What are Polynomials?
(Adding/Subtracting/Simplifying)
AUTHOR: Amber Blakley
DATE LESSON TO BE TAUGHT: ?? 2 days possibly 3days
GRADE LEVEL: Algebra I; 8th 9th or 10th
CONCEPT(S): Students will be taught what polynomials are. They will also be able to add and subtract them. The will need to know the laws of powers in order to do this. They will also be able to simplify polynomials.
OBJECTIVES:
Performance Objectives
TEKS:
(A.4) Foundations
for functions. The student understands the importance of the skills
required to manipulate symbols in order to solve problems and uses the
necessary algebraic skills required to simplify algebraic expressions and solve
equations and inequalities in problem situations.
The student is expected to:
(A) find
specific function values, simplify polynomial expressions, transform and solve
equations, and factor as necessary in problem situations;
(B) use the
commutative, associative, and distributive properties to simplify algebraic
expressions;
MATERIALS LIST and ADVANCED
PREPARATONS:
Pencils/pens
Worksheet
Bags with letters, preferable just
three letters and then bunch of numbers.
ENGAGEMENT:
|
Teacher will do: |
Student will do: |
Probing Questions: |
|
Have the chalk board covered with polynomials and non-polynomials. Write the polynomials in one color and the non-polynomials in a different color, but break the non-p into different groups of: negative exponents, has variable in denominator, variable inside radical, fractional powers. Help students figure out, which are which. Make a list on adjacent board of different groups they come up with. |
Try to decide which are polynomials and which are not The students should start by trying to divide the one they see on the board into different groups. |
Which ones look different? Which ones look the same? What traits do they share in common? WhatŐs a way you could categorize all the objects on the board? |
EXPLORATION:
|
Teacher will do: |
Student : |
Probing Questions: |
|
Go over proper definition of a polynomial: terms, leading terms, and constant. |
Writes down notes. |
|
|
Write a polynomial on the board with like terms. |
The ones with xŐs. ones with just numbers, ones with xŐs to a certain power. Add the numbers together. Add like terms together. |
What are some possible like terms? How might we be able to combine some of the terms? |
|
Split the students in groups of 3-4 and hand out bags. Instruction the students to work with their group members in constructing three different polynomials. |
Will work on constructing polynomials. |
|
|
Go around room to make sure students are working and understanding the idea. If students have like terms have them simply. |
|
Can you simplify or combine to fewest possible terms? Can you mix letters in the same polynomial? Why or why not? |
|
Once each group has finished have the students write their polynomials on the board. Then have the students explain how they got each polynomial and why they chose what they did. |
Present polynomials and explain their logic behind each one. |
Why did you pick that letter? Why did you mix? Why didnŐt you mix letters? Can you combine more terms? Why would you want to combine more terms? Would it be okay not to combine more terms? |
|
Give worksheet with more difficult terms and let students work in groups to try and figure out how to simplify these polynomials. Tell the groups to make a list of properties that apply to this process. |
Divide into groups and work on polynomials. |
|
|
Bring class back together to discuss answers and things they found out. Make list on blackboard to show different techniques different groups used. |
Students talk about combining like terms. Students discuss different strategies for adding like terms and subtracting like terms. |
What strategies did your group use? What was the thought process behind it? Why does that seem right? |
EXPLANATION
|
Teacher will do: |
Student will do: |
Probing Questions: |
|
Go over what are like terms and what arenŐt. |
Think about how this relates to their polynomials and why. |
|
|
The proper way to simplify terms. You can gather all the like terms and kept them together. Whether a term is x squared or just x doesnŐt change that is the xŐs proper or identify you canŐt change a x squared by adding you can change ho many you have, but thatŐs it. Just like if you have pens and pencils and make an equation you can change the amount of either you have, but you canŐt change the fact that one is a pencil and the other is a pen. |
|
|
|
The proper way to add and subtract polynomials. The teacher will need to clarify misconceptions about adding and subtracting: x+x isnŐt x squared and so on. |
Well why canŐt I do it this way? |
|
EXTENSION:
|
Teacher will do: |
Students will do: |
Probing Questions: |
|
Ask students to make their own polynomial. Evaluation of polynomials, if x=a number then what will the numerical value of the polynomial be? |
Come up with a polynomial and evaluate it at the given value. |
What will your polynomial be at 2? 5? |
|
Have a complete of students come up to the board and explain what they did. |
Will share answer with class. |
Why did you take that step? Could you have done it differently? Did anyone else to it differently? |
|
Polynomials are useful for representing shapes because they are flexible. This one reason that bits of cubic polynomials form the basic drawing elements in many computer drafting programs. This is a good example of how polynomials can be related to real world application. |
|
|
EVALUATION:
|
Teacher will do: |
Student will do: |
Probing Questions: |
|
Take up worksheets and grade them. |
Turn in worksheet on appropriate day. |
|
|
Teacher can assign addition problems or quiz, depending on what may be needed. |
|
|
|
|
||
Name:_________________________
Date:__________________________
Period:_________________________