Adding and Subtracting Polynomials Using Algebra Tiles. This is a one day lesson planned for an hour.

Transcription

1 1 Adding and Subtracting Polynomials Using Algebra Tiles This Lesson is designed for an 8 th Grade Algebra Class This is a one day lesson planned for an hour. Materials needed: A class set of Algebra Tiles Overhead Algebra Tiles An Overhead Overhead Markers

2 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.. 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 (005) McGraw-Hill Companies Chapter 8 Pgs

3 3 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. 1. (3x "x + 1 ) + ( x + 4x " 3 ). ( 5x + 4 ) " ( "x + 3 ) 3x " x x 4x " 3 5x x " 3 Answer: 4x + x " Answer: 7x + 1 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 (0 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. x "x x "x 1 "1 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.

4 4 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 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. 3x " x + 1 (+) x + 4x " 3 4x + x " + 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 from the board on the overhead with the tiles. Remember to distribute the negative throughout the second monomial. 5x + 4 (-) "x + 3 7x + 1 -

5 5 Activity (5 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.

6 6 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. 1.( x + 3x + 3 ) + ( x + x " ) 4.( 5x " x + 1 ) " ( x + x " 4 ).( 3x + 4x " 3 ) + ( 4x " x " 4 ) 5.( x + x + 3 ) " ( x + x " ) 3.( x + 3x " 4 ) " ( x + x " 3 ) 6.( "3x + 4x + 3 ) + ( 3x " 3x " 5 )

7 7 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. 1.( x + 3x + 3 ) + ( x + x " ) 4.( 5x " x + 1 ) " ( x + x " 4 ) + + 3x + 5x + 1 4x " 4x + 5.( 3x + 4x " 3 ) + ( 4x " x " 4 ) 5.( x + x + 3 ) " ( x + x " ) ( x + 3x " 4 ) " ( 7x + x " 7 x " x + 5 x + x " 3 ) 6.( "3x + 4x + 3 ) + ( 3x " 3x " 5 ) - + "x + x " 1 x "