Teaching Algebra with Manipulatives

Chapter 9 Teaching Notes and Overview
Using Overhead
Manipulatives
Factoring Trinomials
(pp. 160–161 of this booklet)
Use With Lesson 9-3.
Objective Model and factor trinomials using
algebra tiles.
Materials
algebra tiles*
polynomial models transparency*
transparency pen*
blank transparencies
* available in Overhead Manipulative Resources
This demonstration contains two activities.
• Demonstration 1 deals with factoring x 2
5x 6 using tiles.
• Demonstration 2 involves factoring x 2
3x 4. Students are asked to model the
trinomial using tiles, and then to form a
rectangle with the tiles. In order to form the
rectangle, there is a need to add a zero pair of
x tiles. Also, students learn that there cannot
be a negative 1 tile with a positive width and
a positive length.
Answers
Answers appear on the teacher demonstration
instructions on pages 160–161.
Using Overhead
Manipulatives
Factoring Trinomials
(p. 162 of this booklet)
Use With Lesson 9-4.
Objective Model and factor trinomials using
algebra tiles.
Materials
algebra tiles*
polynomial models transparency*
transparency pen*
blank transparencies
* available in Overhead Manipulative Resources
This demonstration involves an activity for
factoring 2x 2 3x 1 using algebra tiles.
First, students are asked to model the
trinomial. The importance of being able to fit
the x tile(s) after the x 2 tile(s) and 1 tile(s) are
placed is emphasized. Students are asked why
the latter is similar to making an organized list
of factors and their sum as is shown in the
Student Edition.
Answers
Answers appear on the teacher demonstration
instructions on page 162.
Algebra Activity
Factoring Trinomials
(pp. 163–164 of this booklet)
Use With Lesson 9-4.
Objective Model and factor trinomials using
algebra tiles.
Materials
product mat*
algebra tiles*
classroom set of Algebra Activity worksheets
transparency master of Algebra Activity
* available in Overhead Manipulative Resources
Cut the transparency on the dashed line,
then cut the squares and rectangles apart.
Cover Figures 1 and 2 on the Algebra Activity
Transparency. Ask students to identify the area
of the exposed figures.
Have students make a model of x 2 xy with
the algebra tiles. Uncover Figure 1 on the
transparency and discuss the length and width
of the rectangle. Have students state the factors.
Ask students to make a model of x 2 2xy y 2
with the algebra tiles. Uncover Figure 2 on the
transparency and discuss the length and width
of the rectangle. Ask students to state the factors
of x 2 2xy y 2 . As a group or individual activity,
complete the worksheet. Discuss Exercise 5.
Answers
1. See students’ pictures.
2. x 2y; x 3y
Algebra 1—Chapter 9
© Glencoe/McGraw-Hill 153 Teaching Algebra with Manipulatives