Lesson type: lesson on learning new material.
The purpose of the lesson: to systematize, expand and deepen the knowledge and skills of students in bringing similar terms of expressions containing square roots. To promote the development of observation, the ability to analyze, and draw conclusions. Encourage students to exercise mutual control.
Equipment: cards with numbers, projector, presentation.
Lesson steps:
- Organization of the start of the lesson. Setting a goal. Repetition of covered material.
- Oral exercises. Get the picture.
- Historical information.
- Learning new material.
- Independent work with mutual control.
- Summing up.
- Homework.
- Reflection.
Lesson progress
I. Organization of the start of the lesson. Communicating the topic and setting the goal.
Teacher. If we open the Big Encyclopedic Dictionary, we can read what the word “transformation” means. So, “Transformation is the replacement of one mathematical object with a similar object obtained from the first according to certain rules.”
In the Explanatory Dictionary of S.I. Ozhegov we read: “Transform - ... completely remake, transform from one type to another, change for the better.”
The purpose of mathematical transformations is to bring the expression to a form more convenient for numerical calculations or further transformations.
Until now, we have carried out transformations only of rational expressions, using for this the rules of operations on polynomials. A few lessons ago we introduced a new operation - the square root operation.
Let's review the basic information about the arithmetic square root.
Prepare cards with numbers 1, 2, 3 for oral exercises. To answer, raise the card with the number of the correct statement.
Arithmetic square root of a number a called:
1) A number whose square is equal to a.
2) A number equal to a.
3) A non-negative number whose square is equal to a.
„ To enter a factor under the sign of the root, you need to:
1) Multiply radical expressions;
2) Square the factor;
3) Write the square of the multiplier under the root.
... To move the multiplier beyond the root sign, you need to:
1) Present the radical expression as a product of several
multipliers;
2) Apply the rule of the square root of the product of non-negative
multipliers.
II. Get the picture.
Solve the examples and color the box with the correct answer. If everything is done correctly, you will get a picture. Appendix 1.
Answer: square root sign. Appendix 2.
III. Historical information.
The square root sign was introduced by practical necessity. Knowing the area, our ancestors in the 16th century tried to calculate the side of the square. This is how the operation of extracting the square root appeared. But the modern form of the sign was not determined immediately.
Beginning in the 13th century, Italian and many European mathematicians denoted the root with the Latin word Radix (root) or R x for short. In the 15th century they wrote R 2 12 instead of . In the 16th century they wrote V‚ instead of Ö. The Dutch mathematician A. Girard introduced a notation for the root that is close to the modern one.
It was not until 1637 that the French mathematician Rene Descartes used the modern root sign in his Geometry. This sign came into general use only at the beginning of the 18th century.
IV. Learning new material.
Simplify the expression:
V. Independent work.
| Option 1. | Option 2. |
 |
 |
VI. Summing up.
Municipal government educational institution
"Novonikolsk secondary school"
Bykovsky municipal district of Volgograd region
Algebra lesson in 8th grade
Completed: math teacher
Novonikolskoye – 2015
Algebra lesson in 8th grade
on the topic “Converting expressions containing square roots”
Lesson objectives:
repeat the definition of the arithmetic square root, the properties of the arithmetic square root;
consolidate the skills and abilities of solving examples on identical transformations of expressions containing arithmetic square roots;
teach to free yourself from irrationality in the denominator of a fraction;
develop skills of self-control and mutual control, interest in the subject.
Equipment: multimedia projector , interactive whiteboard, assessment sheets, test cards, homework cards.
Lesson progress:
I . Organizational moment
Today in the lesson we will continue transforming expressions containing square roots. The assessment sheet will help you summarize today's lesson. Sign your sheets and answer the first question, “Mood at the beginning of the lesson,” by choosing one of the emoticons.
There's something about mathematics
causing human delight.
F. Hausdorff
II . Oral work
1) Frontal survey.
Give the definition of an arithmetic square root. ( The arithmetic square root of a number is a non-negative number whose square is equal to a).
List the properties of the arithmetic square root. ( The arithmetic square root of the product of non-negative factors is equal to the product of the roots of these factors. The arithmetic square root of a fraction whose numerator is non-negative and whose denominator is positive is equal to the root of the numerator divided by the root of the denominator).
What is the arithmetic square root of x 2? ( |x|).
What is the value of the arithmetic square root of x 2 if x≥0? X X. -X).
2) Oral counting: Come on, put the pencils aside!
No dominoes. No pens. No chalk.
"Oral counting!" We're doing this thing
Only by the power of mind and soul.
The numbers converge somewhere in the darkness,
And the eyes begin to glow,
And there are only smart faces around.
Because we count in our heads!
Calculate orally:
1. Remove the multiplier from under the root sign:
2. Enter the multiplier under the root sign:
3. Square:
4. Give similar terms:
III . Dictation:
| Option-1 | Option-2 | Answers: | Answers: |
IV .PHYSICAL MINUTE
V . Historical background
Radix - has two meanings: side and root. Greek mathematicians, instead of “extracting the root,” said “find the side of the square from its given value (area)”
Beginning in the 13th century, Italian and other European mathematicians denoted the root with the Latin word Radix, or R for short (hence the term “radical”).
German mathematicians of the 15th century. used to denote the square root
dot ·5
Later, instead of a dot, they began to put a diamond ¨5
Then Ú 5. Then the sign Ú and the line began to be connected.
VI stage. Working on new material.
If the denominator of an algebraic fraction contains a square root sign, then it is usually said that the denominator contains an irrationality.
The problem is posed: “Which expression is easier to calculate: or? Why? (Because dividing by a rational number is easier than dividing by an irrational number.)
Today in class we will study the topic
"Liberation from irrationality in the denominator of a fraction." Let's try to free ourselves from irrationality in the denominator in the following examples:
A); b) ; V); G).
By what expression should the denominator of the fraction be multiplied so that the roots “disappear”? What needs to be done to ensure that the fraction does not change? We get the following solution record.
d)= 
Let's draw a conclusion.
A transformation in which the roots in the denominator of a fraction disappear is called liberation from irrationality in the denominator. We saw two main methods of liberation from irrationality in the denominator:
VII . Pin a topic: Textbook. Page 98 No. 431(a,b,g,h), No.433(a,b,c)
Free yourself from irrationality in the denominator of the fraction:
A) ; b) c); G) .
VII I . Test (work in pairs)
The English philosopher Herbert Spencer said: “The treasures are not the knowledge that is deposited in the brain like fat, the treasures are those that turn into mental muscles.”
At this stage of the lesson, you need to apply your knowledge to solve exercises during the test. ( test attached)
Self-test:
Code of correct answers: Option I – 12312 Option II - 32132.
Homework: No. 431 (z, i), No. 432, No. 433 (g, e, f)
IX . Lesson summary:
Complete the assessment sheet completely. Lesson grades.
I want to finish the lesson a poem by the great mathematician Sofia Kovalevskaya.
The sky will be covered with black haze,
This poem expresses the desire for knowledge, the ability to overcome all obstacles that come along the way. How did you and I overcome obstacles today? What did we do in class?
- Today we reviewed the definition and properties of the arithmetic square root; placing a multiplier behind the root sign, adding a multiplier under the root sign, abbreviated multiplication formulas; We became familiar with and consolidated some methods of converting expressions containing square roots. We expanded our horizons and found out who first introduced the modern root sign into general use.
Everyone worked fruitfully, actively and collectively during the lesson.
The lesson is over. Thanks everyone for the lesson!
QUESTIONNAIRE SHEET
F.I. student___________________________
1. Mood at the beginning of the lesson: a) b) c)
2. My perception of the lesson topic:
a) learned everything; b) learned almost everything; c) partially understood, I need help.
3.Score for dictation:
4. Number of incorrect test answers: _________
5. I worked in class:
a) excellent; b) good; c) satisfactory; d) unsatisfactory.
6. I rate my work as ______ (give a rating)
7. I rate the lesson _____ (give it a rating)
8. Mood at the end of the lesson: a) b c)
| Test I option 1. Simplify the expression 1) 2) 3) 2. Open the parentheses and simplify the expression: 1) 18; 2) 12; 3) 22. 3. Simplify: 1); 2) ; 3) . 4. Free yourself from irrationality in the denominator = 1) ; 2) ; 3) . 1) ; 2) ; 3); 4) | Test II option 1. Simplify the expression 1); 2) ; 3) 2. Open the brackets and simplify 1) 8; 2) 12; 3) 10. 3. Simplify: 4. Free yourself from irrationality in the denominator: 1) ; 2); 3) . 5. Remove the multiplier from under the root sign: 1) ; 2)
; 3) No knuckles, no pens, no chalk. Come on, put the pencils aside! "Oral counting!" We're doing this thing Only by the power of mind and soul. The numbers converge somewhere in the darkness, And the eyes begin to glow, And there are only smart faces around. Because we count in our heads!  Oral counting Take the multiplier out from under the sign root: Think a little  Oral counting
Think a little  Oral counting Square: Think a little  Oral counting Give similar terms: Think a little       III . Dictation: Option-1 Option-2 Answers: Answers:  
 German mathematicians of the 15th century. to denote the square root we used the dot ·5 Later, instead of a dot, they began to put a diamond 5 Then 5. Then the sign and the line began to be connected.   Peer review I option II option paragraph 19, page 96, example 3 № 431 (h, i), No. 432, No. 433 (d, e, f) If in life you even for a moment I felt the truth in my heart, If there is a ray of light through darkness and doubt Your path was illuminated with a bright radiance: Whatever your unchanging decision Fate has not appointed you ahead, The memory of this sacred moment Keep it forever like a shrine in your chest. The clouds will gather in a discordant mass, The sky will be covered with black haze, With clear determination, with calm faith You meet the storm and face the thunderstorm. |
Algebra lesson in 8th grade
Subject: General lesson.
Converting expressions containing square roots
Math teacher: Baiturova A.R. school kola-gymnasium No. 31, Astana
2012-2013 academic year
Target: repetition of the concept of a square root and its properties; developing the ability to simplify expressions and calculate square roots.
Tasks:
consolidate previously acquired knowledge, skills and abilities of students on the topic being studied;
consolidate skills in converting expressions containing square roots;
promote the formation of independent choice of solution method.
Lesson type: Improving students' knowledge of learning
Working methods:
Active (the process of cognition comes from students),
Visually - demonstrative,
Partially - search (we teach children to observe, analyze, compare, draw conclusions and generalizations under the guidance of the teacher),
Practical
Forms of work: whole class, individual..
Equipment: interactive whiteboard, PowerPoint slides, assessment sheets, test cards, homework cards.
Innovative technologies:
Computer training,
Activity approach to teaching (knowledge comes from the student),
Verbally productive (at the reflection stage),
Personally-oriented learning (every child will be able to answer).
Progress of the lesson.
I. Organizational moment
- Hello, sit down (Hello, sit down). Look at the topic of our lesson and tell what it would mean ( Look at our lesson and tell me what it means).
That's right, today in the lesson we will repeat the rules for transforming expressions containing square roots, transforming roots of a product, fraction and degree, multiplying and dividing roots, placing a multiplier behind the root sign, introducing a multiplier under the root sign, bringing similar terms and getting rid of irrationality in denominator of the fraction. The estimated page will help to sum up a today's lesson ( An evaluation sheet will help you summarize today's lesson.)
Sign the sheets of paper and answer the first question "Mood at the beginning of a lesson", having chosen one of smilies.( Sign your words and answer the first question “Mood at the beginning of the lesson” by choosing one of the emoticons).
II. Lesson topic message
Topic of our lesson: “Converting expressions containing arithmetic square roots.” (Slide No. 1)
There's something about mathematics
causing human delight. F. Hausdorff(Slide No. 2)
III. Oral work
1) Frontal poll. (Slide No. 3)
1.Give the definition of an arithmetic square root. (The arithmetic square root of a is a non-negative number whose square is equal to a).
2.List the properties of the arithmetic square root. (The arithmetic square root of a product of non-negative factors is equal to the product of the roots of those factors. The arithmetic square root of a fraction whose numerator is non-negative and whose denominator is positive is equal to the root of the numerator divided by the root of the denominator).
3.What is the value of the arithmetic square root of x 2? (|x|).
4.What is the value of the arithmetic square root of x 2 if x≥0? X<0? (х. –х).
2) Oral account ( Oral check) (Slide No. 4)
Come on, put the pencils aside!
No dominoes. No pens. No chalk.
"Oral counting!" We're doing this thing
Only by the power of mind and soul.
The numbers converge somewhere in the darkness,
And the eyes begin to glow,
And there are only smart faces around.
Because we count in our heads!
(Slide No. 5-8)
1. Remove the factor from under the root sign: ; 2) ; 3) ; 4) ; 5) ; 6) ; 7) ; 8) 
2. Enter the multiplier under the root sign: 1) ; 2) ; 3) ; 4) ; 5) ; 6) ; 7) ; 8)
3. Square (Squaring) : 2, 6, 7, 9, 11, 13,15, 18, 22, 25
4. Give similar terms:
IV. Work on the topic of the lesson
1) Individual work (Individual work) (Slide No. 9)
The green correspond to tasks of a basic level, yellow – to tasks of the raised level, red – to tasks of high level.(Green correspond to basic level tasks, yellow to advanced level tasks, red to high level tasks). Students choose the task at their own discretion. Three students, having received a task, solve it in their notebooks
level
Remove the multiplier from under the root sign:
1)
2)
3)
Enter the multiplier under the root sign:
1)
; 2)
; 3)
;
Compare the numbers:
1)
And; 2)
And;
level
Simplify the expression:
1) ; 2) ; 3) 
Find the amount:
1)
2) 
1) 
; 2) 
3rd level
Simplify the expression:
1) 
; 2) 
.
Transform the expression:
1) 
; 2) 
;
Open the parentheses and simplify the expression:
1) ;
2) 
; 3) 
;
2) Work with an interactive board. (Slide No. 10-13)
The rest of the students solve the following tasks:
1. Find the meaning of the expression:
1) 
2) 
3)
2. Transform the expression:
1) 
; 2) 
; 3) 
.
3. Simplify the expression:
1) 
; 2) 
; 3) 
.
4. Get rid of irrationality in the denominator:
1) 
; 2) 
; 3) 
; 4) 
.
VI. Historical information( Historical background) (Slide 14-26)
Radix has two meanings: side and root. Greek mathematicians, instead of “extracting the root,” said “find the side of the square from its given value (area)”
Beginning in the 13th century, Italian and other European mathematicians denoted the root with the Latin word Radix, or R for short (hence the term “radical”).
German mathematicians of the 15th century. to denote the square root we used the dot ·5
Later, instead of a dot, they began to put a diamond 5
Then Ú 5. Then the sign Ú and the line began to be connected.
VI. Test ( Test)
The English philosopher Herbert Spencer said: “Roads are not the knowledge that is deposited in the brain like fat, the roads are those that turn into mental muscles.”(Slide No. 27)
At this stage of a lesson it is necessary to apply the knowledge to the solution of exercises during implementation of the test.(At this stage of the lesson, you need to apply your knowledge to solving exercises during the test).
VII. Mutual testing ( Peer review) (Slide No. 28)
Code of correct answers: Option I – 3124111, option II - 2131222
VIII. Homework.(Slide No. 29)
Which number is smaller 
or 
?
B 2. Simplify the expression: 
,
at 
.
B 3. Follow these steps: 
.
Write detailed and well-founded solutions to the tasks in this part carefully and legibly on a sheet of paper.
C 1. Reduce the fraction: 
.
C 2. Take the square root of the expression: 
.
VIII. Lesson summary
Complete the assessment sheet completely. Marks for a lesson.
I want to end the lesson with a poem by the great mathematician Sofia Kovalevskaya. (Slide No. 30)
If in life you even for a moment
I felt the truth in my heart,
If there is a ray of light through darkness and doubt
Your path was illuminated with a bright radiance:
Whatever your unchanging decision
Fate has not appointed you ahead,
The memory of this sacred moment
Keep it forever like a shrine in your chest.
The clouds will gather in a discordant mass,
The sky will be covered with black haze,
With clear determination, with calm faith
You meet the storm and face the thunderstorm.
This poem expresses the desire for knowledge, the ability to overcome all obstacles that come along the way.
The lesson is over. Thanks for a lesson! ( Lesson is over. Thanks for the lesson!) (Slide No. 31)
Application
QUESTIONNAIRE SHEET
F.I. student___________________________
1. Mood at the beginning of the lesson: a) c)
2. My perception of the lesson topic:
a) learned everything; b) learned almost everything; c) partially understood, I need help.
3. Number of incorrect test answers: _________
4. I worked in class:
a) excellent; b) good; c) satisfactory; d) unsatisfactory.
5. I rate my work as ______ (give a rating)
6. I rate the lesson _____ (give it a rating)
7. Mood at the end of the lesson:
A)b) V)
Test 1 option
A 1. Calculate 
.
1) 7; 2) 
; 3) 5; 4) 
.
A 2. Calculate 
.
1) 7; 2) ; 3) ; 4) 4.
The video lesson “Transforming expressions containing the operation of extracting a square root” is a visual aid that makes it easier for a teacher to develop skills in solving problems containing expressions with a square root. During the lesson, we recall the theoretical foundations that serve as the basis for carrying out operations on numbers and variables present in radical expressions, describe the solution of many types of problems that may require the ability to use formulas for converting expressions containing a square root, and provide methods for getting rid of irrationality in the denominator of a fraction.
The video lesson begins by demonstrating the title of the topic. It is noted that earlier in the lessons transformations of rational expressions were carried out. In this case, theoretical information about monomials and polynomials, methods of working with polynomials, algebraic fractions, as well as abbreviated multiplication formulas were used. This video tutorial discusses the introduction of the square root operation for transforming expressions. Students are reminded of the properties of the square root operation. Among such properties it is indicated that after taking the square root of the square of a number, the number itself is obtained, the root of the product of two numbers is equal to the product of two roots of these numbers, the root of the quotient of two numbers is equal to the quotient of the roots of the terms of the quotient. The last property discussed is taking the square root of a number raised to an even power √a 2 n, which results in a number raised to the power a n. The properties considered are valid for any non-negative numbers.
Examples are considered that require transformations of expressions containing a square root. It is stated that these examples assume that a and b are non-negative numbers. In the first example, it is necessary to simplify the expressions √16a 4 /9b 4 and √a 2 b 4 . In the first case, a property is applied that determines that the square root of the product of two numbers is equal to the product of their roots. As a result of the transformation, the expression ab 2 is obtained. The second expression uses the formula for converting the square root of a quotient to the quotient of roots. The result of the transformation is the expression 4a 2 /3b 3.
In the second example, it is necessary to remove the factor from under the square root sign. The solution to the expressions √81а, √32а 2, √9а 7 b 5 is considered. Using the example of transforming four expressions, we show how the formula for transforming the root of a product of several numbers is used to solve similar problems. In this case, cases are separately noted when expressions contain numerical coefficients and parameters to an even or odd degree. As a result of the transformation, the expressions √81а=9√а, √32а 2 =4а√2, √9а 7 b 5 =3а 3 b 2 √ab are obtained.
In the third example, it is necessary to perform an operation opposite to that in the previous problem. To enter a multiplier under the square root sign, you also need to be able to use the formulas you have learned. It is proposed to introduce a factor in front of the brackets under the sign of the root in expressions 2√2 and 3a√b/√3a. Using well-known formulas, the factor in front of the root sign is squared and placed as a factor in the product under the root sign. In the first expression, the transformation results in the expression √8. The second expression first uses the product horse formula to transform the numerator, and then the quotient root formula to transform the entire expression. After reducing the numerator and denominator in radical expression, we get √3ab.
In example 4, you need to perform actions in the expressions (√a+√b)(√a-√b). To solve this expression, new variables are introduced that replace monomials containing the sign of the root √a=x and √b=y. after substituting new variables, the possibility of using the abbreviated multiplication formula is obvious, after which the expression takes the form x 2 -y 2. Returning to the original variables, we get a-b. The second expression (√a+√b) 2 can also be converted using the shorthand multiplication formula. After opening the parentheses, we get the result a+2√ab+b.
In example 5, the expressions 4a-4√ab+b and x√x+1 are factorized. To solve this problem, it is necessary to perform transformations and isolate common factors. After applying the properties of the square root to solve the first expression, the sum is converted to the square of the difference (2√a-√b) 2. To solve the second expression, you need to enter the factor before the root sign under the root, and then apply the formula for the sum of cubes. The result of the transformation is the expression (√x+1)(x 2 -√x+1).
Example 6 demonstrates the solution to a problem where you need to simplify the expression (a√a+3√3)(√a-√3)/((√a-√3) 2 +√3a). The task is solved in four steps. In the first step, the numerator is converted into a product using the abbreviated multiplication formula - the sum of the cubes of two numbers. In the second action, the denominator of the expression is transformed, which takes the form a-√3a+3. After the conversion, it becomes possible to reduce the fraction. The last step also applies the abbreviated multiplication formula, which helps to obtain the final result a-3.
In the seventh example, it is necessary to get rid of the square root in the denominators of the fractions 1/√2 and 1/(√3-√2). When solving the problem, the basic property of a fraction is used. To get rid of the root in the denominator, the numerator and denominator are multiplied by the same number, with the help of which the radical expression is squared. As a result of the calculations, we obtain 1/√2=√2/2 and 1/(√3-√2)=√3+√2.
The features of the mathematical language when working with expressions containing a root are indicated. It is noted that the content of the square root in the denominator of the fraction means the content of irrationality. And getting rid of the root sign in such a denominator is spoken of as getting rid of irrationality in the denominator. Methods are described on how to get rid of irrationality - to transform a denominator of the form √a, it is necessary to multiply the numerator simultaneously with the denominator by the number √a, and to eliminate irrationality for a denominator of the form √a-√b, the numerator and denominator are multiplied by the conjugate expression √a+√ b. It is noted that getting rid of irrationality in such a denominator greatly simplifies the solution of the problem.
At the end of the video lesson, a simplification of the expression 7/√7-2/(√7-√5)+4/(√5+√3) is discussed. To simplify the expression, the methods discussed above for getting rid of irrationality in the denominator of fractions are used. The resulting expressions are added, after which the simplified form of the expression looks like √5-2√3.
The video lesson “Transforming expressions containing the operation of extracting a square root” is recommended for use in a traditional school lesson to develop skills in solving problems that contain a square root. For the same purpose, the video can be used by the teacher during distance learning. The material can also be recommended to students for independent work at home.
To use presentation previews, create a Google account and log in to it: https://accounts.google.com
Slide captions:
Preview:
Algebra lesson in 8th grade
on the topic “Converting expressions containing square roots”
Math teacher: Kiryukhina Yu.A.
Municipal educational institution secondary school named after. A.I. Pankova s. Golovinshchino
2010-2011 academic year
Goals:
- repeat the definition of the arithmetic square root, the properties of the arithmetic square root;
- consolidate the skills and abilities of solving examples on identical transformations of expressions containing arithmetic square roots;
- summarize and systematize students’ knowledge on this topic;
- develop skills of self-control and mutual control, interest in the subject.
Equipment : multimedia projector, interactive whiteboard, assessment sheets, test cards, homework cards.
Progress of the lesson.
I. Organizational moment
Today in the lesson we will repeat the rules for transforming expressions containing square roots, converting roots from a product, fraction and degree, multiplying and dividing roots, taking a factor out of the root sign, putting a factor under the root sign, bringing similar terms and getting rid of irrationality in the denominator of a fraction .The assessment sheet will help you summarize today's lesson. Sign your sheets and answer the first question, “Mood at the beginning of the lesson,” by choosing one of the emoticons.
II. Lesson topic message
The topic of our lesson is “Converting expressions containing arithmetic square roots.” (Slide No. 1)
There's something about mathematics
Causing human delight.
F. Hausdorff(Slide No. 2)
III. Oral work
1) Frontal survey.(Slide No. 3)
- Give the definition of an arithmetic square root. (The arithmetic square root of a number is a non-negative number whose square is equal to a).
- List the properties of the arithmetic square root. (The arithmetic square root of the product of non-negative factors is equal to the product of the roots of these factors. The arithmetic square root of a fraction whose numerator is non-negative and whose denominator is positive is equal to the root of the numerator divided by the root of the denominator).
- 2? (|x| ).
- What is the arithmetic square root of x? 2 , if x≥0? x x. -X ).
2) Oral counting (Slide No. 4)
Come on, put the pencils aside!
No dominoes. No pens. No chalk.
"Oral counting!" We're doing this thing
Only by the power of mind and soul.
The numbers converge somewhere in the darkness,
And the eyes begin to glow,
And there are only smart faces around.
Because we count in our heads!
(Slide No. 5-9)
1. Remove the multiplier from under the root sign:
2. Enter the multiplier under the root sign:
3. Square:
4. Give similar terms:
IV. Work on the topic of the lesson
1 ) Individual work(Slide No. 10)
The ladybug has red, yellow and green spots. Green correspond to basic level tasks, yellow to advanced level tasks, red to high level tasks. Students choose the task at their own discretion. Three students, having received a task, solve it in their notebooks. (Slide No. 11-13)
2) Working with an interactive whiteboard.
The rest of the students solve the following tasks:
1. Simplify the expression: a) 4b+4b-4b; b) 9a+49a-64a;
B) 63-175+97; d) 28a+0.345s-418a+0.01500s.
2. Follow the steps and match with the correct answer: 15-1215-23 , 4+22-2 , 2-32+3 , 3-422 .
Answers: -1; 6 - 22; 27-125;41-242.
3. Free yourself from irrationality in the denominator of the fraction.
a) b5; b) 23; c) 737; d) ax+a.
4. Reduce the fraction.
a) 5-x2 5+x; b) a -2a2-2; c) 3-33; d) a+ba-b.
VI. Historical background(Slide 14-16)
Radix has two meanings: side and root. Greek mathematicians, instead of “extracting the root,” said “find the side of the square from its given value (area)”
Beginning in the 13th century, Italian and other European mathematicians denoted the root with the Latin word Radix, or R for short (hence the term “radical”).
German mathematicians of the 15th century. to denote the square root we used the dot ·5
Later, instead of a dot, they began to put a diamond¨ 5
Then Ú 5. Then the sign Ú and the line began to be drawn.
VII. Test (Slide No. 17, 18)
The English philosopher Herbert Spencer said: “The treasures are not the knowledge that is deposited in the brain like fat, the treasures are those that turn into mental muscles.”
At this stage of the lesson, you need to apply your knowledge to solve exercises during the test.
VI. Peer review(Slide No. 19)
Code of correct answers: Option I – 12312, II option - 32132.
VIII. Exercise for the eyes(Slide No. 20, 21)
VII. Homework.(Slide No. 22)
VIII. Lesson summary
Complete the assessment sheet completely. (Slide No. 23). Lesson grades.
I want to finish the lessona poem by the great mathematician Sofia Kovalevskaya. (Slide No. 24, 25)
If in life you even for a moment
I felt the truth in my heart,
If there is a ray of light through darkness and doubt
Your path was illuminated with a bright radiance:
Whatever your unchanging decision
Fate has not appointed you ahead,
The memory of this sacred moment
Keep it forever like a shrine in your chest.
The clouds will gather in a discordant mass,
The sky will be covered with black haze,
With clear determination, with calm faith
You meet the storm and face the thunderstorm.
This poem expresses the desire for knowledge, the ability to overcome all obstacles that come along the way. The lesson is over. Thanks for the lesson! (Slide No. 26)
Application
QUESTIONNAIRE SHEET
F.I. student___________________________
1. Mood at the beginning of the lesson: a) b) c)
2. My perception of the lesson topic:
a) learned everything; b) learned almost everything; c) partially understood, I need help.
3. Number of incorrect test answers: _________
4. I worked in class:
a) excellent; b) good; c) satisfactory; d) unsatisfactory.
5. I rate my work as ______ (give a rating)
6. I rate the lesson _____ (give it a rating)
7. Mood at the end of the lesson: a) b c)
Test Option I 1. Simplify the expression 1) 2) 3) 2. Open the parentheses and simplify the expression: 1) 18; 2) 12; 3) 22. 3. Simplify: 5+22 1); 2) ; 3) . 4. Free yourself from irrationality in the denominator = 1) ; 2) ; 3) . 1) ; 2) ; 3); 4) | Test Option II 1. Simplify the expression 1) 3 ; 2) 33 ; 3) 63. 2. Open the brackets and simplify 1) 8; 2) 12; 3) 10. 3. Simplify: 3+52 4. Free yourself from irrationality in the denominator: 411 1) ; 2); 3) . 5. Remove the multiplier from under the root sign: 1) ; 2) ; 3); 4) |
