Teaching objectives

1. Further master the algorithm and operation law of rational numbers;

2. Enable students to skillfully perform mixed operations in the order of rational number operations;

3. Pay attention to cultivating students' computing ability.

Teaching emphases and difficulties

Key point: mixed operation of rational numbers.

Difficulties: accurately grasp the operation order of rational numbers and the symbol problems in operation.

Classroom teaching process design

First, ask questions from students' original cognitive structure

1. Calculation (five minutes practice):

(5)-252; (6)(-2)3; (7)-7+3-6; (8)(-3)×(-8)×25;

( 13)(-6 16)÷(-28); ( 14)- 100-27; ( 15)(- 1) 10 1; ( 16)02 1;

( 17)(-2)4; ( 18)(-4)2; ( 19)-32; (20)-23;

(24)3.4× 104÷(-5).

2. Tell me about the algorithm of rational numbers we have learned:

Additive commutative law: A+B = B+A;

Additive associative law: (a+b)+c = a+(b+c);

Multiplicative commutative law: ab = ba

Law of multiplicative association: (ab) c = a (BC);

Multiplication and distribution law: a(b+c)=ab+ac.

Second, teach new lessons.

We learned the addition, subtraction, multiplication and division of rational numbers. If there are the above mixed operations in an expression, what order should these operations be performed?

1. In the same level operation with only addition and subtraction or only multiplication and division, proceed from left to right in the order of formulas.

Question review: (1) What is the operation sequence?

(2) What about symbols?

Note: Adding and subtracting fractions means adding the integer part and the fraction part, and then calculating the result. When a fraction is divided into an integer part and a fraction part, the symbol is the same as the original fraction.

class exercise

Examination: How to determine the operation sequence?

Pay attention to the negative sign in the result.

class exercise

Calculation: (1)-2.5× (-4.8 )× (0.09) ÷ (-0.27);

2. In the operation of different levels without brackets, first calculate the power, then calculate the multiplication and division, and finally calculate the addition and subtraction.

Example 3 Calculation:

( 1)(-3)×(-5)2; (2)〔(-3)×(-5)〕2;

(3)(-3)2-(-6); (4)(-4×32)-(-4×3)2.

Question: What is the operation sequence?

Solution: (1) (-3) × (-5) 2 = (-3 )× 25 =-75.

(2)〔(-3)×(-5)〕2=( 15)2=225.

(3)(-3)2-(-6)=9-(-6)=9+6= 15.

(4)(-4×32)-(-4×3)2

=(-4×9)-(- 12)2

=-36- 144

=- 180.

Note: Make clear the operation sequence of (1) and (2). In (1), multiply first; In (2), first calculate the one in brackets, and then multiply; In (3), multiply first and then subtract; In (4), the operation sequence should be distinguished; In the first item (-4)

class exercise

Calculation:

( 1)-72; (2)(-7)2; (3)-(-7)2;

(7)(-8÷23)-(-8÷2)3.

Example 4 Calculation

(-2)2-(-52)×(- 1)5+87÷(-3)×(- 1)4.

Question: (1) What levels of operation are there?

(2) How to determine the operation sequence?

Solution: (-2) 2-(-52) × (-1) 5+87 ÷ (-3) × (-1) 4

= 4-(-25) × (-1)+87 ÷ (-3) ×1(power first)

=4-25-29 (multiply and divide again)

=-50. (Last added)

Note: (-2)2=4, -52=-25, (-1)5=- 1, (-1) 4 = 1.

class exercise

Calculation:

( 1)-9+5×(-6)-(-4)2÷(-8);

(2)2×(-3)3-4×(-3)+ 15.

3. In the operation with brackets, calculate the brackets first, then the brackets, and finally the braces.

class exercise

Calculation:

Three. abstract

Teachers guide students to summarize the laws of rational number mixed operation.

1. Multiply first, then multiply and divide, and finally add and subtract;

2. The same level of operation from left to right in turn;

3. If there are brackets, first small, then middle and last big, and then calculate them in turn.

Fourth, homework

1. Calculation:

2. Calculation:

( 1)-8+4÷(-2); (2)6-(- 12)÷(-3);

(3)3? (-4)+(-28)÷7; (4)(-7)(-5)-90÷(- 15);

3. Calculation:

4. Calculation:

(7) 1÷(- 1)+0÷4-(-4)(- 1); (8) 18+32÷(-2)3-(-4)2×5.

5 *. Calculation (the letters in the question are all natural numbers):

( 1)(- 12)2÷(-4)3-2×(- 1)2n- 1；

(4)〔(-2)4+(-4)2? (- 1)7〕2m？ (53+35).

The second copy

Math Test of Junior One (6)

(Chapter 1 Rational Number 200 1, 10, 18) Proposer: Sun Score.

I. Multiple-choice questions: (3 points for each question, 30 points for * * *)

1.|-5 | equals ........................................... ()

(A)-5 (B)5 (C) 5 (D)0.2

2. The number represented by the origin and the point to the right of the origin on the number axis is ....................... ().

(a) Positive number (b) Negative number (c) Non-positive number (d) Non-negative number

3. The algebraic expression "the difference between the products of two numbers B and M" is ..................... ().

(A) (B) (C) (D)

4. The number whose reciprocal equals itself is .................................... ().

(A) 1 (B)2 (C)3 (d) countless.

5. Of the six numbers (n is a positive integer), the number of negative numbers is ..................................................... ().

1 (B)2 (C)3 (D)4。

6. If point A and point B on the number axis correspond to rational numbers A and B respectively, the following relationship is correct ().

(A)a | b |, then a+b 0. (Fill in ">" or "=" or "

17. Fill in the appropriate item on the horizontal line in brackets: 2x-(3a-4b+c) = (2x-3a)- ().

18. Observe the following formula and you will find the law: ; ; ; ..... Please use the same letter to represent the number, and use the equation to represent the law in the above formula.

Three. Calculation (write down the calculation process): (7 points for each question, ***28 points)

19.20.

2 1.(n is a positive integer)

22.

Fourth, if. (1) Find the values of a and b; (4 points for this question)

(2) the value. (6 points for this question)

The third copy

Math Test of Junior One (6)

(Chapter 1 Rational Number 200 1, 10, 18) Presenter: Sun.

Class name score

I. Multiple-choice questions: (3 points for each question, 30 points for * * *)

1.|-5 | equals ........................................ ()

(A)-5 (B)5 (C) 5 (D)0.2

2. The number represented by the origin and the point to the right of the origin on the number axis is ..................... ().

(a) Positive number (b) Negative number (c) Non-positive number (d) Non-negative number

3. The algebraic expression "the difference between the products of b and m" is ................. ().

(A) (B) (C) (D)

4.-12+1-8+39 = (-12-8)+(11+39) is the application of ().

A, additive commutative law b, additive associative law c, additive commutative law and associative law d, multiplicative distributive law.

5. Rewrite 6-(+3)-(-7)+(-2), omit the plus sign, and the total should be ().

a、6-3+7-2 B、6-3-7-2 C、6-3+7-2 D、6+3-7-2

6. If |x|=3 and |y|=7, the value of x-y is ().

A, 4 B, 10c, -4 or-10d, 4, 10.

7. If a× b < 0, there must be ().

A, a > 0, b < 0 b, a < 0, b > 0 c, a and b are the same number, and d, a and b are different numbers.

8. If the sum of two rational numbers is positive and the product is negative, then these two rational numbers ().

A, both are positive numbers. B, the number with the largest absolute value is positive and the other is negative.

C, all negative numbers D, the number with the largest absolute value is negative, and the other is positive.

9. Stationery store, bookstore and toy store are located in an east-west street in turn. The stationery store is 20 meters west of the bookstore, and the toy store is 20 meters east of the bookstore 100 meters. Xiaoming walks 40 meters east from the bookstore, and then walks -60 meters east. At this time, Xiao Ming's position is ().

A, stationery store B, toy store C, stationery store D is 40 meters west, and toy store is -60 meters east.

10. What is the known rational number and its position on the number axis?

As shown in the figure, when 1a > 0, ②-b < 0, ③ a-b > 0,

(4) Among the four relationships of A+B > 0, the correct one is ().

a，4 B，3 C，2 D， 1

2. True or false questions: (For the right picture "+",the wrong picture "○", each question 1, and ***6).

1 1.0.3 is neither an integer nor a fraction, so it is not a rational number. ( )

12. The absolute value of rational number is equal to the reciprocal of this number, which is negative. ( )

13. The increase in income is recorded as +5 yuan in 5 yuan, and the decrease in expenditure is recorded as -5 yuan in 5 yuan. ( )

14. If a is rational, -a must be negative. ( )

15. If you subtract a rational number from zero, you still get this number. ( )

16. Multiply several rational numbers. If the number of negative factors is odd, the product is negative. ( )

Three. Fill in the blanks: (3 points for each question, *** 18 points)

17. Fill in the appropriate items in brackets to make the equation hold: A+B-C+D = A+B- ().

18. Comparative size: │-│-│. (fill in ">" or "

19. As shown in the figure, if the distance between any two adjacent points in the points marked on the number axis is equal, then the value of a =.

?

20. One addend is 0. 1, and the sum is -27.9, and the other addend is.

The sum of 2 1 -9, +6 and -3 are less than the sum of their absolute values.

22. Equation × [(-5)+(- 13)] = According to the algorithm of is.

4. Fill in the results directly in the following lines: (2 points for each question, *** 12 points)

23.-2+3= ; 24.-27+(-5 1)= ; 25.- 18-34= ;

26.-24-(- 17)= ; 27.- 14×5= ; 28.- 18×(-2)= 。

Verb (abbreviation of verb) calculation (write down the calculation process): (6 points for each question on 29 and 30, 7 points for each question on 3 1 32, ***26 points)

29.(-6)-(-7)+(-5)-(+9) 30.

3 1.32.(-5)×(-3 )- 15× 1 +〔 -( )×24〕

6. The following table lists the time differences between several foreign cities and Beijing (numbers with a plus sign indicate that the same time is several hours earlier than Beijing time).

(1) If the current Beijing time is 7: 00, what is the current new york time?

Xiaohua wants to call her grandfather in Paris now. Do you think it's appropriate? (4 points for each small question)

* This is a multiplication symbol.

[-|98|+76+(-87)]*23[56+(-75)-(7)]-(8+4+3)

5+2 1*8/2-6-59

68/2 1-8- 1 1*8+6 1

-2/9-7/9-56

4.6-(-3/4+ 1.6-4-3/4)

1/2+3+5/6-7/ 12

[2/3-4- 1/4*(-0.4)]/ 1/3+2

22+(-4)+(-2)+4*3

-2*8-8* 1/2+8/ 1/8

(2/3+ 1/2)/(- 1/ 12)*(- 12)

(-28)/(-6+4)+(- 1)

2/(-2)+0/7-(-8)*(-2)

( 1/4-5/6+ 1/3+2/3)/ 1/2

18-6/(-3)*(-2)

(5+3/8*8/30/(-2)-3

(-84)/2*(-3)/(-6)

1/2*(-4/ 15)/2/3

-3x+2y-5x-7y

Mixed operation of rational number addition and subtraction

Synchronous outline exercise

1. Multiple choice question:

(1) Write -2-(+3)-(-5)+(-4)+(+3) in the form of omitting brackets, and the correct one is ().

A.-2-3-5-4+3 B.-2+3+5-4+3

C.-2-3+5-4+3 D.-2-3-5+4+3

(2) The result of calculating (-5)-(+3)+(-9)-(-7)+ is correct ().

A.- 10 B.-9 C.8 D.-23

(3) The algebraic sum of-7,-12 and +2 is less than the sum of their absolute values ()

A.-38 B- 4 c . 4d . 38

(4) If +(b+3)2=0, then b%

Ordinary math problems are too difficult to find. There are 50 more questions. We are not math teachers, so there are not so many problems. The above questions are on the 1 test paper.