Game Lesson: "Formulas of Reduced Multiplication"

Objectives:
Educational:

• To summarize and systematize the knowledge of students on this topic.
• Develop the skills of using reduced multiplication formulas when solving tasks.
• Prepare for control work.

Developing:

1. Develop cognitive interest and expand the horizons of students.
2. Learn to apply knowledge in practice.

Educational:

1. To educate students skills and skills in the team.

Type of lesson: a generalized repetition lesson.

Equipment: multimedia installation.

Class progress

Slide 1-2.

1. Organizational moment

Slide 3.

Algebra is nothing but a mathematical language adapted to denote the relations between quantities.
And. newton

Slide 4.

2. The rules of the game "Mathematical sea battle".

• For the game, the class is divided into 2 groups. Teams alternately shoot at ships, naming the cells of the playing field (slide 5). By pressing the symbol * in the specified cell, the effectiveness of the move is checked.
• If one of the teams made a mistake, the move passes (slide 6), if a historical reference falls out, after familiarizing with it, the team has the right to another move, if all teams are hit, the task is offered. The priority right of answer is given to the team that made a successful move. If this team makes a mistake, the opponents respond. Points are awarded to the team that gave the correct answer.
• The time to complete the task is limited. After the allotted time, we check the response. Clicking on the word "points" we go to the table of results (slide 25) and enter the points to the team that correctly completed the task. Then, clicking on the word "back" again return to the playing field (slide 5).

Slide 5.

3. Assignments for implementation

Questions for oral work.
Slide 7.
A-1. What is the difference between the two expressions? (2 points)
Slide 8.
A-5. What is the square of the sum and the square of the difference of two expressions? (2 points)
Slide 9.
A-6. What is the sum of cubes and the difference of cubes of two expressions? (2 points)
Slide 10.
A-7. What is the square of the sum of three expressions? (2 points)
Slide 11.
A-9. What is the cube of difference and cube of the sum of two expressions? (2 points)

Tasks to perform in the notebook.

Slide 12.
B-1. Imagine the polynomial expression(2m+5)(5-2m+4m)²(4 points).
Answer: 25
Slide 13.
B-3. Imagine the polynomial expression (2x+3)²- 4x2 (4 points).
Answer: 12x+9
Slide 14.

B-4. Imagine the polynomial expression(2x-3u)²+(3x+2u)²(4 points).
Answer: 13x²+13²
Slide 15.

B-5. Imagine the polynomial expression (2x-3)(2x+3)-(2x-1)²(4 points).
Answer: 4x-10
Slide 16.

B-6. Imagine the polynomial expression (2x+y)³-6hu(2x+y) (4 points).
Answer: 8x³+³
Slide 17.

B-9. Think of the polynomial expression (m-n)³+3mn(m-n) (4 points).
Answer: m³ +n³
Slide 18.

D-8. Multiply the polynomials (2x+1)²-16 (6 points).
Answer: (2x-3)(2x+5).

Slide 19.
E-2. Multiply the polynomial (x -2)²-(x+1)²(6 points).
Answer: -3(2x-1)

Slide 20.
G-4. Imagine in the form of a work x6 -27 (8 points).
Answer: (x)²-3)⁴+3x²+9)

Slide 21.
G-5. Convert to polynomial (3x+y2)³(8 points).
Answer: 27x³+27x²у²+9ha⁴+u6

Slide 22.
G-7. Solve the equation: 4x2+4x+1=0 (10 points).
Decision
4x²+4x+1=0
(2x+1)²= 0;
2x+1=0;
2x=-1;
x=1:2;
x = 0.5.
4·0,5² + 4·0,5+1=0.
0=0
Answer: 0.5
Slide 23.
G-8. Solve the equation: (7x)²-(x-8)(x+8) = 43 (10 points).
Solution.
(7x)²-(x-8)(x+8) =43;
72-2·7·х+х²-(x2-82) = 43;
49-14x+x²-²+44=43;
-14x=-70;
x=-70:14;
x=5.
(7-5)²-(5-8)(5+8)=43
43=43.
Answer:5
Slide 24.
E-2. Find the lowest value of the square trimember x2 +2 x +7 (12 points).
Solution.
x2 +2 x +7=(x)² +2·1·х+12)-12+7=(х+1)²+6
This three-term assumes the lowest value when (x+1)2 takes the lowest value, i.e. (x+1)²= 0.
Therefore, the smallest value of a square three terms is 6.
Answer: 6
Slide 25.
E-3. At what value x of any values x square three terms x²-12x+50 is the least important? (12 points).
Solution.
х²-12x+50=x²-2·6·х+36)-36+50 = (х-6)²+14
This triad is the least important when
(x-6)²= 0;
x-6=0;
x=6.
Answer: 6
Slide 26.
E-4. Prize. (6 points).

4. Historical background
Since the formulas of abbreviated multiplication are studied in algebra class, these historical references will allow you to learn about where this name came from and which scientists have made a great contribution to the development of this science.
Slide 27.

• The word "Algebra" arose after the appearance of the treatise of the mathematician and astronomer Mohammed ben Musa al-Khwarizmi (787-oc.850). The term al-Jabr, taken from the title of this book, was later used as algebra.

Slide 28.

• Muhammad Al-Khwarizmi (787–about 850) wrote the foundational treatises on arithmetic and algebra.

Slide 29.

• Diophantus Alexandrovsky (III century). In his book “Arithmetic” there are rudiments of letter symbolism and special notations for degrees, as well as an equal sign, a brief record of the rules of multiplication, problems leading to complex systems of algebraic equations.

Slide 30.

• François Viet (1540-1603) introduced algebraic symbols, began to denote numbers with letters, developed the basics of algebra.

Slide 31.

• Pierre Fermat (1601-1665) was engaged in the theory of solving algebraic equations with several variables.

Slide 32.

• René Descartes (1596-1650) expanded the stock of numbers with which actions could be performed. Introduced :x, y, z - variables, unknowns; a, b, c - constants, parameters; division sign.

Slide 33.

• Gottfried Wilhelm Leibniz (1446-1716) created the foundations of mathematical analysis, introduced many concepts and symbols.

Slide 34.
5. Lesson outcome. Counting points and awarding the winning team.

Slide 35.
Checking the location of the ships.

6. Homework.

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