Beijing normal university printing plate seventh grade second volume mathematics courseware
First, the teaching objectives
1. Understand and master the formulas of zero exponential power and negative exponential power, and skillfully use them to calculate.
2. Cultivate students' abstract mathematical thinking ability.
3. Train students' comprehensive problem-solving ability and calculation ability through examples and exercises.
4. The dialectical and unified mathematical thinking view of self-application and reverse application of infiltration formula.
Second, the key points and difficulties
1. Focus
Understand and apply the properties of negative integer exponential power.
2. Difficulties
Understand and apply the nature and function of negative integer exponential power, and express numbers with absolute value less than 1 by scientific notation.
Third, the teaching process
1. Create a situation, review and introduce it.
What is the operational nature of power? Please use the formula.
(2) expressed by scientific notation: ①69600 ②-5746.
(3) Calculation:
2. In-depth guidance to reveal the law.
From this we stipulate that
Law 1: Any number whose power is not equal to 0 is equal to 1.
If the exponent of the divisor is less than the exponent of the divisor,
For example:
It can be calculated by simulating the division property of same base powers.
From this we stipulate that
Generally speaking, we stipulate that
Law 2: The power of -p(p is a positive integer) of any number that is not equal to 0 is equal to the reciprocal of the power of p of this number.
3. Try to give feedback. Understand new knowledge
Example 1 calculation:
Solution: (1) Original formula
(2) the original formula
(3) the original formula
(4) Original formula
Example 2 The following figures are expressed in decimals:
Solution:
Exercise: P 14 1 1, 2.
Example 3 Write 100, 1, 0. 1, 0.0 1, 0.000 1 as the power of 10.
Students draw the following conclusions: ① The number of digits of an integer greater than 1 minus 1 is equal to the exponent of the power of 10; ② The number of consecutive zeros (including zeros before decimal point) is equal to the absolute value of the exponent of the power of 10.
Q: Write 0.000007 as the product of a number with only one integer bit and the power of 10.
Solution:
As above, we can also use scientific notation to represent numbers whose absolute value is less than 1.
Example 4 Use scientific notation to represent the following figures:
0.008、0.0000 16、0.0000000 125
Solution:
The mass of the earth is about
Tons, Jupiter's mass is about 3 18 times that of the earth. What is the mass of Jupiter? Solution: (tons) A: The mass of Jupiter is about tons.
Exercise: P 142 1 2.
Fourth, summarize and expand.
The properties of 1. negative integer exponential power;
2. Use scientific notation to express the law of numbers:
(1) Numbers with large absolute values.
N is a non-negative integer, and n= the integer part of the original number minus 1.
(2) Numbers with smaller absolute values
N is a negative integer, which is the number of all zeros before the first non-zero number in the original number (including zeros before the decimal point).
Verb (abbreviation for verb) assigns homework.
P 143 A group 4, 5, 6; Group b 1, 2, 3, 4.