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- Открытый урок по английскому языку на тему ' Формулы сокращенного умножения ' (7 класс)
Открытый урок по английскому языку на тему ' Формулы сокращенного умножения ' (7 класс)
Theme: The sum and difference of cubes of two expressions
Subject: Algebra in English
Grade: 7 B ( 7 Б )
Type of the lesson: mixed
Methods : forming the new mathematical skills and techniques
Objectives:
Developing aims: 1) to develop an ability to reason logically, to classify, to generalize and to prove; 2) to develop an ability to respond orally to questions correctly, discuss mathematical ideas and carry out mental calculations, practical and investigational work ( развивать способность думать логически, классифицировать, способствовать развитию умения обсуждать математические идеи, обобщать и давать четкие и ясные ответы )
Educational aims : 1) to educate appreciation of patterns and relationship in Maths, 2) to educate imaginative and creative work from Maths ideas;
3) to raise interest to the subject ; 4) to educate accuracy and understanding of part which mathematics plays in the world around pupils ( способствовать грамотной устной речи в понимании математических терминов, прививать любовь и интерес к предмету, воспитание критического и логического мышления у учащихся )
Teaching aims : 1) to teach to recognize when and how to apply Short Multiplication Formulas ( the sum and difference of cubes ) and select an appropriate mathematical method to solve the problems ( знакомство с формулами суммы кубов и разности кубов , и формирование у учащихся навыков применения формул сокращённого умножения )
Resources : computer, active board, slides , cards , examiner- cube
Lesson structure
1) Organization moment
2) Aims of the lesson ( map of expedition )
3) Ask questions ( orally )
4) New material
5) Work at the board
6) Music pause
7) Find your partner ( game )
8) Work with copy-books ( self check )
9) Examiner - cube ( solving problems )
10) Conclusion
Lesson Procedure:
1) Organization moment
Teacher checks pupils' preparation for the lesson and says them to write the date and theme of the lesson.
- Today we have an unusual lesson We are going to make journey on foot. But we will do it with Short Multiplication Formulas.
Let us look at the map of our expedition.
2) Aims
Our journey on foot we start at " Memory " Pond ( " Естеліктер " көлшігі ) ( here we have to remember what formulas do you know). Then we have the " Science " Forest on the way ( " Ғылым " орманы ) ( get to know the new formulas ). After forest we are going to go to the " Knowledge " Waterfall ( " Білім " сарқырамасы )( solve some problems ). From waterfall we shall go to the " Finding " Desert ( " Табыс " шөлі ). Further " Mistakes " Sea ( " Қателік " теңізі ) is waiting for us ( try to find mistakes in expressions ) and finish our route at " Result " Harbor ( " Қортынды " жағалау).
Are you ready? Let's go !
3) " Memory " Pond
a) Square the expressions: c ; -4 ; 3m ; 5x2y3
b) Read the expressions : a2 + b2 ; ( a + b )2 ; a2 - 2ab + b2
c) Write the formulas : ( a + b )2 ; ( a - b )2 ; a2 - b2
4) " Science " Forest
Today we will study the new formulas The Sum and Difference of Cubes
To factorize the sum of cubes the following identity is used :
a3 + b3 = ( a + b )( a2 - ab + b2 )
To do this I need your help. ( One pupil proves the identity on the board, the others in copy books )
( a + b )( a2 - ab + b2 ) = a2 - a2b + ab2 + a2b - ab2 + b3 = a3 + b3
To factorize the difference of cubes the following identity is used :
a3 - b3 = ( a - b )( a2 + ab + b2 )
One pupil proves the identity on the board, the others in copy books
( a - b )( a2 + ab + b2 ) = a2 + a2b + ab2 - a2b - ab2 - b3 = a3 - b3
5) " Knowledge " Waterfall
( Three pupils work at the board, the rest two examples by themselves )
Factorize the expressions:
a) m3 - n3 = ( m - n )( m2 + mn + n2)
b) 8 + a3 = ( 2 + a )( 4 - 2a + a2 )
c) 1 + 27y3 = ( 1 + 3y )( 1 - 3y + 9y2 )
d) 125a3 - 64b3 = ( 5a - 4b )( 25a2 + 20ab + 16b2 )
e) x6 -
6) Music pause ( " Happy " song )
7) " Finding " Desert
Pupils call the expressions on their sheets of paper to find the partner. At the end of the activity the word " FRIENDS " should appear.
8) " Mistakes " Sea
Find mistakes in the expressions ( Pupils write the right variants in copybooks then teacher checks the answers and put marks )
a) ( 5x - 2y )2 = 25x2 - 4y2
b) x3 - 8y6z9 = ( x - 2y2z3)( x + xy2z3 + 4yz6 )
c) 36a2 + 49b2 = ( 6a - 7b )( 6a + 7b )
d) a3 + 27b3 = ( a - 3b )( a2 + 6ab + 9b2)
e) ( 2 + 5a )2 = 2 - 20a + 5a2
f) m3 - n6k9 = ( m - nk3 )( m2 + mnk3 + n4k6 )
Right variant :
a) ( 5x - 2y )2 = 25x2 - 20xy + 4y2
b) x3 - 8y6z9 = ( x - 2y2z3)( x2 + 2xy2z3 + 4y4z6 )
c) 36a2 - 49b2 = ( 6a - 7b )( 6a + 7b )
d) a3 + 27b3 = ( a + 3b )( a2 - 3ab + 9b2)
e) ( 2 + 5a )2 = 4 + 20a + 25a2
f) m3 - n6k9 = ( m - n2k3 )( m2 + mn2k3 + n4k6 )
7) Examiner - cube ( These tasks are for weak pupils to put them marks )
The cube is rolled by pupil and task is chosen randomly
Tasks Answers
a) ( x2 - 5 )2 x4 - 10x2 + 25
b) ( 7 - y3 )2 49 - 14y3 + y6
c) ( 15x - x3 )2 225x2- 30x4 + x6
d) ( 3y + 8y5 )2 9y2 + 48y6 + 64y10
e) m3 - 27n3 ( m - 3n )( m2 + 3mn + 9n2)
f) a6 + b3 ( a2 + b )( a4 - a2b + b2 )
8) " Result " Harbor ( ask questions )
a) What do you come to know today ?
b) Do you like the lesson?
c) What was the most interesting for you ?
d) What was the most difficult for you ?
e) How is your mood ?
A
D
E
B
C
F
a) ( x2 - 5 )2 = x4 - 10x2 + 25
b) ( 7 - y3 )2 = 49 - 14y3 + y6
c) ( 15x - x3 )2 = 225x2- 30x4 + x6
d) ( 3y + 8y5 )2 = 9y2 + 48y6 + 64y10
e) m3 - 27n3 = ( m - 3n )( m2 + 3mn + 9n2)
f) a6 + b3 = ( a + b )( a4 - a2b + b2 )