Rational number multiplication mathematics teaching plan 1
Teaching objectives
1。 Understand the significance of rational number multiplication, master the symbolic law and absolute value operation law in rational number multiplication law, and initially understand the rationality of rational number multiplication law;
2。 Can skillfully carry out rational number multiplication operation according to the rational number multiplication law, so that students can master the symbolic law of the product of multiple rational numbers multiplication;
3。 When three or more rational numbers that are not equal to 0 are multiplied, the multiplication exchange law, association law and distribution law can be correctly applied to simplify the operation process;
4。 Through the application of rational number multiplication law and operation law in multiplication operation, students' operation ability is cultivated;
5。 This lesson explains the rationality of the rational number multiplication rule through the trip question, so that students can feel that mathematical knowledge comes from life and is applied to life.
Teaching suggestion
(A) Analysis of key points and difficulties
Key points:
Whether you can skillfully multiply rational numbers. According to the multiplication law and operation law of rational numbers, it is the basis of further learning division and multiplication to multiply rational numbers flexibly. Multiplication of rational numbers, like addition, includes two steps: symbol judgment and absolute value operation. In multiplication operations where the factor does not contain 0, the sign of the product depends on the number of negative signs contained in the factor. When the number of negative signs is odd, the sign of the product is negative; When the number of negative signs is even, the sign of the product is positive. The absolute value of the product is the product of the absolute value of each factor. The operation process can be simplified by using the multiplication and exchange law and appropriate combination factors.
Difficulties:
Understand the multiplication rule of rational numbers. In the law of rational number multiplication, "the same sign is positive and the different sign is negative" is only for the multiplication of two factors. The multiplication rule gives a method to determine the sign of product and the absolute value of product. That is, the sign of the two factors is the same, and the sign of the product is positive; The signs of the two factors are different, and the sign of the product is negative. The absolute value of the product is the product of the absolute values of these two factors.
(B) knowledge structure
(3) Suggestions on teaching methods
1。 The law of rational number multiplication is actually a rule. The problem of travel is to understand the rationality of this regulation.
2。 When two numbers are multiplied, the basis for judging the sign is "the same sign is positive and the different sign is negative". Absolute value multiplication is also the arithmetic multiplication in primary school.
3。 Students with poor foundation should pay attention to the difference between the symbolic law of multiplication and quadrature and the symbolic law of addition and summation.
4。 Multiply several numbers. If a factor is 0, the product is equal to 0. Conversely, if the product is 0, then at least one factor is 0.
5。 The multiplicative commutative law, associative law and distributive law in elementary school are still applicable to rational number multiplication. It should be noted that the letters A, B and C here can be positive rational numbers, 0 or negative rational numbers.
6。 If the factor is a fraction, it should generally be converted into a false fraction to facilitate restoration.
Example of instructional design
Rational number multiplication (first order)
Teaching objectives
1。 On the basis of understanding the significance of rational number multiplication, students can understand the law of rational number multiplication and preliminarily understand the rationality of the law of rational number multiplication.
2。 Cultivate students' computing ability through rational number multiplication;
3。 Through the trip question given in the textbook, we know that mathematics comes from practice and reacts to practice.
Teaching emphases and difficulties
Key points: According to the multiplication law of rational numbers, skillfully perform the multiplication operation of rational numbers;
Difficulty: Understanding of rational number multiplication rule.
Classroom teaching process design
First, ask questions from students' original cognitive structure
1。 Calculate (-2)+(-2)+(-2).
2。 What are the rational numbers? In what rational number range are the four operations in primary school? (Non-negative number)
3。 What is the key problem of rational number addition and subtraction? What is the main difference between primary school and primary school? (Symbolic problem) [
4。 According to the addition and subtraction of rational numbers, the new problem is mainly the addition and subtraction of negative numbers, and the key of operation is to determine the symbol. Can you guess the new contents and key issues that will be introduced in the multiplication of rational numbers and the division to be learned later? (Negative number problem, determination of symbol)
Second, teachers and students learn the rational number multiplication rule together.
Question 1 The water level of the reservoir rises by 3cm per hour, and by how many centimeters in two hours?
Solution: 3×2=6 (cm) ①
A: It has increased by 6 cm.
Question 2: The average water level of the reservoir drops by 3 centimeters per hour, and how many centimeters does it rise in 2 hours?
Solution: -3× 2 =-6 (cm) ②
Answer: -6 cm up (that is, 6 cm down).
Guide students to compare ① and ②, and draw the following conclusions:
Replace a factor with its inverse, and the product is the inverse of the original product.
This is a very important conclusion. Applying this conclusion, 3× (-2) =? (—3)×(—2)=? (Student answers)
Comparing 3× (-2) with ①, a factor "2" is replaced by its opposite number "-2", and the product obtained should be the opposite number "-6" of the original product "6", that is, 3× (-2) =-6.
Comparing (-3) × (-2) and ②, a factor "2" is replaced by its opposite number "-2", and the product obtained should be the opposite number "6" of the original product "-6", that is, (-3 )× (-2) = 6.
In addition, (-3) × 0 = 0.
According to the above situation, guide students to summarize the law of rational number multiplication:
Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value;
Any number multiplied by 0 is 0.
Then the teacher stressed:
Multiplying the positive number in "the same sign is positive" is the multiplication of primary school learning, paying special attention to "negative is positive" and "different sign is negative" in rational numbers.
Compared with primary school multiplication, rational number multiplication is much more complicated than primary school multiplication because it involves negative numbers, but it is not difficult. The key is the symbolic law of multiplication: "The same sign is positive and the different sign is negative". Once the symbol is determined, it comes down to elementary school multiplication.
Therefore, when multiplying rational numbers, it is always important to set the symbol first and then the fixed value.
Third, the use of examples, variant exercises
The temperature of an object rises by one degree every hour, and now the temperature is 0 degrees.
What is the temperature after (1)t hours?
(2) The result when a and t are the following numbers respectively:
①a=3，t = 2； ②a=—3，t = 2；
②a=3，t =—2； ④a=—3，t =—2；
Teachers guide students to check whether the result in (2) is true.
class exercise
1。 Oral answer:
( 1)6×(—9); (2)(—6)×(—9); (3)(—6)×9;
(4)(—6)× 1; (5)(—6)×(— 1); (6)6×(— 1);
(7)(—6)×0; (8)0×(—6);
2。 Oral answer:
( 1) 1×(—5); (2)(— 1)×(—5); (3)+(—5);
(4)—(—5); (5) 1×a； (6)(- 1)×a .
After this group of questions is finished, let the students sum up by themselves: a number multiplied by 1 equals itself; A number multiplied by-1 equals its reciprocal. +(-5) can be regarded as 1× (-5), -(-5) can be regarded as (-1 )× (-5). At the same time, the teacher emphasized that A can be positive, negative or 0. -A is not necessarily a negative number, but can also be a positive number or 0.
3。 Fill in the blanks:
( 1) 1×(—6)=______; (2) 1+(—6)=_______;
(3)(— 1)×6=________; (4)(— 1)+6=______;
(5)(— 1)×(—6)=______; (6)(— 1)+(—6)=_____;
(9)|—7|×|—3|=_______; ( 10)(—7)×(—3)=______。
4。 Determine whether the solution of the following equation is positive or negative or 0:
( 1)4x =— 16； (2)—3x = 18； (3)—9x =—36； (4)—5x=0 .
Four. abstract
Today, I mainly studied the multiplication rule of rational numbers. We should keep in mind that two negative numbers are multiplied to get a positive number, and simply say "negative is positive".
Verb (short for verb) homework
1。 Calculation:
( 1)(— 16)× 15; (2)(—9)×(— 14); (3)(—36)×(— 1);
(4) 100×(—0。 00 1); (5)—4。 8×(— 1。 25); (6)—4。 5×(—0。 32)。
2。 Fill in the blanks (use ">" or "