Teaching Algebra with Manipulatives

Chapter 9 Teaching Notes and Overview
• Demonstration 1 involves factoring the
perfect square trinomial x 2 2x 1. Algebra
tiles are used to model the factoring.
• Demonstration 2 deals with factoring the
perfect square trinomial x 2 4x 4. Algebra
tiles are used to model the factoring.
• The Extension focuses on analyzing the
information gained from the demonstrations.
Answers
Answers appear on pages 168–169.
Mini-Project
Multiplying Trinomial Squares
(p. 170 of this booklet)
Use With Lesson 9-6.
Objective Model and factor perfect square
trinomials using algebra tiles.
Materials
algebra tiles*
* available in Overhead Manipulative Resources
Have students work in small groups to draw the
rectangular regions that model each trinomial.
Algebra tiles may be used for this activity. You
may want to check the models made by each
group. Discuss the answers when the groups
are ready. Allow time to exchange and share
ideas on Exercises 9 through 12. Have students
show their model for Exercise 12.
Answers
1. They are the same. 2. (x 2) by (x 2)
3. (x 3) 2 4. (2x 1) 2
5. (x 3)(x 1) 6. (x 1) 2
7. (x 4) 2 8. (3x 1)(x 1)
9. x 2 6x 9, 4x 2 4x 1, x 2 2x 1,
x 2 8x 16
10. perfect square trinomial
11. The first and third terms are squares and
the middle term is twice the product of the
square roots of the first and third terms.
12. (x 2)(x 2)
Algebra Activity
Factoring Trinomial Squares
(pp. 171–172 of this booklet)
Use With Lesson 9-6.
Objective Model and factor trinomial squares
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.
Display the transparency and identify the
representation of each shape. Algebra tiles may
also be used. Arrange the model of x 2 2x 1
to form a square.
Ask students to state the length of each side.
Ask what the relationship is between the length
of the sides and the factors of x 2 2x 1.
Display x 2 4x 4 on the transparency and
arrange the models to form a square. Have students
use algebra tiles at their seats if they wish.
Students may cut their own models or use
algebra tiles to complete the worksheet.
Answers
1. They are the same. 2. (x 2) by (x 2)
3. (x 3) 2 4. (2x 1) 2
5. (x 1)(x 3) 6. (x 1) 2
7. 2(x 2) 2 8. (x 4) 2
9. (3x 1) 2 10. (3x 1)(x 1)
11. (x 2)(x 2) 12. 1, 3, 4, 6, 7, 8, 9
13. a perfect square trinomial
14. The first term is a perfect square, last term
is a perfect square, and the middle term
must be twice the product of the square
roots of the first and last terms.
15. Write two factors that are the sum or
difference of the square root of the first and
last terms (and the same sign as the
middle term).
Algebra 1—Chapter 9
© Glencoe/McGraw-Hill 155 Teaching Algebra with Manipulatives