Mathematics is aesthetic and the spiritual home of students. Mathematics is a prism that reflects the colorful colors of utility, science and aesthetics. As a ninth-grade math teacher, you might as well write a ninth-grade math teaching plan before class, which is of great help to your work. Whether you are looking for or preparing to write the first volume of the third grade mathematics teaching plan, I have collected relevant information below for your reference!

The pattern design of 1 in the teaching plan of the first volume of the third grade mathematics.

Use one or combination of translation, axial symmetry and rotation to design the pattern, and design a satisfactory pattern.

By reviewing the knowledge of axis symmetry, translation and rotation, and then using this knowledge, let students use their brains and boldly associate to design beautiful patterns.

1, design mode.

2. How to use one or a combination of translation, axial symmetry and rotation to get the pattern.

First, review the introduction.

1. As shown in the figure, it is known that the line segment CD is the figure after the translation of the line segment AB, and D is the symmetrical point of the point B. Make the line segment AB and answer the positional relationship between AB and CD.

2. As shown in the figure, given the line segment CD, make the symmetrical line segment C'D' of the line segment CD about the symmetrical axis L, and explain the relationship between CD and the symmetrical line segment C'D'.

3. As shown in the figure, given the line segment CD, make the rotation figure of the line segment CD about point D. What is the relationship between the two line segments?

1.AB parallel, equal to CD;

2. Let point D be DE⊥l, vertical foot be E and extend, so that ED ′ = ED. Similarly, let point C' connect with C'D', then C'D' is what you want.

The extension line of CD intersects the extension line of C'D' at a point, which is on L, and CD=C'D'.

3. Take point D as the center of rotation. After rotation, CD⊥c'd, vertical foot is d, CD = c' d.

Second, explore new knowledge.

Please use one or more of the above graphic transformations such as translation, axial symmetry and rotation to complete the following pattern design.

Example 1 (student activities) Students do exercises by themselves.

According to the following steps, ask each student to complete a unique pattern.

(1) Prepare a regular triangular piece of paper (prepare before class) (as shown in Figure A);

(2) Tear the paper into two parts at will (as shown in Figure B and Figure C);

(3) Axisymmetric the torn figure B along one side of the regular triangle to obtain a new figure;

(4) rotate the graph obtained in (3) with one vertex of the regular triangle as the rotation center to obtain graph (d) (graph C is unchanged);

(5) Translate Figure (d) to the right of Figure (c) to obtain Figure (e);

(6) Make appropriate modifications to Figure (e) to obtain a unique and beautiful pattern as shown in Figure (f).

Teachers can give some guidance when necessary.

Third, the class summary

This lesson should master:

The pattern is designed by one or a combination of translation, axial symmetry and rotation.

The third grade mathematics teaching plan Volume I Quadratic Radical 2

Teaching objectives

1, understand the concept of quadratic radical,

2. Master the basic properties of quadratic radical.

teaching process

First, ask questions.

In the last section, we learned the meaning of square root and arithmetic square root, and introduced a new symbol. Now, please think about and answer the following two questions:

1, what do you mean?

2. What conditions does A need to meet? Why?

Second, solve problems through cooperation and communication.

Let the students cooperate and communicate, and then answer the questions (which can be supplemented), which can be summarized as follows;

1. When a is a positive number, it represents the arithmetic square root of a, that is, one of the two square roots of a positive number;

2. When a is zero, it means zero, which is also called the arithmetic square root of zero;

3.a≥0, because the square of any rational number is greater than or equal to zero.

Third, summarize the characteristics and introduce the concept of quadratic radical.

1, basic properties,

Question 1 Can you sum up the above three conclusions in one sentence?

Let one student answer and the other students supplement, which can be summarized as follows: (a≥0) means the arithmetic square root of non-negative number A, that is, (a≥0) is non-negative, that is, ≥0(a≥0).

Question 2 () What is 2 (a ≥ 0) equal to? State your reasons and verify them with examples.

Ask students to discuss in groups or explore independently, and come to the conclusion: () 2=a(a≥0), such as () 2=4, () 2=2, etc.

The conclusions of the above two questions are basic, especially () 2=a(a≥0) can be used as a formula and directly applied to calculation. On the other hand, write () 2=a(a≥0) as a=()2(a≥0), indicating that any non-negative number A can be written as the square of a number, for example, 3=()2, 0.3= ()2.

Ask questions:

(1)0=()2, right?

(2)-5=()2, right? If not, what's the problem?

2. The concept of quadratic radical

The formula in the form of (a≥0) is called quadratic radical,

Note: the quadratic radical must have the following characteristics;

(1) has a quadratic root sign;

(2) The number of square roots cannot be less than 0.

Ask the students to give several examples of quadratic roots and judge, (a)

Fourth, examples.

Example 1. What conditions must the value of the letter x meet to make the formula meaningful?

Ask questions:

If the formula is changed to, what conditions must the value of the letter X meet?

Verb (abbreviation of verb) classroom practice

Exercise 1, 2,

Sixth, think about improvement.

We have studied that () 2(a≥0) equals A, what is it now?

Ask questions:

1. What strategies are often used in learning abstract problems?

2. Is there a limit to the value of a in?

3. Take some numerical values to verify. What laws can be found through verification?

So when we meet in the future, we can rewrite it as the absolute value of a |a| first, and then take a positive value, 0 or negative value according to a, such as X.

4. () Is 2 the same as? Say your reasons and communicate with your classmates.

Seven. abstract

1, what is a quadratic radical? Can you give some examples?

2. What are the two formal characteristics of quadratic radical?

3. What is the nature of quadratic radical?

Eight, homework

Exercise 22. 1, question 1, 2,3,4,

Postscript of teaching:

Third grade mathematics teaching plan Volume I Article III One-variable quadratic equation

course content

The concept of quadratic equation with one variable, the general formula of quadratic equation with one variable and related concepts.

Teaching objectives

Understand the concept of unary quadratic equation; General formula ax2+bx+c=0(a≠0) and its derived concepts; The concept of quadratic equation in one variable is applied to solve some simple problems.

1. By setting questions, establish a mathematical model, imitate the concept of a linear equation, and define a quadratic equation.

2. The general form of quadratic equation with one variable and its related concepts.

3. Solve some conceptual problems.

4. Learn mathematics through life, solve problems in life with mathematics, and stimulate students' enthusiasm for learning.

Difficulties and the key to difficulties

1. Focus: the concept of quadratic equation in one variable and its general form, as well as the related concepts of quadratic equation in one variable and solving problems with these concepts.

2. Key and difficult points: By asking questions, the mathematical model of quadratic equation with one variable is established, and then the concept of quadratic equation with one variable is transformed into the concept of quadratic equation with one variable.

teaching process

First, review the introduction.

Student activity: Make equations.

Problem (1) An interesting problem in ancient calculation: "Holding the pole into the house"

The stupid man tried to enter the house with a pole, but the bamboo was blocked by the door frame, and he couldn't cry.

A clever neighbor taught him to tilt the pole to two corners. Fools try as they say, more or less just arrived.

Excuse me, how long is the pole? I admire anyone who works out.

If the height of the door is assumed to be x feet, then the width of the door is _ _ _ _ _ feet and the length is _ _ _ _ _ _ _ feet.

According to the meaning, you get _ _ _ _ _.

Tidy up and simplify, and you get: _ _ _ _ _ _ _.

Second, explore new knowledge.

Student activity: Please answer the following questions orally.

(1) How many unknowns are there in the above three equations?

(2) According to the polynomials in algebraic expressions, what is their highest degree?

(3) Is there an equal sign? Or is there only one polynomial-like formula?

Teacher's comments: (1) all contain only one unknown X; (2) Their highest frequency is twice; (3) Everyone has an equal sign, which is an equation.

So an equation with algebraic expressions on both sides like this, which contains only one unknown (unary) and the highest degree of the unknown is 2 (quadratic), is called a unary quadratic equation.

Generally speaking, any univariate quadratic equation about X can be transformed into the following form ax2+bx+c=0(a≠0) after sorting. This form is called the general form of quadratic equation with one variable.

The order of the unary quadratic equation is ax2+bx+c=0(a≠0), where ax2 is the quadratic term and A is the coefficient of the quadratic term; Bx is a linear term, and b is a linear term coefficient; C is a constant term.

Example 1. The equation 3x(x- 1)=5(x+2) is transformed into a general form of a quadratic equation with one variable, and the coefficients of quadratic term, linear term and constant term are written.

Analysis: The general form of unary quadratic equation is ax2+bx+c=0(a≠0). Therefore, the equation 3x(x- 1)=5(x+2) must be sorted by algebraic expression operation, including removing brackets and shifting items.

Solution: Omit

Note: Quadratic term, quadratic term coefficient, linear term, linear term coefficient and constant term all contain the preceding symbols.

Example 2. (Student activity: invite two or three students to practice on stage) Transform the equation (x+1) 2+(x-2) (x+2) =1into the general form of a quadratic equation with one variable, and write out the quadratic term and the quadratic term coefficient; Linear term and linear term coefficient; constant term

Analysis: (x+1) 2+(x-2) (x+2) =1is transformed into ax2+bx+c=0(a≠0) by the complete square formula and the square variance formula.

Solution: Omit

Third, consolidate the practice.

Textbook exercise 1, 2

Supplementary exercise: judge whether the following equation is quadratic?

( 1)3x+2 = 5y-3(2)x2 = 4(3)3 x2-= 0(4)x2-4 =(x+2)2(5)ax2+bx+c = 0

Fourth, application expansion.

Example 3. It is proved that the equation about x (m2-8m+17) x2+2mx+1= 0 is a quadratic equation regardless of the value of m.

Analysis: To prove that no matter what value M takes, the equation is a quadratic equation, just prove m2-8m+ 17≠0.

Proof: m2-8m+17 = (m-4) 2+1.

∫(m-4)2≥0

∴(m-4)2+ 1>； 0, that is, (m-4)2+ 1≠0.

No matter what value m takes, this equation is a quadratic equation.

? Exercise: 1 Equation (2a-4) x2-2bx+a = 0. Under what conditions is this equation a quadratic equation? Under what conditions is this equation a linear equation?

2. When m is what value, the equation (m+ 1)x/4m/-4+27mx+5=0 is a quadratic equation.

Verb (abbreviation of verb) summary (student summary, teacher's comment)

This lesson should master:

The concept of (1) unary quadratic equation; (2) The general form of unary quadratic equation ax2+bx+c=0(a≠0), the concepts and applications of quadratic term, quadratic term coefficient, linear term, linear term coefficient and constant term.

Distribution of intransitive verbs

The direct Kaiping method in the fourth lesson of the first volume of mathematics in the third grade

Understand the mathematical idea of "reduction"-transformation of a quadratic equation, and can apply it to solve some specific problems.

This paper puts forward the problem, lists the unary quadratic equation ax2+c=0 which lacks the elementary term, solves this equation according to the meaning of the square root, and then transfers the knowledge to solving the A-type unary quadratic equation (ex+f)2+c=0.

focus

The equation with the shape of (x+m)2=n(n≥0) is solved by Kaiping method, and the mathematical idea of conversion-transformation is understood.

difficulty

By solving the equation with the shape x2=n according to the meaning of the square root, knowledge is transferred to solving the equation with the shape (x+m)2=n(n≥0) according to the meaning of the square root.

First, review the introduction.

Student activity: Please complete the following questions.

Question 1: Fill in the blanks

( 1)x2-8x+_ _ _ _ _ _ _ _ =(x-_ _ _ _ _ _ _ _)2； (2)9 x2+ 12x+_ _ _ _ _ _ _ _ =(3x+_ _ _ _ _ _ _ _)2； (3)x2+px+________=(x+________)2。

Solution: According to the complete square formula: (1)164; (2)4 2; (3)(2p)22p。

Question 2: What equations have we learned so far? How to convert binary into binary? What's the difference between quadratic equation and linear equation? How to turn the second into the first? How to downgrade? What methods have you learned to demote before?

Second, explore new knowledge.

We have said that x2=9. According to the meaning of square root, you can get x = 3 by square directly. If the substitution of x is 2t+ 1, that is, (2t+ 1)2=9, can it also be directly squared?

(Students discuss in groups)

Teacher's comment: The answer is yes. If the above 2t+ 1 is replaced by x, then 2t+ 1 = 3.

That is 2t+ 1=3, 2t+ 1=-3.

The two roots of the equation are t 1= 1, and t2=-2.

Example 1 Solving equation: (1) x2+4x+4 =1(2) x2+6x+9 = 2.

Analysis: (1)x2+4x+4 is a complete square formula, then the original equation is transformed into (x+2)2= 1.

(2) From what is known, (x+3)2=2.

Direct square, x+3 =

That is x+3=, x+3=-

Therefore, two x 1=-3+ and x2=-3-

Solution: Omit.

The municipal government plans to increase the per capita housing area from 10 m2 to 14.4 m2 in two years to seek the annual per capita housing area growth rate.

Analysis: If the annual growth rate of per capita housing area is X, the per capita housing area after one year should be10+10x =10 (1+x); After two years, the per capita housing area should be10 (1+x)+10 (1+x) x =10 (1+x) 2.

Solution: let the annual per capita housing area growth rate be x,

Then:10 (1+x) 2 =14.4.

( 1+x)2= 1.44

Square directly and you get 1+x = 1.2.

That is 1+x= 1.2, 1+x=- 1.2.

So the two roots of the equation are x 1=0.2=20% and x2=-2.2.

Because the annual growth rate of per capita housing area should be positive, x2=-2.2 should be abandoned.

Therefore, the annual per capita housing area growth rate should be 20%.

(Student summary) Teacher's question: What are the similarities between them when solving a quadratic equation with one variable?

* * * Same feature: the quadratic equation of one variable is transformed into two quadratic equations of one variable. We call this kind of thinking "the thought of one change and one change".

Third, consolidate the practice.

Exercise on page six of the textbook.

Fourth, class summary.

What we should master in this lesson is that if the equation with the shape of x2=p(p≥0) is solved by direct Kaiping method, then x = is transformed into the equation with the shape of (mx+n)2=p(p≥0) by direct Kaiping method, and then MX+n = is reduced. If p < 0, the equation has no solution.

Verb (abbreviation for verb) assignment

Textbook 16 page review and consolidation.