Area calculation of combined graphics

Teaching objectives:

1. Let the students know the characteristics of the circular ring according to the specific situation, master the method of calculating the area of the circular ring, and accurately calculate the area of some simple combination figures.

2. Through independent inquiry and group cooperation, further apply the formula of circumference and area to solve some practical problems related to life.

3. Make students further experience the connection between graphics and life, feel the learning value of plane graphics, and improve their interest in mathematics learning and confidence in learning mathematics well.

Teaching focus:

Mastering the method of calculating the area of circular ring can accurately calculate the area of some simple combined figures.

Teaching difficulties:

The perimeter formula and area formula of a circle are applied to solve some practical problems related to life.

Teaching preparation:

Compass, circular picture, teaching situation map.

First, create situations and introduce new knowledge.

1. Show some circular pictures of nature.

Look at the pictures and tell me what these pictures are made of.

(2) Can you give some examples of cycles?

2. Introduction: In today's lesson, let's learn the calculation method of annular area.

Second, cooperate and exchange, and explore new knowledge.

1. Teaching examples 1 1.

(1) Give an example of 1 1 and read the title.

(2) Question: This is a circle composed of two concentric circles. Is there any good way to calculate its area? Think independently.

(3) Group discussion, to clarify the problem-solving ideas.

(4) Collective communication

① Find the area of the excircle.

② Find the area of the inner circle.

③ Calculate the area of the ring.

(5) Students calculate independently according to the steps.

(6) Organize the exchange of problem-solving methods, and teachers write on the blackboard.

① Find the area of the excircle: 3.14×102 = 314 (square centimeter).

② Find the area of the inner circle: 3.14× 62 =113.04 (square centimeter).

③ Calculate the area of the ring: 314-113.04 = 200.96 (square centimeter).

(7) Question: Is there a simpler calculation method?

(8) Summary after the students answer: Generally, the area of the circle is calculated by subtracting the area of the outer circle from the area of the inner circle.

You can also use the multiplication distribution rate for simple calculation.

Simple calculation

3. 14× 102-3. 14×62

=3. 14×( 102-62)

=3. 14×64

= 200.96 square centimeters

A: The area of this iron sheet is 200.96 square centimeters.

2. Generalization: If R is used to represent the radius of the big circle and R is used to represent the radius of the small circle, can the formula for calculating the annular area be derived according to the above calculation process?

After the students answered, the teacher wrote on the blackboard.

or

3. Complete "Give it a try".

(1) Show questions and pictures and read questions.

(2) Question: What are the basic figures that make up this combined figure?

(3) What is the connection between a semicircle and a square?

After the students communicate, it is clear that the side length of a square is the diameter of a semicircle.

(4) Think about how to calculate the area of a semicircle.

(5) Students calculate independently.

(6) Communicate problem-solving methods, and pay attention to remind students that the area of a semicircle must be divided by the area of the whole circle 2 0.

4. Summary: Basic plane figures such as circles and semicircles are combined to produce many beautiful combined figures. When calculating the area of combined graphics, we should see clearly which basic graphics constitute the whole graphics, and then calculate.

Third, consolidate practice and deepen understanding.

1. Complete the Exercise.

Look at the picture and find out the meaning of the question.

(2) Question: What basic graphic areas need to be calculated to find the area of the colored part?

(3) In the first graph, what is the connection between the two basic graphs? What about the second graphic?

Clear: the width of the rectangle in the left picture is equal to the radius of the circle, and the diameter of the semicircle in the right picture is the height of the triangle.

(4) Students calculate independently.

(5) Collective communication.

2. Complete exercise 15 Question 9.

(1) Let's test the relevant data first.

(2) Calculate independently according to the data.

(3) Collective communication.

3. Complete the exercise 15, question 13.

(1) Estimate the fraction of each flower in the circular area.

(2) Calculate the planting area of each flower.

(3) Collective communication.

4. Complete the exercise 15, question 14.

(1) Students make intuitive judgments according to the graphics, and talk about the methods of intuitive judgments.

(2) Check the judgment made by calculation.

5. Complete the exercise 15, question 15.

(1) Students read the questions and observe the schematic diagram.

(2) Question: What is the actual requirement for the area of the path? What do I have to know to ask for the area of a ring?

Conditions? What conditions does the title tell us? What other conditions do we require?

(3) Students calculate independently.

(4) Collective communication.

6. think about the problem.

(1) Students should think carefully before doing calculations.

(2) Organize communication.

Fourth, class summary.

Teacher: What did you learn in this class? What is your inspiration?

First, the students speak independently, and then the teacher complements them.

Blackboard design:

① Find the area of the excircle: 3.14×102 = 314 (square centimeter).

② Find the area of the inner circle: 3.14× 62 =113.04 (square centimeter).

③ Calculate the area of the ring: 314-113.04 = 200.96 (square centimeter).

Simple calculation

3. 14× 102-3. 14×62

=3. 14×( 102-62)

=3. 14×64

= 200.96 square centimeters

A: The area of this iron sheet is 200.96 square centimeters.

Formula for calculating annular area: or