Teaching Algebra with Manipulatives
Teaching Algebra with Manipulatives
Teaching Algebra with Manipulatives
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Chapter<br />
12<br />
Rational Expressions and Equations<br />
<strong>Teaching</strong> Notes and Overview<br />
Using Overhead<br />
<strong>Manipulatives</strong><br />
Dividing Polynomials by Monomials<br />
and by Binomials<br />
(pp. 195–196 of this booklet)<br />
Use With Lesson 12-5.<br />
Objective Dividing polynomials by monomials<br />
and by binomials using algebra tiles.<br />
Materials<br />
algebra tiles*<br />
product mat transparency*<br />
transparency pen*<br />
blank transparencies<br />
* available in Overhead Manipulative Resources<br />
This demonstration contains two activities.<br />
Both activities use algebra tiles and the area<br />
of a rectangle to model dividing polynomials.<br />
Students need to know what the 1 tile, x tile,<br />
and x 2 tile represent.<br />
• Demonstration 1 shows how to use algebra<br />
tiles to divide 2x 2 6x by 2x. First, 2x 2 6x<br />
is modeled. From this model, the two x 2 tiles<br />
and one x tile are placed on the product mat<br />
transparency. Students are asked to build the<br />
rectangle <strong>with</strong> the remaining tiles on the<br />
mat. The length is 2x and the width is x 3.<br />
The width, x 3, is the quotient of 2x 2 6x<br />
and 2x.<br />
• Demonstration 2 models the quotient of x 2 <br />
5x 6 and x 2. Like in Demonstration 1,<br />
x 2 5x 6 is modeled using algebra tiles.<br />
Then the x 2 tile and two of the 1 tiles are<br />
placed on the product mat. Next, students<br />
are asked to build the rectangle <strong>with</strong> the<br />
remaining tiles on the mat. The length is<br />
x 2 and the width is x 3. The width, x 3,<br />
is the quotient of x 2 5x 6 and x 2.<br />
Provide additional examples showing how to<br />
use algebra tiles to model dividing polynomials.<br />
Let students discover that algebra tiles cannot<br />
be used to divide polynomials <strong>with</strong> non-zero<br />
remainders. The latter situation is addressed in<br />
the <strong>Algebra</strong> Activity on page 667 of the Student<br />
Edition. Discuss <strong>with</strong> students how they can<br />
divide <strong>with</strong>out using models.<br />
Answers<br />
Answers appear on the teacher demonstration<br />
instructions on pages 195–196.<br />
<strong>Algebra</strong> Activity<br />
Recording Sheet<br />
Dividing Polynomials<br />
(p. 197 of this booklet)<br />
Use With the activity on page 667 in Lesson<br />
12-5 of the Student Edition.<br />
Objective Divide a polynomial by a binomial<br />
using algebra tiles.<br />
Materials<br />
algebra tiles*<br />
* available in Overhead Manipulative Resources<br />
Have students read and study the illustration<br />
of x 2 3x 2 divided by x 1. Discuss the<br />
process as a class. Form groups of two or three<br />
students to use algebra tiles to complete the<br />
<strong>Algebra</strong> Activity. Ask students to draw the<br />
completed rectangle for each of the Exercises<br />
1–4 and to draw around the dimension that is<br />
the quotient. Discuss the quotients. Next, have<br />
them work Exercise 5. Students cannot model<br />
this division using algebra tiles, because of the<br />
existence of a non-zero remainder. Discuss <strong>with</strong><br />
students how they can divide <strong>with</strong>out using<br />
models.<br />
Answers<br />
See Teacher Wraparound Edition p. 667.<br />
Mini-Project<br />
Rational Roundup<br />
(p. 198 of this booklet)<br />
Use With Lesson 12-9.<br />
Objective Solve rational equations.<br />
Add, subtract, multiply, and divide rational<br />
expressions.<br />
Materials<br />
scissors<br />
<strong>Algebra</strong> 1—Chapter 12<br />
© Glencoe/McGraw-Hill 193 <strong>Teaching</strong> <strong>Algebra</strong> <strong>with</strong> <strong>Manipulatives</strong>
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