Mathematics Courseware for the Sixth Grade of Primary School: Understanding of Circle

# Courseware # Introduction Courseware is a course software that is made according to the requirements of the syllabus, through the determination of teaching objectives, the analysis of teaching contents and tasks, the structure of teaching activities and the design of interface. It is directly related to the course content. Using courseware can attract students' attention, improve their learning mood, and thus arouse their interest in learning. The following is the channel without courseware.

Mathematics Courseware for Grade Six in Primary School Part I: Understanding of the Circle

Teaching objectives:

1. Knowledge objectives: to master the names of various parts of the circle and its characteristics; Can draw circles with compasses.

2. Ability goal: With the help of hands-on activities, cultivate students' ability to use what they have learned to solve practical problems.

3. Emotional goal: Infiltrate the idea that knowledge comes from practice and the purpose of learning is application.

teaching methods:

guided practice, transfer and example

teaching preparation:

multimedia courseware, compasses, rulers, etc.

teaching process:

First, introduce new lessons with practice and conversation.

Introduction: Today, I am very happy to study and

study a math problem with my classmates. We have known the circle before. Can you find out which things in life are round in shape?

teacher: it seems that people usually have to pay attention to observation. Before class, please draw two circles of different sizes and cut them out. Are you ready?

teacher: lift them up and let's have a look at each other. Looking back on the process of drawing and cutting a circle, can you tell me what a circle looks like? (teacher holds a circle in each hand)

teacher: the students have observed it very carefully. The edge of a circle is curved, which is different from that of a rectangle or a square. Today, we are going to study the curve figure on this plane. (writing on the blackboard)

Examples of students

The teacher emphasized that the surface of an object

has no edges and corners, and the edges are curved; The edge of a circle is a curve.

second, guide to explore new knowledge.

1. Guide: What secrets are hidden in the circle? Let's do a little experiment. Fold your circle in half, fold it again, fold it several times, draw the crease, see what you find, and report your findings in the group. Finally, let's see who gets more. (1 minute)

2. Teacher: Your group has observed it carefully! You've made a lot of discoveries. Now let's sort out what we just found.

3. Show the results of the inquiry. With the help of multimedia courseware, fully understand the characteristics of the circle (8 minutes)

Who will tell the teacher and what new discoveries have you made?

what's the reason?

how did you find out?

Combine the students' communication and report the results of the inquiry, and guide them in time. Mainly from the circle center, radius, diameter, etc. Here, special attention should be paid to helping students with new knowledge and purposeful arrangement through blackboard writing.

4. learn to draw a circle (5 minutes).

how do you draw a circle?

The courseware shows how to draw a circle. Then the students begin to practice and emphasize what should be paid attention to when drawing a circle. -reveal the size of the circle

Determine the position

The school is going to build a flower bed with a diameter of 2 meters. Can you help the school draw this circle? Student demonstration operation

Third, application expansion.

1. Basic exercises (4 minutes).

< 1 > Projection show

Find the radius and diameter of the following circle.

< 2 > Related calculation of radius and diameter.

Judgment and identification of the concept of < 3 >.

2. Application exercises. (1 minutes)

< 1 > Why are the wheels round and where should the axles be installed?

if the wheels are made into squares and triangles, how will we feel when we sit on them? Demonstrate with courseware

< 2 > Can you explain some life phenomena with the knowledge of circle learned today

(When holding a bonfire party, people always unconsciously form a circle, why?

what happens when a pebble is thrown on a calm lake? Why?

Moon cakes are generally round. Why? )

It seems that many phenomena in life are rich in truth, and we need to explore constantly to understand it, explain it and use it.

< 3 > Students are very tired after learning, so let's relax. The teacher guessed a riddle for everyone. A man nailed a stake in a grass field and tied a sheep there with a rope. (using computer to match the picture)

Teacher: Is the situation of sheep grazing related to the knowledge learned today? Let's take a look at the extent to which sheep graze, shall we?

Use a computer to demonstrate the situation that a sheep tightens a rope and rotates once, so that students can intuitively see that the range of grass that the sheep can eat is a circle. Does the rope tied to the sheep have anything to do with this circle?

(It is the radius of this circle) What is the stake nailed there? (It's the center of this circle) What can I do if I want this sheep to graze a little more? (Make the rope longer, that is, enlarge the radius) What should I do if I want the sheep to eat grass in another place? (you can move the stake one place, that is, the position of the center of the circle), which shows what is the relationship between the radius of the circle and the center of the circle and the circle?

the radius of a circle determines its size, while the center of a circle can determine its position.

Fourth, summarize the whole class (3 minutes)

1. Query

(Is basketball round? Can the letters representing the center, radius and diameter be changed at will? )

2. What did you learn in this class?

anyway, the teacher thinks that the students' academic performance is good, so I propose that we reach out and draw a satisfactory conclusion together. (The period is round)

Extension

1. Draw with a circle.

2. talk about the circle in my eyes.

blackboard writing design:

understanding of the circle-plane curve figure

center (o) is a point in the center of the circle, determine the position of the circle

radius (r) line segment

connect the center to any point on the circle, and determine that the size and length of the circle are equal < in the same circle >

diameter (d) line segment. < in the same circle >

The relationship between radius and diameter d=2r

Teaching reflection:

Let students understand that all radii are equal only in the same circle or in the same circle; All diameters are equal; The radius is half the diameter, and the diameter is twice the radius.

Mathematics Courseware for Grade Six in Primary School Part II: Understanding of Circle

Teaching objectives:

Knowledge and skills

(1) Knowing the circle and the names of its parts.

(2) enable students to master the characteristics of a circle, understand and master the relationship between radius and diameter in the same circle, find any radius and diameter in the same circle, and independently complete the problem of finding a diameter with a known radius or finding a radius with a known diameter.

(3) Make students learn to draw circles with compasses. A circle with a known radius or a circle with a known diameter can be drawn with a compass.

process and method

(1) to train students' drawing ability through hands-on activities.

(2) through group learning, hands-on operation, active exploration and other activities to cultivate students' innovative consciousness, abstract generalization and other abilities, and further develop students' spatial concept.

(3) In the process of learning, cultivate students' ability to cooperate with others and exchange thinking process and results.

Emotion, attitude and values

Through the understanding of the circle, I feel that beauty comes from life, and experiencing the circle is closely related to daily life, and I feel the charm of mathematical knowledge.

Teaching objectives:

1. Observe and experience the characteristics of a circle, know the names of various parts of the circle, and understand the relationship between diameter and radius in the same circle or an equal circle.

2. Understand and master various methods of drawing circles, and learn to draw circles with compasses initially.

3. In the activity, feel the difference between the circle and other figures, communicate with them, gain rich experience of mathematical beauty, and enhance students' recognition of mathematical culture.

Teaching emphasis:

Explore the names, characteristics and relationships of various parts of a circle.

Teaching difficulties:

Experience the characteristics of circle through practical hands-on operation.

Teaching process:

1. Perceive the circle as a whole

1. Show the slide: the circle in life

Photographic works. What figures did you find in these beautiful pictures? Where have you seen a circle in your life?

2. Reveal the topic: The circle is everywhere, so we will know it in this lesson.

writing on the blackboard: understanding the circle

3. Do students like to play the game of hoop? Why don't you try it now

I have a toy here, and you are required to stand three meters away from it and throw a circle. Where can you stand?

We use three centimeters to represent three meters. Can you mark your position in this book?

2. Really invest in students' achievements (from drawing a few points to many points until the circle)

Q: Is it ok to stand on these points? Why? Can we only stand on these points?

after the circle appears, ask, is there any place to stand?

3. Courseware demonstration

Teacher: So where can I stand? (Any point on the circle)

How many such points are there on the circle?

2. Knowing the circle in operation

1. There is a circle on the screen. Can students make a circle with existing tools?

2. Students draw a circle, and the teacher makes a tour

3. Report on different methods of drawing a circle (look for the report of drawing with a circular tool first)

Show the blackboard with a rope

Talk: This classmate drew such a big circle on the blackboard with such a long rope. What if I want to draw a big circle on the playground?

practical demonstration of compasses

4. Summarize the method of drawing a circle with compasses

5. Students practice drawing several circles with compasses

Since we can draw circles with the help of circular tools, why did people invent compasses?

6. Observe the circle you draw. What else is there besides a closed curve? (a little)

Give it a name-the center of the circle (let the students say it if they can) is represented by the letter O.

7. Take out the circular paper in your hand. Is there any way for you to determine the center of the circle?

Students start folding

Q: What else did you find besides the center of the circle? (crease)

What does the crease you found look like?

teacher: who wants to go to the front and introduce their findings? Reveal the definition of diameter and radius

Can you draw the diameter and radius on the circle?

Mark the center, draw the radius and diameter on the circle you draw

Third, communicate and explore the circle

What is the function of the center and radius? Draw a picture and you will know

1. Draw several different circles on the book with a compass to see who draws beautifully.

2. Projection display

Q: Some circles you draw are above, some are below, some are to the left and some are to the right. What is the decision?

Students report, why is the circle so obedient?

Teacher's summary: The center of the circle determines the position of the circle. No wonder people call it the center of the circle.

These circles are different in size, so how to draw them can make them big and small?

Summary: The radius of the circle determines the size of the circle (the distance between the two feet of the compass)

3. Teacher: The radius is not small. Do you want to know what other characteristics of the radius are? Shall I tell you directly or study it myself?

Then combine the teacher's tips and use the tool group in your hand to study together.

4. Research tips

What is the relationship between radius and diameter in the same circle?

how many radii are there in the same circle?

Are the radii equal in length in the same circle?

Report

The diameter of the same circle is twice the radius on the blackboard d=2r

Q: How do you know?

There are countless radii of the same circle. Why? (There are countless points on the circle, found in creases)

There are countless radii of the same circle, so what is the diameter?

blackboard writing: there are countless inner radii of the same circle.

The radii of the same circle are all equal. Why? (Through measurement and reasoning)

The radii of the same circle are all equal, so are the diameters all equal?

blackboard writing: the inner radius of the same circle is equal.

so the ancients said: round, one with the same length is also

what does this middle finger mean? What does the same length mean?

read this sentence while watching the slide show.

A circle with the same length is widely used in life

4. Why are wheels made round? Can you explain?

why not make the wheels into these shapes? (Show regular polygon pictures)

Fourth, deepen the understanding of the circle in comparison

1. What has changed from regular triangle to regular dodecagon?

2. Imagine what a regular 1-sided polygon would look like. (Close to a circle, but not a circle)

What about the regular 372 polygon? (Closer to a circle, but not yet a circle)

How many sides is a circle?

3. There is a record in The Classic of Weekly Calculations that "the circle comes from the square, and the square comes from the moment". The so-called circle comes from the square, which means that the original circle was not drawn with the current compasses, but was continuously cut from the square. Now, if I tell you that the side length of the square is 6 cm, what information can you get about the circle?

4. Taiji diagram of Yin and Yang.

teacher: do you want to know how this picture is formed? It is composed of a big circle and two small circles with the same size. Now, if I tell you that the radius of the small circle is 3 cm, what can you know?

5. Next, we will face the challenge of three practical problems. Do students dare to accept the challenge?

question 1. can you measure the diameter of a coin? (Reference tool: ruler, a set of triangles)

Question 2. Can you draw a circle with a radius of 1 meter on the ground? (Reference tools: rope, chalk)

Question 3. The wheels are all round. Where are the axles? Why? (Reference tool: bicycle)

After class, each student chooses a topic that interests him most to study.

V. Summary

After learning this lesson, do the students have any ideas? There are endless mysteries hidden in the circle, waiting for the students to study and discover! May our study and life be as perfect as a circle!