Addition and Subtraction of Polynomials ) Students will be able to identify degree of both a term and polynomial. 2) Students will be able to identify like terms within an epression. 3) By the end of the lesson students will be able to add and subtract simple polynomials. Lesson objectives Teachers' notes
Teacher: Subject: Topic: Grade(s): Maria Morris MPM D MFM P Adding and Subtracting Polynomials Grade 9 Prior knowledge: addition and subtraction of integers and like and unlike terms Epectations MPM D manipulate numerical and polynomial epressions, add and subtract polynomials with up to two variables [e.g., (2 5) + (3 + ), (3 2 y + 2y 2 ) + (4 2 y 6y 2 )], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil); MFM IP simplify numerical epressions involving integers and rational numbers, with and without the use of technology; add and subtract polynomials involving the same variable up to degree three [e.g.,(2 + ) + (2 3 + 4)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil); Lesson notes: Students should be familiar with the use of algebra tiles, and it would be beneficial for each student or a pair of students to have a package of tiles to work with throughout lesson. The homework assigned on the last page of lesson is for the MPM and is from McGraw Hilland Ryerson, "Principles of Mathematics 9". Lesson objectives Teachers' notes 2
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Julio says that the term 2 has a coefficient of 2 and a variable. Is Julio correct? Eplain. 4
Are these epressions equivalent? Eplain. a) 2w + t and 2w + t b) 3 + and 3 Eplain when you must write the number, and when you do not need to. 5
Addition & Subtraction of Polynomials (Collecting Like Terms) 6
What is a like term? Like terms are terms that have identical variables. Therefore, they have the same variable with the same eponent on the variable. Eamples: 7
Polynomials should be written in standard form. This means that the powers of the variables should go from the highest eponent to the lowest eponent. E. 4 3 + 3 2-8 + 6 8
So How Do We Add/Subtract Polynomials? Only like terms can be combined when adding or subtracting polynomials. Therefore, you are collecting like terms. They MUST contain the same variable and eponentor they are not like terms and therefore can not be combined. E. Only 2 terms can be combined with other 2 terms. Therefore, 2 and cannot be combined because they don't fit the rule for like terms. There are the same variable but not the same eponent. 9
Algebra Tiles can help us to visualize how to add/subtract polynomials by combining like terms: 2 y 2 y 2 y 2 y If an algebra tile is WHITE, then the sign of the term is NEGATIVE. However, if it is any other color, then the sign of the term is POSITIVE. Therefore, when adding a WHITE tile with a COLORED tile of the SAME term, the result will be zero, and they will cancel each other out. 0
A polynomial can be represented using algebra tiles. 2 2 Now drag the algebra tiles to represent the polynomial 4 2-2 + 5. 4 2-2 + 5 2 2 2 2
Let's try modeling some polynomials by dragging the algebra tiles: 2 2 3 2-2 + 4 2 2 2 2
Now model: 2 +3-2 2 2 2 +3-2 2 3
Now, let's add the two polynomials we just represented: (3 2-2 + 4) + ( 2 + 3-2) + Let's have a volunteer come up to group our like terms together 2 2 2 2 4
After combining like terms, our algebra tiles should look like this: 2 2 2 2 We need another volunteer to come up to cancel out our positive and negative like terms. 5
After canceling, our algebra tiles should look like this: 2 2 2 2 Can you write the polynomial that is now represented after we added: (3 2-2 + 4) + ( 2 + 3-2)? If you calculated 4 2 + + 2, you're right! Give yourself a hand! 6
2 Now, let's subtract: (3 2-2 + 4) - ( 2 + 3-2) 2 2 Start by dragging tiles out to represent the first polynomial. 2 2 Now, that our first polynomial is represented we need to take away the 2nd one from the st. Any Volunteers?? 7
After subtracting and combining like terms, our algebra tiles should look like this: 2 2 Can you write the polynomial that is now represented after we subtracted: (3 2-2 + 4) - ( 2 + 3-2)? If you calculated 2 2-5 + 6, you're right! Give yourself a hand! 8
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Now it's time for you to practice adding and subtracting some polynomials by yourselves. Remember to use your algebra tiles if you get stuck. There are also more eamples in your tetbook in the pages that precede your homework questions. So now go to your tetbook pg 5-52 #-8, 0 23
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