Teaching Algebra with Manipulatives

Chapter 8 Teaching Notes and Overview
is a monomial or the sum of monomials.
Make sure students understand what the
1-tile(yellow), x-tile(green) and the x 2 -tile(blue)
represent and that their opposites are red tiles.
Go over the three examples with the class. In
groups, have students complete the exercises.
As soon as the groups have completed the work,
talk about the answers. If some students are
having difficulty representing the polynomials
with algebra tiles, let them model additional
polynomials.
Answers
See Teacher Wraparound Edition p. 431.
Algebra Activity
Recording Sheet
Adding and Subtracting
Polynomials
(p. 137 of this booklet)
Use With Lesson 8-5 as a preview activity.
This corresponds to the activity on pages
437–438 in the Student Edition.
Objective Add and subtract polynomials using
models.
Materials
algebra tiles*
* available in Overhead Manipulative Resources
This activity may be used as a preview to
Lesson 8-5. It shows how algebra tiles can be
used to model addition and subtraction of
polynomials. Students need to know the
meaning of like terms, combining like terms,
and removing and adding zero pairs. Like terms
are represented by tiles that are the same
shape and size. Be sure students know that you
can remove or add zero pairs without changing
the polynomial. Go over Activities 1–3 as a
class. Activities 2 and 3 illustrate two ways
to model the same subtraction. Point out to
students that you can subtract a polynomial by
adding its opposite. In groups, have students
use algebra tiles to complete the exercises.
Answers
See Teacher Wraparound Edition pp. 437–438.
Using Overhead
Manipulatives
Adding and Subtracting
Polynomials
(pp. 138–140 of this booklet)
Use With Lesson 8-5.
Objective Add and subtract polynomials using
models.
Materials
polynomial models transparency*
algebra tiles*
transparency pen*
blank transparencies
colored acetate sheets (optional)
* available in Overhead Manipulative Resources
This demonstration contains two activities and
an extension.
• Demonstration 1 shows how to add two
polynomials using algebra tiles. First, the
polynomials to be added are modeled. Then
like terms are combined and all zero pairs
are removed. The polynomial that remains
models the sum.
• Demonstration 2 illustrates subtracting
polynomials using algebra tiles. Remind
students that subtraction is taking away
or removing. The polynomial that remains
models the difference.
• The extension deals with adding polynomials
that have x 2 , xy, and y 2 terms. The y 2 -tile is
represented by a square that is larger than
the x 2 -tile. The xy-tile is shown with a length
of x and a width of y. You may want to
prepare some y 2 and xy models using colored
acetate and use these as tiles. Both addends
are modeled. Then to find the sum, combine
like terms and remove any zero pairs, the
remaining tiles represent the sum.
Discuss with students how you can add or
subtract polynomials without using models.
Answers
Answers appear on the teacher demonstration
instructions on pages 138–140.
© Glencoe/McGraw-Hill 130 Teaching Algebra with Manipulatives