Tisch
Teaching content:
This section belongs to the last section of Unit 4 "Cuboid (II)" in the fifth grade of primary school mathematics of Beijing Normal University Press: interesting measurement (finding the volume of irregular objects).
Teaching material analysis:
This lesson is based on students' knowledge of cuboids and cubes, their knowledge of surface area and volume, and the content of volume. It is necessary for students to master the solution of irregular object volume by observing and comparing, which expands their knowledge and permeates the idea of reduction.
Analysis of learning situation:
Most students in this class are conscientious, down-to-earth and self-conscious, with a solid foundation, eager to learn and make progress, and some boys are lively and active and love to think. I am very interested in exploring mathematical problems and like to solve them by myself. There is also an obvious child nature, active and curious. Most students have a solid knowledge of this unit.
Teaching objectives:
1. Experience the experimental process of measuring the volume of mango, stone and water bottle, explore the method of measuring the volume of irregular objects, and infiltrate and transform ideas.
2, master the measurement method of irregular objects, and can measure the volume of irregular objects.
3. In the process of practical exploration, try to solve practical problems in various ways and improve the ability to solve practical problems flexibly.
Teaching focus:
Let students master the method of measuring the volume of irregular objects.
Teaching difficulties:
Flexible use of "drainage method" and "overflow method" to solve practical problems.
Teaching aid preparation:
Rubik's cube, mango, cylindrical measuring cup, cuboid sink, stone and several bottles of apple vinegar.
Teaching process:
First, import
1, classmate, the teacher found a Rubik's cube from the cupboard when cleaning the room at the weekend, and I especially like it.
Mathematically speaking, what kind of object is the Rubik's Cube? (cube)
How to find the volume of this cube? (blackboard writing: V plus =a3)
Its side length is 10 cm. What is its volume? (1000 cubic centimeter)
2. Besides cubes, what other three-dimensional figures do you want? (blackboard writing: v length =abh)
3. Like cuboids and cubes, we can directly calculate their volumes through formulas. Such objects are called "regular objects". (blackboard writing: general object)
Now, please look at the Rubik's cube in the teacher's hand again. Still a cube? (Rotating) What shape is it?
Such an object whose specific shape cannot be accurately expressed in words can be seen everywhere in our lives. We call them "irregular objects". (Blackboard: No)
5. What is the volume of this Rubik's Cube now? (Or 1000cm3) What do you think? (blackboard writing: transformation)
Design intention: I use cubes to infiltrate the main mathematical ideas used in this class to students, paving the way for the later experiments, and at the same time stimulating students' enthusiasm for learning.
6. The Rubik's Cube is a special object. Look again, the mango in the teacher's hand is also an irregular object. Can it be directly converted into a regular object?
Then what is its volume and how to find it?
In this lesson, we will study the volume of irregular objects through interesting measurements.
Second, new funding.
(1) Measure the volume of mango.
1. How do you want to measure the volume of this mango? (Student Report)
2. On the desktop, the teacher prepared two measuring tools for each group: a measuring cup and a cuboid container.
Which measuring tool do you think can be used to quickly calculate the volume of mango? Why? (Choose a measuring cup because it has a scale)
3. This can really get the turnover of mango quickly. Take a look (ppt demonstration).
There is a part of water in the measuring cup, which is exactly 300 ml. What does this 300mL mean? (Volume of water)
Observe carefully, what happened to the water surface after mango was put into the water? Why does the water surface rise? So, what does 400mL mean now? (Volume of water and mango)
Now, do you know the volume of mango?
100 is the volume of mango. What is its volume? (Rising water volume)
In the experiment just now, we completed a transformation with the help of measuring cup. What has it become? (The volume of mango is converted into the volume of rising water, or irregular mango is converted into a regular cylinder.)
The method of measuring the volume of irregular objects like just now is called "drainage method".
Design intention: The teacher guides the students to observe the first experiment: try it with a cup and water and measure the volume of mango. Through a series of activities such as discussion, communication and observation, students can initially understand that the volume of irregular objects can be converted into the volume of water in the rising part, which is the basic method to measure the volume of irregular objects.
(2) Measuring the volume of stone
1. Now the teacher also wants to make a measurement. What I want to measure is the volume of this stone.
What tool should I choose to measure? Why? (Choose a rectangular container because the stone is too big)
2. How to find the volume of this stone with this cuboid container? Talk to the partners in your group. (After discussion, students report)
3. What should I pay attention to when measuring? (emphasis: measured from the inside)
Display data: length 25cm, width 18cm and water height 8cm. Slowly put the stone into the water and observe what happens to the water surface. Why?
Can't you put it like this (vertically)? Why? (The stone is not completely immersed in the water)
The stone has been completely immersed in the water, and the water level is 10cm.
Can you calculate the volume of this stone according to the data displayed on the screen? (Students write calculations)
Just now, with our joint efforts, we measured the volume of this stone.
In this experiment, we completed another transformation. What have we become? (The volume of stone is converted into the volume of rising water, or it can be said that irregular stone is converted into a regular cuboid.)
Design intention: Students have the foundation of the first experiment, and teachers exchange experimental supplies for the second experiment, using rectangular containers instead of measuring cups to further explore the volume of irregular objects. With the foundation of the first experiment, students will easily explore how to convert the volume of irregular objects into the volume of computable cuboids, thus breaking through the difficulties of this lesson. In this link, the teacher stressed in time that the stone should be completely immersed in the water when measuring, so as to apply the idea of transformation to find the volume.
6. Do you have any other methods to measure the volume of this stone? (Show the reverse application of "overflow method" and "drainage method")
Design intention: Teachers guide students to think about other methods to measure the volume of irregular objects, so that students can understand the diversity of problem-solving methods.
7. In fact, as early as more than 2,000 years ago, the great physicist Archimedes used the method mentioned by his classmates just now to help the king solve a difficult problem and showed a "mathematical kaleidoscope" for students to read.
(3) measuring the volume of the apple vinegar bottle
1, do you want to measure the volume of irregular objects yourself now?
The opportunity is just around the corner. There is a bottle of apple vinegar on the table of each group. Before you start, please guess "What is the volume of this bottle?" ? (net content: 260ml)
Let's do it now. Fill in the records in the experimental report.
Design intention: The new curriculum standard of mathematics emphasizes that "doing" is more important than "knowing" in teaching. Mathematics activity class should grasp the opportunity of practical activities and let students play whatever they design; Let students do their best.
In the experiment just now, we completed another transformation. Who can tell us?
(4) Summary
Through these experiments, we found that both "drainage method" and "overflow method" are actually completing a transformation. What is this? (Convert irregular objects into regular objects)
Design intention: let students know the essence of "transformation" thought.
Third, question
Look at this page. Is there anything you don't know about what we learned today?
Fourth, classroom exercises.
(1) Fill in the blanks
1, a measuring cup has a water surface scale of 200mL. When a part is put in, the measuring cup has a water surface scale of 450mL, and the volume of this part is ().
2. A cuboid container filled with water, the bottom is 8 meters long, 5 meters wide and 3 meters high. After putting in an irregular object, it overflows 30 liters of water. The volume of this irregular object is ().
3. A cuboid container, measured from the inside, is 3cm long, 2cm wide and 5cm high. It is filled with water 3 meters deep. If a small cuboid is put into water, its length is10cm, its width is 8cm and its height is 5cm. The volume of rising water is ().
Purpose of exercise: to strengthen the essence of "transformation" thought.
(2) Solving problems
the first group
1, a cuboid container with a bottom of 4dm and a width of 2dm. After putting a stone, the water level rises by 0.5dm. What is the volume of this stone?
A 20 cm long cubic container is now filled with 5 cm deep water. After placing an object, the water surface rises to 8 cm. What is the volume of this object in cubic centimeters?
Purpose of practice: Through comparative practice, from intuition to abstraction, to stimulate students' interest in learning and improve teaching efficiency and benefit.
the second group
1, cuboid container, length 20cm, width15cm, height10cm. Put the iron block into a container, fill it with water and take it out. At this time, the water level in the container is 6 cm. What is the volume of this iron block?
2. A cubic container is filled with water. Put a cuboid in it, and 48 liters of water will overflow from the container. It is known that a rectangular object is 8 decimeters long and 2 decimeters wide. How many centimeters is the height?
3. A cubic container with a length of 15 cm and a water depth of 8 cm. After immersion in irregular steel blocks, the water surface rises to 3 cm from the mouth of the container. What is the volume of this steel block?
The purpose of the exercise: from the shallow to the deep, from layer to layer, in the form of group cooperation, let students participate in the whole teaching process and enhance their sense of ownership.
Verb (abbreviation of verb) class summary
1. What did you get from this lesson? (Student Report)
There are many irregular objects in life, and we can convert them into regular objects to calculate the volume. We often need to think flexibly when solving mathematical problems.
3. Expanding exercise: So, can you find a way to measure the volume of a soybean? (Student Report)
A soybean is very small. When we put it into the water, it is difficult for us to see the rise of the water surface and calculate its volume. We can measure the volume of a certain number of soybeans first, and then divide it by the number of soybeans, and we can get the volume of a soybean.
Blackboard design:
change
Interesting measurement: the volume of irregular objects, the volume of regular objects.
V is positive = the volume of A3 mango and the volume of rising water.
V length =abh stone falling
Bottle overflow
extreme
Teaching objectives:
1. Knowledge goal: Based on the knowledge of cuboids and cubes, explore the measurement methods of some irregular objects in life, and deepen the understanding and deepening of the learned knowledge.
2. Ability goal: Experience the process of exploring the volume measurement method of irregular objects and experience the transformation process of "equal product deformation". By comprehensively applying the learned knowledge, we can obtain the activity experience and specific methods of measuring the volume of irregular objects, and cultivate the team spirit and problem-solving ability.
3. Emotional goal: Feel the interrelation between mathematical knowledge, experience the close connection between mathematics and life, and establish confidence in using mathematics to solve practical problems.
Teaching process:
First, check the import.
1, review the volume of a long (regular) cube, and the conversion between volume and unit of volume.
2. Listen to the story. Cao Chong is called an elephant (the mass of an elephant is converted into the mass of a stone) \ Archimedes' story (the volume of a crown is converted into the volume of water). Will this story help and inspire us in this class?
3. Observe the shape of (stone \ potato) and draw an irregular object (blackboard writing) by comparing it with a cuboid or a cube.
Is the crown in the story also an irregular object?
Comparing stones and potatoes, which object is more irregular, points out that we are going to measure the volume of stones today. (blackboard writing)
Second, experimental operation, measuring the volume of stone.
1. Take out the measuring tools under the table. According to the given measuring tools, each group works out the measuring scheme and what to do (division of labor). Division of labor and cooperation:
Scheme 1: Take water, measure the length and width of the bottom and the height of the water surface, and then measure the height of the water surface after putting stones. The difference between the bottom area and the height is the volume of the stone. (Note: the amount of water should be moderate, neither too little nor too much, subject to the fact that the stones are submerged and the rising water does not overflow. )
Scheme 2: Take water, fill the empty container with water, then slowly put the stones into the water, and then pour the spilled water into the measuring cup to measure the volume of the water.
2. The group reports their own practices, and the teacher writes on the blackboard while listening to the students' reports. Appropriate amount of water: the proposed volume of water is equivalent to the volume of stone. Add water: the volume of spilled water is equivalent to the volume of stone. )
It's really good. Everyone has measured the volume of this stone. Please pour the water back into the bucket. We exchange measuring tools and re-measure the volume of the stone to verify whether the measurement results are roughly the same.
3. Besides the above two schemes, are there any other measurement schemes? Tell me, will Cao Chong be the second in our class?
Default 1: small objects-measure the volume directly with a cup.
Preset 2: First put the stone into the container, add water to the container until the water is higher than the stone, measure the height of the water, take out the stone, measure the height of the water again, and multiply the bottom area of the container by twice the height difference to get the volume of the stone.
Premise 3: When the filled water is too high, we can add water to the increased water volume, or we can find out the volume of the stone.
Premise 4: There is a method to find the volume of stones by weighing. We weigh and estimate the stones we measure, and then find the volume of stones of any size according to this pair of data.
Premise 5: Use plasticine instead of water. Put the stone into an empty cuboid container, fill the container with plasticine, take out the stone, and then fill it with plasticine (flatten it, measure the height of plasticine, and multiply the difference between the container height and plasticine height by the bottom area to get the volume of the stone. ……
Third, consolidate and improve.
Today, everyone's performance was really good, and some plans were unexpected by the teacher. Apply what you have learned, apply what you have learned, and see how to do the questions on the blackboard.
1. A cuboid container with a bottom length of 2 decimeters and a width of 1.5 decimeters. After putting a potato in, the water level rose by 0.2 decimeter. What is the volume of this potato? (Students do it independently. )
2. Measure the volume of the bouncing ball.
Count 25 jumping beads, put them into a measuring cup with a certain amount of water, measure the volume of water according to the rise of the water surface, and then calculate the volume of one jumping bead. (Students experiment and calculate the volume)
Fourth, summarize and improve.
What did you gain from today's study? I learned how to find the volume of stones, how to find the volume of irregular objects, and how to transform one object into another to solve problems. )
Tisso
Teaching objectives:
1. Combined with the specific activity situation, experience the experimental process of measuring stone volume and explore the measurement method of irregular objects.
2. In the process of practice and inquiry, try to solve practical problems by various methods.
Teaching emphases and difficulties:
Explore the method of irregular object volume and try to solve practical problems in many ways.
Teaching activities:
First, create situations and introduce new knowledge.
1. Show me the stone.
Q: How to measure the volume of a stone? What is the volume of a stone?
Extreme book title.
2. Take the group as the unit, discuss and formulate the measurement scheme first.
Q: Can I use the formula directly? What if I can't?
3. The team sent representatives to introduce the measurement scheme.
Students observe stones.
Think about how to measure the volume of stones.
Students discuss in groups and make a measurement plan.
The student's measurement plan may include:
Scheme 1: Take a cube container, put a certain amount of water into it, measure the water level, then sink the stones into the water and measure the water level again. At this time, calculate how many centimeters the water surface has risen, and use "bottom area × height" to calculate the volume of rising water, that is, the volume of stones. You can also calculate the difference between the volume of water before putting the stone and the total volume after putting the stone.
Scheme 2: Put the stone into a container filled with water, pour the spilled water into a graduated measuring cup, and then directly read out the volume of the spilled water, which is the volume of the stone.
Option 3: Fine sand can be used instead of water, and the method is the same as methods 1 and 2.
Design intention: Create scenarios to stimulate students' interest in learning new knowledge. Guide students to cooperate in groups and make measurement plans.
Guide students to explore and experience the method of measuring the volume of irregular objects.
Second, carry out experiments.
Students are required to work together according to the plan made by their respective groups.
Group representatives receive the necessary measuring tools, and students measure and calculate continuously together.
Design intention: Through experiments, let students understand that there is more than one way to convert irregular stone volume into water volume.
Third, give it a try.
1. In a cubic container, measure the volume of an apple.
2. Measure the volume of a soybean.
Students measure together.
3. summary.
Teacher: What did you get from the experiment?
Ask some students to talk about their gains.
Design intention: Let students use the measurement method obtained in cable handling activities to measure the volume of other irregular objects again.
Fourth, mathematical kaleidoscope.
The courseware shows the story of Archimedes taking a bath.
Students listen to the teacher's story about Archimedes taking a bath.