Lesson Objectives
When the students have completed this lesson they should
be able to:
NYS Standards:
8A5 Use physical models to perform operations with
polynomials .
8A7 Add and subtract polynomials with integer coefficients.
NCTM Standards:
1. create and use representations to organize, record, and
communicate mathematical
ideas.
2. select, apply, and translate among mathematical
representations to solve problems .
3. recognize and use connections among mathematical ideas.
4. understand how mathematical ideas interconnect and
build on one another to produce
a coherent whole.
5. communicate their mathematical thinking coherently and
clearly to peers, teachers,
and others.
6. model and solve contextualized problems using various
representations, such as graph ,
tables, and equations .
Text Book Resources
Algebra 1, Glencoe Mathematics (2005) McGraw-Hill
Companies
Chapter 8 Pgs. 437-438
Adding and Subtracting Polynomials Using Algebra Tiles
Objective: The student will be able to use algebra
tiles to add and subtract polynomials
Materials: Class set of algebra tiles, Overhead
Algebra Tiles, and an overhead
Procedure:
Warm Ups (10 minutes):
The beginning of the lesson will consist of the teacher reviewing students prior
knowledge of adding and subtracting polynomials by doing two examples on the
board.
Students will work along in their notebooks as the teacher works on the board.
First, students distribute to drop the parenthesis.
Second, they combine like terms . All
work must be shown in their notebooks. The teacher will then go on to introduce
the
Algebra Tiles.
Activity 1 (20 minutes):
Using the overhead, the teacher will display one of each tile to represents the
size, color,
and value. Students can also refer to the poster hanging in front of the class
throughout
the lesson for the value of each algebra tile. At this point, the teacher will
pass out
student sets of algebra tiles. Allow students a few minutes to explore the tiles
on their
own. Note that all the red tiles are negative and the blue , green and yellow are
positive.
The students know about zero pairs from adding and
subtracting polynomials. Briefly
describe a zero pair on the overhead using the algebra tiles. Explain that
adding a zero
pair to the polynomial does not change its value because the zero pairs are
equal to zero.
Using the first example of adding polynomials from the
board, display the algebra tiles
to match the polynomial. As the teacher is working at the overhead, the students
are
recreating the polynomial with their set of tiles. The teacher will explain that
when
adding and subtracting polynomials, it is easier to use the tiles to model the
polynomials
if they arrange the tiles in the same order that the monomials are arranged
within each
polynomial. Therefore, arrange the tiles in descending order form left to right
on their
desks. All the x^2 tiles go on the left, the x tiles go in the middle, and the 1
tiles go on
the right. Show students how the result of the model can show a way to add the
polynomials. Remember to combine like terms and take away zero pairs.
Give students a chance to explore the other example
problem with the algebra tiles before
having them work independently on their class work. Demonstrate Example 2 from
the
board on the overhead with the tiles. Remember to distribute the negative
throughout the
second monomial .
Activity 2 (25 minutes):
Have students complete the “Exploring adding and subtracting polynomials”
worksheet
#1-6, with their algebra tiles. Students are to complete each problem in their
notebook as
well as using the tiles to solve the problems. After students have completed the
first
problem on their own, the teacher will work out the problem on the overhead with
the
algebra tiles and show students how to arrive to the correct answer. The teacher
will then
allow the students to continue working on the worksheet exploring how to use the
tiles.
After students have had time to explore, the teacher can then ask students to
volunteer
their solution by coming up to the overhead and demonstrating how they used the
tiles to
get their answers.
Closing (5minutes):
The teacher will then wrap up the lesson by asking a student to summarize the
lesson on
algebra tiles for the rest of the class. The teacher will add any other comments
needed
and let the class know how the lesson went. Assign Page 438, #1-7 for homework.
Let
students know they can use their algebra tiles to help them solve the homework
problems.
All problems must be done in their math notebook.
Exploring Adding and Subtracting Polynomials
Directions: Solve each polynomial when adding or
subtracting and draw the
representation of algebra tiles for each problem as well.
Exploring Adding and Subtracting Polynomials (Ans.Key)
Directions: Solve each polynomial when adding or
subtracting and draw the
representation of algebra tiles for each problem as well.
