Chapter 1 Rational Numbers
(1) How much did Xiao Zhang spend this week? How much money have you saved?
According to the above records, Q: In which days did you produce more motorcycles than planned? On which day of the week do you produce the most motorcycles? How many motorcycles are there? What day of the week produces the least number of motorcycles? How many?
Solid foundation
(1) Which part number is closest to the standard?
④-(-) ? 0.025.
The second classroom addition algorithm
Teaching objectives:
1. Addition can be simplified by using the law of addition.
2. Understand the role of addition algorithm in addition operation, and conduct reasoning training appropriately.
Teaching emphasis: how to simplify the operation by using the addition algorithm.
Teaching difficulty: flexible application of addition algorithm.
Interactive design of teaching and learning;
(A) the creation of situations, the introduction of new courses
Thinking: What are the addition algorithms we learned in primary school? What are their contents? Can you give me one or two examples? Do these addition laws still apply to the rational number range? Today, let's discuss this issue together.
(2) Cooperation and exchange, interpretation and exploration
Calculation: Is the sum of 20+(-30) and (-30)+20 the same?
Draw a conclusion: 20+(-30)=(-30)+20.
Try changing the number of groups: get additive commutative law: a+b=? (to be filled in by students).
In fact, students have been exposed to the algorithm in primary school. At this time, students can recall what kind of addition operation laws they learned in primary school besides the exchange law of addition. (Association Law)
Calculation: (1) [8+(-5)]+(-4);
(2)8+[(-5)+(-4)].
Draw a conclusion: the law of additive association: (a+b)+c=? .
Example 1 calculation:
16+(-25)+24+(-35)
Example 2 Textbook P20 Example 3
Note: Adding a pair of opposite numbers can simplify the operation. This method is based on additive commutative law's law of addition.
Summary: When adding multiple rational numbers, additive commutative law's law of addition can be used to simplify the operation in the following situations: ① When some addends can be added to get integers, they can be added first; 2 There are antonyms that can cancel each other out. If the sum is 0, you can add them first. (3) When multiple positive numbers and negative numbers are added, the numbers with the same sign can be added first, that is, positive numbers and positive numbers are added, negative numbers and negative numbers are added, and then a positive number and a negative number are added.
(3) Application of migration, integration and improvement
Example 3 makes the operation simple by using the addition algorithm of rational numbers.
( 1)(+9)+(-7)+(+ 10)+(-3)+(-9)
(2)(+0.36)+(-7.4)+(+0.03)+(-0.6)+(+0.64)
(3)(+ 1)+(-2)+(+3)+(-4)+…+(+2003)+(-2004)
One afternoon, a taxi driver's operation was all on the east-west Renmin Avenue. If the east is positive and the west is negative, his mileage this afternoon is as follows: (in km)+ 15,+14, -3,-1 1,+18.
(1) He sent the last passenger to his destination. What is the distance between the driver and the departure point in the afternoon?
(2) If the fuel consumption of a car is one liter/km, how many liters will this car consume this afternoon?
(4) Summing up reflection and expanding sublimation.
In this lesson, we discussed additive commutative law and the associative law of rational numbers. Flexible use of the addition algorithm will make the operation simple. Generally, we will combine the opposite numbers with the fractions of the denominator, combine the numbers that can form integers, and add the positive and negative numbers separately, so that the calculation is simple.
(E) classroom tracking feedback
Solid foundation
1. It is the most suitable () to calculate (+6)+(-18)+(+4)+(-6.8)+18+(-3.2) by the arithmetic rule of addition.
A.[(+6)+(+4)+ 18]+[(- 18)+(-6.8)+(-3.2)]
B.[(+6)+(-6.8)+(+4)]+[(- 18)+ 18+(-3.2)]
C.[(+6)+(- 18)]+[(+4)+(-6.8)]+[ 18+(-3.2)]
D.[(+6)+(+4)]+[(-3.2)+(-6.8)]+[(- 18)+ 18)]
2. Calculation: (-2)+4+(-6)+8+…+(-98)+100.
Improve ability
3. Xiao Li went to the bank to handle four transactions, the first deposit 120 yuan, the second withdrawal from 85 yuan, the third withdrawal from 70 yuan and the fourth deposit 130 yuan. If these four deals are merged into one, how do you plan this deal for him?
4. An overhaul team takes a bus to overhaul the route along the expressway, and agrees that the forward direction is positive and the backward direction is negative. The route (unit: km) to go to work from place A on a certain day is+10, -3, +4, +2, -8,+13, -2, +65438+.
(1) How far is a place from where we call it a day?
(2) If the fuel consumption per kilometer is 0.2 liters, how many liters does it take to get off work from A place?
Third kind of rational number subtraction
Teaching objectives:
1. Experience the process of exploring the law of rational number subtraction and understand the law of rational number subtraction.
2. Proficient in rational number subtraction.
Teaching emphasis: rational number subtraction rules and operations.
Teaching difficulty: deduction of rational number subtraction rules.
Interactive design of teaching and learning
(A) create scenarios and introduce new lessons.
Observation thermometer:
Can you see from the thermometer how many degrees 4℃ is higher than -3℃?
Students can generally intuitively see that 4℃ is 7℃ higher than -3℃, and further suppose that' the temperature in a certain place is -3~4℃ in a day, then how can the temperature difference (minus the lowest temperature, unit℃) be expressed by a formula?
According to the results just observed, we can see that 4-(-3)=7 ①, while 4+(+3) = 7 ②. It can be seen from ① ② that 4-(-3)=4+(+3) ③. Students are free to answer the above conclusions.
(B) hands-on practice, discover new knowledge
Observe, explore and discuss: Can we see from Formula ③ that -3 is equivalent to the addition of any number?
Conclusion: Subtracting -3 is equal to adding the reciprocal of -3 +3.
(C) analogy to explore, summarize and improve
If you change 4 to-1, is there a conclusion similar to the above?
Let the students observe intuitively first, and then the teacher will use "subtraction is the antonym of addition" to guide the students to test from another angle.
To calculate (-1)-(-3) is to find a number X, so that the sum of X and -3 is-1, because the sum of 2 and -3 is-1, so X should be 2, that is, (-1)-(-3).
And because (-1)+(+3)=2 ②,
(- 1)-(-3)=- 1+(+3) ③,
That is, the above conclusion is still valid.
Try it: If you change 4 into 0 and -5, and consider 0-(-3) and (-5)-(-3) in the above way, is the result of subtracting -3 from these numbers the same as that of adding +3?
Ask students to use "subtraction is the inverse of addition" to get the result, and then compare it with the result of addition formula, so that the result of subtracting -3 from these numbers is the same as that of adding +3 to them.
Try again: change -3 to a positive number. What is the result?
Calculate 9-8 and 9+(-8); 15-7 and 15+(-7)
Can we find something new from it?
Ask students to sum up the following conclusions through calculation: subtracting a positive number is equal to adding the inverse of this positive number.
Induction: From the above experiments, we can find that the subtraction of rational numbers can be converted into addition.
Law of subtraction: subtracting a number is equal to adding the reciprocal of this number.
Expressed in letters: a-b=a+(-b).
(In the above experiments, an important mathematical thinking method-transformation has been gradually infiltrated. )
(D) Case analysis, application of rules
Example calculation:
( 1)(-3)-(-5); ? (2)0-7;
(3)7.2-(-4.8); (4)-3-5.
(v) Summary, synthesis and preliminary application
What mathematical knowledge and ideas have we learned in this class? Can you talk about it?
Teachers guide students to recall what they have learned in this lesson, and students can recall and communicate, and teachers and students complement each other to make students more clear about what they have learned.