Presentation for the lesson "Addition and subtraction of polynomials". Presentation "Addition and subtraction of polynomials" A monomial is a product
Algebra Lesson Plan Grade 7
"Addition and subtraction of polynomials"
Type of lesson: lesson learning new material.
Equipment and materials: computer, projector, interactive whiteboard.
Educational: introduce the rule of addition and subtraction of polynomials; teach how to apply the rule when simplifying an expression; to consolidate the skills of partially exploratory cognitive activity: to be aware of the problem, to draw conclusions and generalizations.
Developing: to excite students' interest in educational material and cognitive actions in which the above skills are formed; development of logical thinking, intuition, attention; development of the ability to independently solve educational problems and work with additional literature.
Educational: to instill interest in the subject; the formation of communication skills, the ability to work in a team.
During the classes.
I. Organizational moment
Polynomials are the foundation on which the majestic edifice of algebra rests. Actions with polynomials are widely used in solving various kinds of exercises both in the 7th grade and in the senior grades. Historical information.
The topic “Polynomials” is a very important topic in algebra. Many scientists have worked on this topic. In 1799, the German scientist Gauss proved the fundamental theorem of the algebra of polynomials with complex coefficients, at the end of the 18th century. French mathematician Bezout proved the fundamental polynomial theorem with real coefficients.
II. Updating the basic knowledge of students
Let's check how you learned the material of the last lesson!
III. Learning new material
So, in today's lesson, we have to find out what happens as a result of adding two or more polynomials or subtracting from one other polynomial
a) Sum the polynomials 5x 2 + 2x - 1 and 7x + 4 and convert it to a polynomial of standard form. The teacher decides and explains, with the involvement of students.
b) Compose the difference of the polynomials 5x 2 + 2x - 1 and 7x + 4 and transform it into a polynomial of standard form.
Ask students to draw conclusions.
Adding and subtracting polynomials again results in a polynomial .
Find the rule in the textbook and review the examples on page 109 of the textbook.
In order to perform the inverse problem - to represent a polynomial as a sum or difference of polynomials, you must use the rule:
If a plus sign is placed before the brackets, then the terms that are enclosed in brackets are written with the same signs; if a minus sign is placed in front of the brackets, then the terms enclosed in brackets are written with opposite signs.
For example, 3x 3 -2x 2 -x+4=3x 3 -2x 2 +(-x+4)
3x 3 -2x 2 -x+4=3x 3 -2x 2 -(x-4)
Algorithm for addition and subtraction of polynomials
Expand brackets
Bring Like Members
Two polynomials whose sum is zero are called opposite.
Fill the gaps:
a) (2a -3b) + _____________ \u003d 0
b) (7 a 2 - 12a + 4) - (___________) = 0
c) (__________) + (-4a +3b) = 0
d) (___________) + (-3a 2 -2a +1) = 0
IV. Consolidation of the studied material
1. Find the algebraic sum of polynomials
a) (7x-19y) -(18y -3x) + (6x-16y)
b) (x 3 -2x 2 -x-7) - (-3x -2x 2 + x 3 +5)
2. Solve the equations:
(2x - 1) + (- x + 5) = 2
(43 - 12x) - (- 7x + 33) = -2
(2x - 10) - (3x - 4) = 6.
Solve at the blackboard No. 3.35 (h), No. 3.39 (h)
Fizkultminutka.
V. Primary control of mastering the material
Checking the test results.
VI. Homework
P. 3.5, No. 3.35(n), 3.39(n)
VII. Lesson summary
Review the rules for adding and subtracting polynomials.
Orally solve No. 3.34(1 - 4)
IX. Reflection.
The children are invited to choose a token with a certain color:
Black - boring, not interesting. Blue is not always clear. Green is interesting.
This survey allows you to assess the quality of the lesson and adjust it for further use.
Lesson summary: "Addition and subtraction of polynomials"
Bondarenko Marina Eduardovna, teacher of preschool I-III levels No. 101 of the city of Donetsk, Donetsk regionMaterial Description: summary of an algebra lesson for students in grade 7 on the topic "Addition and subtraction of polynomials." The lesson is focused on the textbook "Algebra, Grade 7" edited by S.A. Telyakovsky, Moscow, 2016
The purpose of the lesson:
- the formation of students' ability to perform addition and subtraction of polynomials, to apply the learned theoretical material in practice
- development of logical thinking; development of skills in mathematical terms
- formation of a conscious attitude to the acquisition of new knowledge and skills
Lesson type: learning new material
During the classes
I. Organizational moment
Greeting students, checking readiness for the lesson
II. Updating of basic knowledge
In order to move on to the study of new material, we need to repeat the material of the previous lesson. And for this we will conduct a mathematical dictation.
Mathematical dictation
1. What is the sum of monomials called? (polynomial)
2. The monomials that make up the polynomial are called. . . (members of the polynomial)
3. If the polynomial consists of two terms, then it is called. . . (binomial)
4. A monomial is a polynomial consisting of (one member)
5. If the terms have the same letter part, then they are called. . . ( similar)
6. If each term of a polynomial is a monomial of the standard form, and this polynomial does not contain similar terms, then it is called. . . (polynomial of standard form)
7. The degree of a standard form polynomial is called (the greatest degree of its monomials)
Having written a dictation, the correct answers are displayed on the slide. Students give points to each other through peer review.
III. Motivation
What are expressions in parentheses called?
What actions with polynomials written in brackets need to be performed?
Tell me, what are we going to do in class today?
So, the topic of our lesson is "Addition and subtraction of polynomials"
What are the goals of our lesson? (Students answer)
IV. Learning new material
Let's get back to our task. So, make a plan on how to add (group 1) or subtract (group 2) a polynomial.
Students offer a plan for adding (subtracting) polynomials for discussion.
We write the conclusion in a notebook in the form of an algorithm.
While pronouncing this algorithm, two students at the blackboard write down the solution to the task. (all others in notebooks)
V. Consolidation of the studied material
What types of assignments can be offered to us on this topic? (textbook work)
- Convert to standard form polynomial
- Simplify expressions
- Find expression value
- Solve the equation
Work on multimedia and textbook
No. 2 Find the value of the expression
#3 Prove that the value of the expression does not depend on the variable
#4 Solve the equation
Next, students are invited to solve independently tasks from the textbook, followed by a check with an explanation.
№ 587, 595,
№ 597, 605
№ 602, 603
For repetition No. 612 (1st column)
VI. Lesson summary
What new did we learn today? What have you learned?
Homework Learn item 26, answer questions on page 134 solve No. 589, 598, 606
Presentation on the topic: Addition and subtraction of polynomials
- Warm-up "Own game"
- Myths and mathematics
- Game "Arrow"
- Pair work "Don't let me down"
- Constructor
Slide 2-Category Selection
This slide is the main game board. You go here to begin the game, and you return here after each Question/Answer slide. This is where the “contestant” selects one of the five categories and a dollar value for the question. The higher the value, the more difficult the question. When you open this slide, the categories appear one at a time, and the dollar values appear at random with an accompanying laser beep. Here's how it works: if the contestant selects the first category for $300, you would click on the $300 text under
Polynomials
monomials
From theory
Properties
degrees
the 1st category(i.e., the 3rd dollar box in column one). As a result, the corresponding Question/Answer slide will automatically appear. Once the question, and then the answer, for that slide have been shown, you will click on the arrow in the bottom right of that slide to return to this main slide. When you return to this slide, the dollar amount for the box you selected will have changed from white to blue to show that that particular question has already been used. Below, you will see how to tailor the game for your particular categories.
Five different categories are used in the game. The category names appear at the top of the columns on this slide and on the five associated Question/ Answer slides (one for each dollar value). Rather than changing all of these separately, you will use the Replace command to change each placeholder category name only once.
1. Under Edit , choose Replace
- Type the placeholder name for category 1 as shown in the pop-up at the right. Type in your
- Type the placeholder name for category 1 as shown in the pop-up at the right.
- Type in your category name (e.g., Mixed Numbers) under Replace with:
- The Replace pop-up should now look like the one on the right, only with your category name.
- Click the Replace All button to make the changes.
You will then see this pop-up
- You will then see this pop-up
- Click the OK button. This replaces the six occurrences of the specified placeholder category name with your category name. After this, the top of the slide will look like this:
Notice that in this case, “Mixed Numbers” doesn’t fit on the line. To fix this, simply click on the text right before the “N” and press Backspace followed by Enter. Now it's on two lines:
2. Now, repeat Step 1 for the remaining four category placeholder names:
Slide 3-Question/Answer (Cat1, $100)
This slide is the first Question/Answer slide. It corresponds to Category 1 for $100. Once you have followed the instructions on Slide 2 to replace category name placeholders with your actual categories, the text “Cat1” on this slide will be replaced with your 1st category name.
When you click on Category 1 for $100 on the main slide, this slide opens automatically, with the Question appearing at the top. (Note: On TV Jeopardy, the contestant is actually shown an
Properties of degrees for 10
Perform transformations:
answer and is asked to offer a related question. Since this concept is sometimes difficult to understand and implement, this PowerPoint version shows a question followed by the corresponding answer.)
One way to play the game in class is to set up three teams. For each round, have one person from each team stand up as contestants. Have one pick the category and dollar value; click on that box and then ready the question that appears. Call on the first contestant that raises his or her hand for the answer. If they are correct, their team gets corresponding points or dollars (e.g., 1 point for each $100). If the first contestant misses the question or does not answer quickly enough, his or her team loses the corresponding points. Then, offer the question to the remaining two contestants in order of their raised hands. After the question has been correctly answered, or after all three contestants miss it, or after no contestant wants to try, return to the main slide by clicking on the yellow arrow. The current contestants then sit down, and the game moves to the next round.
Note that this Jeopardy game does not have a Double Jeopardy question.
To tailor this slide, follow these instructions:
You are now ready to put in your questions and answers, but you might want to go ahead and save this file first, using Save As and giving it a new name-one that makes sense for this particular Jeopardy game (e.g., Fractions Jeopardy) .
- If your Question is short, simply double click on the word “Question” and type in your specific question (e.g., “50% of 150” or “Capitol of France”). If the text you enter will not fit on one line, there's room for two lines at this font size. If you need more room, reduce the font size by triple clicking on the text and using the Font Size selector in the toolbar. In some cases, your question may need a drawn figure or graphic. You can use PowerPoint features to draw the figure you need or to insert graphics. A few examples are shown below.
- Double click on the word “Answer” and type in your answer in the same way.
- Do the same steps to tailor the remaining Question/Answer slides, remembering to make questions of higher dollar value more difficult. Also remember to save your work.
Example Questions:
Properties of degrees for 20
Perform transformations:
Welcome to Power Jeopardy
Calculate:
Properties of degrees for 30
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Calculate:
Properties of degrees for 40
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Name the coefficients
monomial:
Monomials for 10
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Determine the degree
monomial:
Monomials for 20
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Monomials for 30
Bring monomial to standard form
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Represent in the form
monomial square:
Monomials for 40
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
From theory for 10
Formulate a definition
polynomial
A polynomial is called
sum of monomials
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Formulate a definition
monomial
A monomial is a product
numbers, variables
and their degrees
From theory for 20
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
What monomials
called similar?
monomials that differ
only from each other
coefficients are called
similar
From theory for 30
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
What is a ratio?
The numerical factor of the monomial,
written in standard
form called
coefficient
From theory for 40
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Give similar
Polynomials in 10
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Give similar
Polynomials for 20
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
What is the degree
polynomial?
Polynomials for 30
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
Find the value
expressions
Polynomials for 40
Welcome to Power Jeopardy
© Don Link, Indian Creek School, 2004
You can easily customize this template to create your own Jeopardy game. Simply follow the step-by-step instructions that appear on Slides 1-3.
The appearance of some mythical characters consists
from the head and torso, taken from different creatures.
Decipher their names.
character
ANSWER
Centaur
Minotaur
Sphinx
Chimera
Exit
2a+4c a-3c 3a+c 4a-2c
5x-3y -2x+y 3x-2y x-y
2a+4s a-3s a +7s -10s
5x-3y -2x+y 7x-4y -9x+5y
1 option
6a - 5a = a
Option 2
- 3a + (-5 b) = -8b
3 a
3 a
2 a
3 option
- 4c - 6c = -10c
4 option
-12x+ 10 x = - 2 x
- 90 points and above - score "5"
- 70 - 89 points - score "4"
- 50 - 69 points - score "3"
- below 50 points - score "2"
"4" - No. 596, No. 606 (a)
"5" - No. 596, No. 606 (a), No. 609 *
Presentation and handout for the lesson in grade 7 "Addition and subtraction of polynomials"
Goals and objectives of the training session:
- Educational:
- introduce students to the rules of addition and subtraction of polynomials;
- to form the skills and abilities of adding and subtracting polynomials, bringing like terms and opening brackets.
- Educational:
- to form the ability to carry out mental operations: highlight the main thing, systematize, analyze;
- develop literacy of mathematical writing, memory, listening skills.
- Educational:
- instill diligence, perseverance, accuracy, accuracy;
- to form a positive attitude to the subject and interest in knowledge.
Equipment: textbook, blackboard.
Download:
Preview:
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Slides captions:
Addition, subtraction of polynomials. MBOU lyceum No. 1, Volzhsky, Volgograd region. Mathematics teacher: Korotova I.V.
Lesson outline. Theory Preparation for UPD Practice Homework Learning new material Individual survey
Theory Monomial. Monomial of the standard form. similar terms. Reduction of similar terms. Polynomial. Polynomial of standard form. Algorithm for reducing a polynomial to a standard form. Expanding brackets preceded by a plus sign (minus sign)
Choose monomials: 2 x + y; 3xy; 27ab2; gh + 4; 2m+5n; one ; 1 + k . Theory
Give similar terms: -11ak + 8ak + 5ak; 7x 3 y 2 - 12 + 4x 2 y - 2y 2 x 3 + 6 Theory
Write the polynomial in standard form: 6 ab - 2 b 2 - 6 ba + 5 a 2 + 0.6 b 2 - 4 a b a + 2 a 2 b + 0.2 a 2 b 2 - 2 a 2 b 2 Theory
Open brackets. - (32 - 2a 2 b - 5b + 4a) + (-7 x + 8 y - 5xy + 7) Mutual check
Mutual verification. Select the monomials: Mark 2 3 6 Give like terms: 2ak 5x 3 y 2 + 4x 2 y - 6 Write the polynomial in standard form -1.4 b 2 +5a 2 -1.8 a 2 b 2 - 2a 2 b Open brackets : -32+2a 2 b + 5b – 4a -7x + 8y – 5xy + 7 Final grade: Lesson outline
Individual survey. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Individual survey. Low level 1 2 3 4 Medium level 1 2 3 4 High level 1 2 3 4 Class work Lesson outline
1. Low level Standardize the polynomial: Individual survey
2. Low level Standardize the polynomial: Individual survey
3. Low level Standardize the polynomial: Individual survey
4. Low level Standardize the polynomial: Individual survey
1. Average level Present the polynomial in standard form: 16a (-a 2 b) + 18a 3 b - 12aa b + 14a 2 b Individual survey
2. Intermediate level Standardize the polynomial: 5 x (-4x 4) - 2 x 2 Z x 3 + 27 x 5 - x 6 Individual survey
3. Average level Present the polynomial in standard form: 2y y 3 - Zu 2 4y 2 + 6y 4 - 8 y 4 - 11 Individual survey
4. Average level Present the polynomial in standard form: 23x 3 - 7 xx 2 y + 6x 2 x - 2 x 2 8y + 4 Individual survey
1. High level Express the polynomial in standard form: 3 a 2 b n+2 + 5 a 0.2 a b n+2 - 4 a 2 b n 0.5 b 2 + 2 a 2 b n bb Individual survey
2. High level Standardize the polynomial: 3.2x 2 x n x - 3.4 x n+1 2x 2 - 4.8x n+2 0.1x + x n+3 Individual survey
3. High level Standardize the polynomial: 0.3 y n+3 y 2 - 0.12y 2 y 0.1 y n+2 - 1.6 y n+2 yyy – 3 Individual survey
4. High level Standardize the polynomial: 3x n-2 x 5 -2x n 7x 2 x+4y n+1 4y 0.2y-12y n+1 0.1y 2 Individual survey
Write down the sum of polynomials - 2 a + 5 b and - 2 b - 5 a 5y 2 + 2y - 3 and 7y 2 - 3y + 7. Write down the difference of polynomials - 2a + 5b and - 2b - 5a 8y 2 + 5y + 3 and 5y 2 - 3y + 7 .
Write down the difference of polynomials - 2 a + 5 b and - 2 b - 5 a 8y 2 + 5y + 3 and 5y 2 - 3y + 7.
Simplify the expression. (– 2 a + 5 b) + (– 2 b – 5 a) = Check
Simplify the expression. (5y 2 + 2y - 3) + (7y 2 - 3y + 7) = Check
Simplify the expression. (– 2 a + 5 b) + (– 2 b – 5 a) = – 2 a + 5 b – 2 b – 5 a = – 3 b – 7 a
Simplify the expression. (5y 2 + 2y - 3) + (7y 2 - 3y + 7) = 5y 2 + 2y - 3 + 7y 2 - 3y + 7 = 12y 2 - y + 4
Simplify expression (- 2 a + 5 b) - (- 2 b - 5 a) = Check
Simplify expression (8y 2 + 5y + 3) - (5y 2 - 3y + 7) = Check
Simplify the expression (- 2 a + 5 b) - (- 2 b - 5 a) = - 2 a + 5 b + 2 b + 5 a = 7 b + 3 a
Simplify the expression (8y 2 + 5y + 3) - (5y 2 - 3y + 7) = 8y 2 + 5y + 3 - 5y 2 + 3y - 7 = 3y 2 + 8y - 4 Lesson outline
Addition and subtraction of polynomials.
The rule of addition (subtraction) of polynomials. Let two polynomials be given. To add them, they are written in brackets and put a plus sign between them. When subtracting, we put a minus sign between the brackets. In order to find the algebraic sum of several polynomials, you need to open the brackets according to the appropriate rule and bring like terms. As a result of addition (subtraction) of polynomials, a polynomial is obtained. Lesson outline
Practical tasks. No. 587 (a, d) No. 588 (b) Lesson scheme
Homework: Item 26 No. 589 (a, c) No. 595 (a) No. 612 (b)
a - b b a - x - y 2 x - y 3 y 3 a 0
2 a a - b b b - a a - b - b b + a 0 - x - y 2 x - y - x + 2 y 3 y 0 - 3 y x – 2 y - 2 x + y x + y
Low level Medium level 3 a 2 b 3 + 5 a 0.2 a b 2 - 4 a 2 b 2 0.5 b + 2 a 2 b 2 High level 5 x n +4 2y - 10x n y 4x 4 -14 x n y 2 +18x n yy Check
Low -a b 2 Intermediate a 2 b 3 + 3 a 2 b 2 High -30x n +4 y + 4 x n 2 Lesson outline
Preview:
one . Mutual verification.
2. Class work
Answer: | mark |
one . Mutual verification.
2. Class work
Answer: | mark |
3 . Write in the cells of each square such expressions that their sum in each column, each row and each diagonal is equal to the expression written in the triangle:
Preview:
Express the polynomial in standard form:
16a(-a 2 6) + 18a 3 6 - 12aa6 + 14a 2 6
5 x (-4x 4) - 2 x 2 W x 3 + 27 x 5 - x 6
2y y 3 - Zu 2 4y 2 + 6y 4 - 8 y 4 - 11
23x 3 - 7 xx 2 y + 6x 2 x - 2 x 2 8y + 4
3.2x 2 x n x - 3.4 x n +1 2x 2 - 4.8x n +2 0.1x + x n +3 .
0, 3 y n +3 y 2 - 0, 12 y 2 y 0.1 y n + 2 - 1.6 y n +2 yyy – 3
3x n-2 x 5 -2x n 7x 2 x+4y n+1 4y 0.2y-12y n+1 0.1y 2
Preview:
Mutual verification.
Choose monomials: | |
- Addition and subtraction of polynomials
- Algebra lesson
- in the 7th grade
- Teacher MOSSh No. 29 Khachankova T.V.
- Educational:
- To test the knowledge, skills and abilities of students on the topic of the sum and difference of polynomials.
- Educational:
- Raise interest in algebra by applying interesting tasks using various forms of work.
- Developing:
- To develop the ability of students to work both individually (independently) and collectively (work in pairs and in a group).
- Develop the ability to assess your strengths, using tasks of different levels of complexity.
- Answer:
- Answer:
- Answer: a
- After opening parentheses:
- "Brain Ring"
- In the Middle Ages, people who knew how to produce THIS IS AN ARITHMETIC OPERATION could almost be counted on the fingers. They were respectfully called "masters ...".
- They moved from city to city at the invitation of merchants who wanted to put their accounts in order.
- In Italy, the saying is still preserved: “This is a difficult task - ...”. This is what they usually say when they face an almost insoluble problem.
- What is this action?
- A man who wanted to be both a lawyer and a philosopher, but became a mathematician. He was the first to introduce a rectangular coordinate system.
- What is the name of this person?
- This word among jewelers means the proportion of gold in the product, equal to 1/24 and a unit of mass equal to 200 mg.
- What is this value?
- Before us is the picture of Bogdanov-Belsky "Oral Account". 11 students find in their minds the meaning of the expression written on the blackboard by teacher Rachinsky. Let's help these students find the answer. Example written on the board:
- What answer?
- Name an ancient geometrical instrument, which, according to the Roman poet Ovid (Iv.), was invented in ancient Greece.
- Clue. We often use this tool in algebra and geometry lessons.
- What is this geometric tool?
- To the question: "How many fish did you catch?", the fisherman replied: "A half of eight, six without heads and nine without a tail."
- How many fish did the fisherman catch?
- How old is the ancient Oak, if the number-lovers reported that it has been standing in this place for exactly 2964 months.
- How old is the oak tree?
- This number comes from the Latin word "solus".
- Both in Ancient Russia and in Ancient Rome it was associated with the Sun, while among the ancient Greeks this number was not considered a number.
- What is this number?
- The player bets $30. When he wins, he returns his bet plus $60. He spends a third of the total amount on a gift for his wife, $ 10 on a taxi and 10% of the remaining amount he gives to the driver for a tip.
- How much money does he have left?
- Thank you for your attention!