Lesson Game: Shortened Multiplication Formulas

Lesson objectives:
Educational:

• To summarize and systematize students' knowledge on this topic.
• Work out skills in using reduced multiplication formulas when solving problems.
• Prepare for control work.

Developmental:

1. Develop cognitive interest and broaden students' horizons.
2. Teach to put knowledge into practice.

Educational:

1. Educate students with skills and abilities to work in a team.

Lesson type: a lesson in generalizing repetition.

Equipment: multimedia installation.

Lesson progress

Slide #1-2

1 Organizational moment

Slide #3

“Algebra is nothing more than a mathematical language adapted to indicate the relationship between quantities of”.
I.Newton

Slide #4

2 - Getting to know the rules of the game Mathematical Sea Combat

• To conduct the game, the class is broken into 2 groups Teams alternate "shoot" ships, naming the cells of the playing field (slide 5).By clicking on the symbol * in the specified cell, the progress performance is checked.
• If one of the teams misses, a move is made (slide 6), if a historical note is drawn, after reading it the team has the right to the next move, when hit, all teams are offered a task. The first right of reply is for the team that made the effective move. If this team makes a mistake, the opponents respond. Points are awarded to the team that gave the correct answer.
• Job lead time is limited After allotted time we check the answer, By clicking on the word "points" we move to the results table (slide 25) and enter points to the team that completed the task correctly. Then, by clicking on the word "back", we return to the playing field again (slide 5).

Slide #5

3, Tasks to complete

Questions for oral work.
Slide #7
A-1 - What is the difference between the squares of the two expressions? (2 points)
Slide #8
A-5 - What is the sum squared and the difference squared of the two expressions? (2 points)
Slide #9
A-6 - What is the sum of the cubes and the difference between the cubes of the 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 difference cube and the cube of the sum of the two expressions equal to? (2 points)

Tasks to complete in the notebook.

Slide #12
B-1. Imagine the expression (2m+5)(5-2m)+4m as a polynomial² (4 points).
Answer: 25
Slide #13
B-3 - Imagine as a polynomial the expression (2x+3)² - 4x2 (4 points).
Answer: 12x+9
Slide #14

B-4 - Imagine as a polynomial the expression (2x-3u)² +(3x+2u)² (4 points).
Answer: 13x²+13u²
Slide #15

B-5. Imagine the expression (2x-3)(2x+3)-(2x-1) as a polynomial² (4 points).
Answer: 4x-10
Slide #16

B-6. Imagine the expression (2x+y) as a polynomial³-6hu(2x+y) (4 points).
Answer: 8x³ +u³
Slide #17

B-9. Imagine the expression (mn) as a polynomial³ +3mn(mn) (4 points).
Answer: m³ +n³
Slide #18

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

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

Slide #20
G-4 - Imagine as a product x6 -27 (8 points).
Answer: (x²-3)(x⁴+3x²+9)

Slide #21
W-5 Convert to polynomial (3 x + y2)³ (8 points).
Answer: 27x³+27x²u²+9hu⁴+u6

Slide #22
Z-7 Solve the equation: 4x2+4x+1=0 (10 points).
Solution
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
Z-8 Solve the equation: (7-x)²-(x-8)(x+8)=43 (10 points).
Solution.
(7-x)²-(x-8)(x+8)=43;
72-2·7·x+x²-(x2 -82)=43;
49-14x+x²-x²+44=43;
-14x=-70;
x=-70:14;
x=5.
(7-5)²-(5-8)(5+8)=43
43=43.
Answer:5
Slide #24
I-2 Find the smallest value of the square trinomial x2 +2x+7 (12 points).
Solution.
x2 +2x+7=(x² +2·1·x+12)-12+7=(x+1)²+6
This trinomial takes the smallest value when (x+1)2 takes the smallest value, i.e. (x+1)²=0.
Therefore, the smallest value of a square trinomial is 6.
Answer: 6
Slide #25
I-3. At what value x any values x square trinomial x²-12x+50 takes the lowest value? (12 points).
Solution.
x²-12x+50=(x²-2·6·x+36)-36+50 = (x-6)²+14
This trinomial takes the smallest value when
(x-6)²=0;
x-6=0;
x=6.
Answer: 6
Slide #26
I-4. Prize. (6 points).

4 Historical references
Since we study the formulas of reduced multiplication in an algebra lesson, these historical references will allow you to find out where this name came from and which scientists 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 Muhammad bin Musa al-Khwarizmi (787-c.850). The term "al-jabr", taken from the title of this book, later began to be used as algebra.

Slide #28

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

Slide #29

• Diophantus of Alexandrine (3rd century) In his book Arithmetic, the beginnings of letter symbolism and special notation for degrees appear, as well as the equal sign, a brief record of multiplication rules, problems leading to complex systems of algebraic equations

Slide #30

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

Slide #31

• Pierre Fermat (1601 - 1665) dealt with the theory of solving algebraic equations with several variables

Slide #32

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

Slide #33

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

Slide #34
5, Lesson outcome. Scoring and awarding of the team - winner.

Slide #35
Checking the location of ships.

6 Homework

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