factor perfect square
trinomials using algebra tiles.
Materials
algebra tiles*
polynomial models transparency*
transparency pen*
blank transparencies
* available in Overhead Manipulative Resources
This demonstration deals with two activities
and an extension.
© Glencoe/McGraw-Hill 154 Teaching Algebra with Manipulatives