1. Knowledge and skills
(1) Understand the concept of cube root, and initially learn to express the cube root of a number with a root sign;
(2) In order to solve the inverse operation between cubes, cube operation will be used to find the cube roots of some numbers; ③ Understand the difference and connection between cube root and square root;
(4) Students can use calculators to find cube roots, so that students can personally realize that using calculators can not only bring great convenience to calculation, but also bring convenience to exploring the relationship and changes between quantities.
2. Process and method
① In the process of exploring the concept of cube root and related knowledge, experience the idea of analogical mathematics and develop their own reasoning ability and organizational language expression ability;
② Experience the process of using calculator to explore mathematical laws and develop reasonable reasoning ability.
3. Emotions and attitudes
(1) By studying cube roots, we can understand the close relationship between mathematics and human life;
② Exercise the will to overcome difficulties through inquiry activities, build up self-confidence and improve the enthusiasm of learning mathematics.
Important and difficult
Teaching emphasis: the concept and solution of cube root.
Teaching difficulties: the difference and connection between cube root and square root.
Teaching methods and learning methods
(A) teaching philosophy:
The concept of cube root: adopting analogy method;
The essence of cube root: step by step, from special to general.
process analysis
(a) Activity 1: Create a scenario and introduce the cube root.
Question 1: Practical problems in mathematics.
Students have seen electric water heaters at home or in shopping malls. We usually use a volume of 50 liters in our home. If you want to produce a cylindrical water heater with a volume of 50 liters, so that its height is twice the diameter of the bottom surface, how many decimeters should the radius of the bottom surface of this container take?
(The teacher shows pictures and asks questions; Solution: Let the radius at the bottom of the cylinder be x decimeter, then the diameter is 2x decimeter and the height of the cylinder is 4x decimeter.
x24x50
x3≈3.98 1
(Students' existing knowledge can only go so far.)
The analysis of the quantitative relationship in this practical problem is not a problem for students, but it is a challenge for students to introduce new problems in the process of solving problems, thus stimulating their interest in learning.
Question 2: Have the students encountered similar practical problems?
Students will give examples of cubes. Students will encounter more cubes, and the volume formula is a cube with long sides. Guide students to add examples to math problems;
For example, students give an example: the volume of a cube is 27, and the side length of the cube is found;
Continue to guide students to analyze this problem and get: x3=27.
The teacher asked: which knowledge point is similar to what we learned before?
Contact the square root concept learned before and summarize the concept of cubic root with the above questions; Related to the concept of square root, the concept of publisher is given.
Students organize their thoughts and expound their opinions.
The teacher summed up the cube root concept of students' answers.
(2) Activity 2: Apply concepts and explore nature.
Example 1. Find the cube root of the following numbers.
( 1) 64 (2)0. 125 (3)0
8(4)- 8 (5)27
Teachers standardize students' language narration, write a complete problem-solving process on the blackboard, and demonstrate standardized problem-solving steps for students.
Explore 1
Question 1: What did the students find through the example 1
What are the characteristics of cube roots of positive numbers, zero numbers and negative numbers?
Induction: the cube root of a positive number is a number;
The cube root of a negative number is a number;
The cube root of zero is.
Question 2: Can you tell the difference between the square root and the cube root of a number?
(3) Activity 3: Improve your ability and re-explore nature.
1. Give the representation of cube root: a;
Where 3 is the root index and A is the root number;
Reading: the third root number A puts forward the precautions: the root index 3 of A cannot be omitted.
Inquiry 2: Explore the relationship between cube roots which are opposites.
8(2),(288;
27(3),27(3),2727; 1 1 1 1 1 1(),(. 1255 1255 125 125
Question: What did you find by filling in the blanks? Can you express your findings in relational expressions? Through the design of the above two links, the difficulty of this course has been broken through.
(4) Activity 4: Apply new knowledge and consolidate new knowledge.
1. Example 2. Look for the following values:
( 1)(2) 125(3)27
64(4)2 197
Students think independently and teachers and students work together;
2. Use the calculator to find the cube root of a number and complete the following exercises.
( 1)
(2) 15625
(3) 2744
(4)0.426254
The teacher encourages students to explore the use of calculators themselves.
For some students who have not learned to find the cube root of a number with a calculator for the time being, students can help each other and learn from each other.
3. Explore 3:
Use a calculator to calculate ... 000216, .216, 216, 216000 ... What laws can you find? Approximate value calculated by calculator (accurate to 0.00 1). Use the law you found to find. 1, 0.338+0.
(5) Activity 5: Summarize the assignments.
1. What did the students learn from this lesson?
Homework
(1) Required question: P80 3 4 5 6
(2) Inquiry after class: Find the values of 23, (2)3, (3)3, 43 and 303. For any number a, what is a equal to? Find the values of 27, 27 and 0. What is a for any number a? 333333333
The classic "13.2 cube root" teaching design Part II: Teaching objectives
Knowledge and skills
1, understand the concept of cube root, and initially learn to express the cube root of a number with a root sign.
2. In order to solve the inverse operation between cubes, cube operation will be used to find the cube roots of some numbers.
Process and method
1, let students understand the uniqueness of the cube root of a number.
2. Cultivate students' ability to find cubic roots by analogy, understand the reciprocity of cubic and square operations, and infiltrate the idea of mathematical reduction.
Emotional attitudes and values
Through the introduction of cube root symbols, we can experience the beauty of simplicity in mathematics.
Second, the key points and difficulties
focus
The concept and solution of cubic root.
difficulty
The difference between cube root and square root, the solution of cube root
Thirdly, the analysis of learning situation.
I have learned the knowledge of square root before. Because there are many similarities between the learning of square root and cube root, I mainly use analogy in teaching design. On the basis of a comprehensive review of square roots, I will guide students to learn the knowledge of cubic roots, so that students can feel that the knowledge of cubic roots is not difficult. By comparing with the knowledge of square roots, students can overcome their strange psychology of learning new knowledge. In terms of learning methods, students are encouraged to learn through reflection, and make appropriate reflection after drawing the concept, the nature of induction and solving problems. Looking at and understanding new knowledge and new problems in reflection will be more rational and comprehensive, and there will be greater progress.
Fourth, the teaching process design
On designing teacher-student activities for teaching problems
Situation creation question: What should be the side length of a cubic packing box with a volume of 27m3?
Let the side length of this box be xm, then =27. This is to find a number so that its cube is equal to 27.
Because =27, x=3, that is, the side length of this box should be 3m.
Induction:
The concept of cube root:
Create problem situations, stimulate students' interest in learning, and introduce concepts after group discussion.
The concept of cube root is obtained through specific problems.
Inquiry 1:
Fill in the blanks according to the meaning of cube roots and see what are the characteristics of positive, zero and negative cube roots?
Because of (), the cube root of 0. 125 is ().
Because of (), the cube root of -8 is ()
Because of (), the cube root of -0. 125 is ().
Because of (), the cube root of 0 is ()
Positive numbers have positive cubic roots.
0 has a cube root, which is itself.
Negative numbers have negative cubic roots.
Any number has a unique cube root.
summary
The cube root of a number is called "cube root number", here it is called root number, and 3 is called root number. Cannot be omitted. If omitted, it means square.
Question 2:
Because of this =
Because, so = summary:
Using the reciprocal operation relationship between the issuing bank and the cube to find the cubic root of a number, we can use this reciprocal relationship to test its correctness and find the cubic root of a negative number. We can first find the cubic root of the absolute value of this negative number, and then take its reciprocal, that is.