The seventh grade mathematics "algebraic expression" teaching plan design daquan 1
Teaching objectives:
1. Know how to represent numbers with letters.
2. Will use the formula with letters to express the quantitative relationship.
Emphasis and difficulty in teaching: letters will be used to express the quantitative relationship.
Teaching process:
First, create problem situations and introduce new courses.
1. Read the textbook P53, the problems introduced in this chapter:
Question 1: S stands for distance, v stands for speed and t stands for driving time. What is the relationship between these three quantities?
Question 2: use s to represent the area of a circle, c to represent the circumference of a circle, r to represent the radius of a circle, and use a formula containing r to represent s and C.
Question 3: A and B stand for two rational numbers, and the letter stands for additive commutative law.
Question 4: There are X students in the class, of whom 54% are girls. What are the numbers of girls and boys respectively? Represented by a formula containing X.
2. Cooperate to exchange the above questions and ideas:
What can the letter (1) stand for?
(2) Use letters to indicate the function of numbers.
3. Summary: Numbers are represented by letters, which can participate in operations like numbers, and the quantitative relationship can be concisely expressed by formulas.
4. Textbook P54 Case 1, P55 Case 2.
(1) Students do it independently.
(2) Communication, discussion and help among students with difficulties.
Second, feedback exercises
1. Textbook P56 Exercise 1~4.
2. Ability improvement exercises.
(1) The section of the first section of the canal is trapezoidal, with an upper mouth a meter wide, a lower bottom b meters wide and a depth of 0.8 meters. If the length of this canal is l meters, it is necessary to dig earth and stone to build this canal.
(2) The relevant data between the quality x(g) and the selling price c (yuan) of bagged melon seeds are as follows:
Quality of melon seeds (x g) Price C (Yuan)100 2.4+0.5 200 4.8+0.5 300 7.2+0.5 400 9.6+0.5 50012+0.5. ...
The formula with the letter X indicates that the sales price C is ...?
The second kind of monomial
Teaching objectives:
1. Understand the concepts of monomial and monomial coefficient and degree.
2. Will accurately and quickly determine the single coefficient and times.
Teaching emphasis: master the concepts of single item and single item's coefficient and frequency, and determine a single item's coefficient and frequency accurately and quickly.
Teaching difficulty: the establishment of single concept.
Teaching process:
First, review the introduction.
1. column algebra
(1) If the side length of a cube is a, the area of the cube is; ?
(2) If one side of a triangle is long and the height of this side is h, then the area of this triangle is; ?
(3) If x represents the side length of a cube, the volume of the cube is: ?
(4) If m represents a rational number, what is its inverse?
2. Ask the students to say the meaning of the listed algebraic expressions.
3. Ask students to observe which operations are included in the listed algebraic expressions and what are the characteristics of * * * identity operations.
Second, teach new lessons.
1. Single item:
Through the description of characteristics, students are guided to generalize the concept of monomial, thus introducing the topic: monomial, and summarizing the concept of monomial on the blackboard, that is, the algebraic expression composed of the product of numbers and letters is called monomial. Then the teacher added: a single number or letter is also a single item, such as a, 5.
2. Exercise: Determine which of the following algebraic expressions is a monomial?
( 1) ; (2)ABC； (3)B2； (4)-5ab 2；
(5)y； (6)-xy2； (7)-5.
3. The coefficient and number of monomials:
Instruct students to further observe the structure of monomial, and draw the conclusion that monomial is composed of number factor and letter factor. Take four monomials a2h, 2πr, abc, -m as examples, let students tell what their numerical factors are, thus introducing the concept of monomial coefficient and writing on the blackboard. Then ask the students to say what the letter factor of the above monomial is and what the index of each letter is, so as to introduce the concept of monomial times and write it on the blackboard.
4. Example:
Example 1 Determine whether the following algebraic expressions are monomials. If not, please explain why. If yes, please indicate its coefficient and frequency.
( 1)x+ 1； (2); (3)πR2； (4)-a2b。
Is the judgment of the following question correct?
The coefficient of (1)-7xy2 is 7;
(2)-x2y3 and x3 have no coefficients;
(3) The degree of Ab3c2 is 0+3+2;
(4) The coefficient of-a3 is-1;
(5) The number of times of 32x2y3 is 7;
The seventh grade mathematics "algebraic expression" teaching plan design daquan II
Teaching objectives
I. Knowledge and skills
Let students understand the concepts of polynomial and algebraic expression, which will accurately determine the degree and degree of a polynomial.
Second, the process and methods
By enumerating examples of algebraic expressions, students' ability to analyze and solve problems is cultivated.
Third, emotional attitudes and values
Cultivate students' positive thinking attitude and awareness of cooperation and communication, understand the actual background of algebraic expressions, and further feel the meaning of letters representing numbers. Teaching focus
Understand the meaning of negative number correctly and master the method of judging whether a number is positive or negative.
Teaching difficulties
1. Key points: polynomials and related concepts.
2. Difficulties: the teaching method of accurately determining the degree and term of polynomial.
Prepare the projector before class.
The teaching time is 2 hours.
teaching process
(Yuan), three basketballs, five volleyballs and two footballs cost _ _ _ _ _ _.
(3) As shown in figure 1, the area of the triangular ruler is _ _ _ _ _.
(4) As shown in Figure 2, it is the building plan of a residential building with a building area of _ _ _ _ _ square meters.
( 1) (2)
Verb (abbreviation for verb) newly granted
Please read page 57 of the textbook and answer the following questions.
1. The sum of several monomials is called _ _ _ _ _ _ _ _;
2. In polynomial, each monomial is called _ _ _ _ _ _ _ _;
3. In a polynomial, an item without letters is called _ _ _ _ _ _ _ _ _;
4. In a polynomial, _ _ _ _ _ _ _ _ _ _ _ _ _ is called the degree of this polynomial.
(2) The concept of degree of polynomial is different from that of single term, but they are related. First find the degree of each term (single term) of this polynomial, and the highest degree is the degree of this polynomial.
(3) The highest term and the second highest term of a polynomial may not be unique. For example, in the polynomial 3x2y-xy2+x2- xy-5, the highest terms are 3x2y and-xy2, and there are two quadratic terms x2 and-xy. This polynomial is a quadratic quintic polynomial.
Monomial and polynomial are collectively called algebraic expressions, for example, 100t, 6a3, vt, -n, 2x-3, 3x+5y+2z are all algebraic expressions.
Example 1. Fill in the blanks with polynomials and point out their terms and degrees.
(1) When the temperature drops by 5℃ from t℃, it is _ _ _ _ _ _ _℃
The seventh grade mathematics "Algebraic" teaching plan design daquan 3.
1. column algebra
(1) If the surface area of a cube with side length a is _ _ _ _ _ _ _ _, the volume is;
(2) The unit price of a pencil is X yuan, the unit price of a ballpoint pen is 2.5 times that of a pencil, and the unit price of a ballpoint pen is _ _ _ _ _ _ _ (3) The speed of a car is V km/h, and the distance traveled in t hours is _ _ _ _ _ _ km.
(4) Let n be a number, then its inverse is _ _ _ _ _.
(5) Xiaoming saves X yuan from his monthly pocket money and donates it to Project Hope. Xiaoming donates X yuan a year.
2. Ask the students to say the meaning of the listed algebraic expressions.
(Design intention: Let students express the quantitative relationship in real life with monomial, and further realize the simplicity, convenience and universality of using letters to represent numbers. )
3. Ask students to observe which operations are included in the listed algebraic expressions and what are the characteristics of * * * identity operations.
(After the group discussion, the person recommended by the group will answer)
(Design intention: Teachers ask questions to stimulate students' desire, enthusiasm and initiative in learning, so as to realize the characteristics of monomial as a carrier and prepare for the induction of monomial concepts)
Second, the newly granted content
1, single
Through the description of the above characteristics, the concept of single item is summarized:
Monomial: An algebraic expression consisting of the product of _ _ _ and _ _ _ is called a monomial.
Supplement: _ _ _ _ _ _ _ or _ _ _ _ _ is also a monomial, such as A, 5.
2. Exercise: Determine which of the following algebraic expressions is a monomial?
( 1); (2)ABC； (3)B2； (4)-5ab 2； (5)y+x； (6)-xy2； (7)-5。
Solution: It is a single item (fill in the serial number): _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Seventh grade mathematics "algebraic" teaching plan design daquan 4.
Teaching and learning objectives
I. Knowledge and skills
(1) The number relation in practical problems can be expressed by algebraic expressions.
(2) Understanding the concepts of single item, single item frequency and coefficient will point out the single item frequency and coefficient.
Teaching, talking and discussing.
Teaching focus
Related concepts of monomial
Teaching difficulties
Determination of negative coefficient and accurate determination of monomial degree
Preparation before class
Teachers prepare courseware for teaching.
teaching process
First, the introduction of new courses.
Teachers operate the courseware and show the patterns and subtitles before the chapters. Students watch and think about the following questions:
1. On the Qinghai-Tibet Railway, there is a long frozen soil between Golmud and Lhasa. The speed of the train in the frozen section is 100 km/h, and the speed in the unfrozen section can reach120 km/h. Please answer the following questions according to these data:
(1) How many kilometers can a train travel in 2 hours when it travels in frozen soil? How about three hours? What about t hours?
(2) From Xining to Lhasa, the time required for the train to pass through the unfrozen area is 2. 1 times that of the frozen area. If it takes t hours to pass through a frozen area, can the total length of this railway be expressed by a formula containing t?
(3) From Grimu to Lhasa, it takes 0.5 hours more for the train to pass through the frozen section than the unfrozen section. If it takes u hours to cross the frozen soil section, what is the total length of this railway? How many kilometers is the difference between frozen area and unfrozen area?
Analysis: (1) According to the relationship between speed, time and distance: distance = speed × time. The distance of a train traveling in frozen soil for 2 hours is 100×2=200 (km), the distance of traveling for 3 hours is 100×3=300 (km), and the distance of traveling for t hours is.
(2) It takes 2. 1t hours for the train to pass through the frost-free area, and the traveling distance is120× 2.1t (km); The distance that the train passes through the frozen soil is 100t, so the total length of this railway is120× 2.1t+100t (km).
(3) From Grimu to Lhasa, it takes u hours for the train to pass through the frozen section, and then (u-0.5) hours for the train to pass through the unfrozen section. The distance between the frozen section and the unfrozen section is 100u km and 120(u-0.5) km, respectively. The total length of the railway in this section is [100.
Thinking: The above questions (1) can be completed by students themselves. On the basis of students' thinking and communication, teachers guide students to analyze how to form problems (2) and (3).
The quantitative relations in the above three questions are all expressed by formulas with letters. Through the study of this chapter, we can also add and subtract the above questions (2) and (3) to simplify the complex.
Kb2。 Next, let's look at a few questions about the quantitative relationship expressed by letters.
Fill in the blanks with formulas containing letters and see what features the listed formulas have.
(1) A cube with a side length of a has a surface area of _ _ _ and a volume of _ _ _ _.
(2) The unit price of a pencil is X yuan, the unit price of a ballpoint pen is 2.5 times that of a pencil, and the unit price of a ballpoint pen is _ _ _ _ _ _ _ _.
(3) The speed of the car is V km/h, and the distance traveled in t hours is _ _ _ _ _ _ km.
(4) The reciprocal of the number n is _ _ _ _ _.
Teachers patrol the classroom, pay attention to the middle and lower level students, guide them in time, and students explore and communicate.
The algebraic expressions of the above problems are: 6a2, a3, 2.5x, vt,-n. 。
What are the characteristics of the operations in the above categories?
In the above formula, numbers and letters, letters and letters are multiplication operations, and they are all products of numbers and letters. For example, 6a2 stands for 6×a2, a3 stands for 1×a3, 2.5x stands for 2.5×x, vt stands for 1×v×t, and -n stands for-/kloc-0 /× n.
As mentioned above, formulas that only contain the product of numbers and letters are called monomials. A single number or letter is also a monomial. For example, -2, a, and are all monomials, while 1+x is not monomials.
The numerical factor in a single item is called the coefficient of the item. For example, the coefficient of 6a2 is 6, the coefficient of a3 is 1, the coefficient of -n is-1, and the coefficient of-is-.
When the monomial represents a number multiplied by a letter, the number is generally written in front, and when the coefficient of the monomial is 1 or-1, it is generally omitted.
In a monomial, the sum of the exponents of all the letters is called the degree of the monomial. For example, the exponent of the letter X in 2.5x is 1, and 2.5x is a monomial; The exponential sum of letters V and T in vt is 2, vt is a quadratic monomial, the exponential sum of letters A, B and C in -ab2c is 4, and -ab2c is a quartic monomial.
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