"Perfect Square Formula" PPT courseware for operation of integers

Description

"Perfect Square Formula" PPT courseware for operation of integers

instructional design

(1) The status and role of teaching materials:

The perfect square formula is a sublimation of the knowledge of integer multiplication operations and is also an important part of the multiplication formula. Therefore, the perfect square formula is at the foundation of algebra. At the same time, it is the basis for learning factorization, quadratic equations, functions and other knowledge in the future, so this lesson serves as a link between the past and the following. The content of this lesson is based on students understanding what multiplication of integers is, summarizing formulas and using them to solve practical problems. Through learning, students can realize the convenience of the perfect square formula, and understand that the perfect square formula is a more powerful mathematical tool, breaking the tediousness of operations, and then the application of the perfect square formula has a breakthrough effect.

(2) Three-dimensional target:

1. Knowledge and skill objectives:

A. Master the characteristics of the perfect square formula and be able to correctly use the formula to solve problems.

B. Understand the general steps to use the perfect square formula to solve practical problems.

2. Process and method objectives:

By summarizing simpler calculation methods in the process of integer multiplication and using mathematical problems to solve practical problems, students can further appreciate the regularity of mathematical knowledge and the breadth of practical applications, and then penetrate the mathematical modeling ideas.

3. Emotional attitude and value goals:

A. Through learning, you can feel the application value of mathematics and enhance the awareness of using mathematics, thereby stimulating students' enthusiasm for learning mathematics.

B. Understand the importance of communication and cooperation among classmates in the process of solving problems.

(1) Student situation analysis and countermeasures:

Through the study of the previous few lessons, students have initially mastered the specific methods of integer multiplication, but they cannot fully understand and apply the flexibility of the complete square formula, so the content of this section is difficult for students and is relatively more abstract. Challenging. In response to this situation, I adopted the strategy of "asking questions - students trying - teacher assistance - students trying - solving problems" to strengthen the practice, so that students can realize that learning mathematics well can solve many problems in life.

(2) Organization and arrangement of teaching content:

The teaching content of this section is processed based on students' cognitive rules, step by step, and depth step by step. Therefore, the organization and arrangement of the teaching content of this section is as follows:

(1) Asking questions (2) Introducing new lessons

(3) Trial exercises (4) Inference and induction

(5) Feedback practice (6) Assignment

Use the formula: (a+b)2 =a2+2ab+b2 to calculate

Solution (1) (4m+n)2= (4m)2+2(4m)(n)+(n)2=16m2 +8mn+n2

(2) (x+6)2= x2+2 ? x ? 6+62=x2 +12x+36

What is the multiplication rule for polynomials?

Multiply each term of one polynomial by each term of the other polynomial and add the products.

Can you prove it?

(a+b)2=a2+2ab+b2;

(a?b)2=a2 ?2ab+b2.

(1) Can you use the polynomial multiplication rule to show that it holds true?

(2)(a?b)2=?

Proof ?(a+b)2 =(a+b)(a+b)

=a2+ab+ab+b2

=a2+2ab+b2

(a?b)2=[a+(?b)]2

=a2+2a(-b)+(-b)2

=a2-2ab+b2

Observe the following perfect square formula

1: What are the characteristics of the left and right sides? What are the characteristics of symbols?

2: Can you describe this formula in your own words?

Structural features of the formula:

1. The left side is the square of the binomial, and the right side is a trinomial;

2. Two terms in the trinomial are the sum of the squares of the two terms on the left, and the other term is twice the product of the two terms on the left;

3. The two formulas are different in sign.

Please divide into groups of four to discuss!

Comparing the two equations above, what did you find? Express it in your words.

Explore and discover: (a+b)2___(-a-b)2 , (a-b)2 ___(-a+b)2

Discover patterns:

When the given binomials have the same sign, use _______________;

When the given binomials have different signs, use ____________________.

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For more information about the PPT courseware "Operations of Integers with Complete Square Formulas", please click on the PPT tab of "Operations of Integers with Complete Square Formulas".

"Perfect Square Formula" PPT courseware for multiplication and division of integers (Lesson 2):

"Perfect Square Formula" Multiplication and Division of Integers PPT Courseware (Lesson 2) Part One: Learning Objectives 1. Further master the perfect square formula; (Key Points) 2. Flexibly use the perfect square formula for calculations. (Difficulty) ... ... ... Complete Square Formula PPT..

"Perfect Square Formula" Multiplication and Division of Integers PPT Courseware (Lesson 1):

"Perfect Square Formula" Multiplication and Division of Integers PPT Courseware (Lesson 1) Part One: Learning Objectives 1. Understand and master the derivation process and structural characteristics of the perfect square formula; (Key Points) 2. Be able to use formulas to perform simple operations.( Difficulty) ... ... ... ... ..

"Perfect Square Formula" PPT on multiplication and division of integers:

"Perfect Square Formula" Multiplication and Division of Integers PPT Part One Content: Objectives of this Section 1. Explore the operation process of the perfect square formula, and develop cooperative communication skills, reasoning skills and organized expression skills. 2. Correctly use the perfect square formula to perform simple operations and...

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Update Time: 2024-07-04

This template belongs to Mathematics courseware Beijing Normal University Edition Seventh Grade Mathematics Volume 2 industry PPT template

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