Review of two-week course on length measurement

A brief review of the main learning content of length measurement in the first two weeks of school.

Each step below is roughly a three-day rhythm. It goes through "do it first on the first day and discover it in life, and then review and discuss it on the second day for a more in-depth experience." , thinking and summarizing on the third day” is a process like this.

Knowledge must be truly internalized into children's experience and thinking. It cannot be done by talking about it in class or copying the content from the main textbook. It is easy to follow the teacher's or other people's ideas in the inquiry activities in the classroom. When you go home, you must do, write, and draw by yourself in order to transform it into your own understanding.

The first step: open your body to compare and measure

On the first day of school, after not being together for more than half a year, the children have grown taller and the class is here New classmates. We greeted each other, compared ourselves, and posted our own photos on the photo wall. When learning crochet in the handicraft class, Teacher Caiyun led the children to use braided needles to crochet the height ruler, and compared the measurements while crocheting. In the carpentry class, Teacher Sai Peng led everyone to make wooden crates. First, they divided the wood into groups and cut out wooden strips of corresponding lengths...

The next day, we reviewed the measurement work we had done. The children came up with various measurement methods, such as aligning the drawn lines, measuring the length with their hands, using string, using playing cards (card stock), etc. The most interesting thing is that some children suggested that they can use their eyes to measure, which naturally led to "visual inspection" estimation.

Question: A long piece of wood given by Teacher Sai Peng is required to be cut into one length. Can you please visually check how many pieces it can be cut into?

Some say five paragraphs, some say six paragraphs. Let the children come to the blackboard to demonstrate and operate. (Mou Rongxuan came up and carefully drew six short sections along the wooden strips. He was very attentive during the whole working process. The first three sections were basically uniform, and the next three sections began to be shorter and longer.) The children thought of various ways. Verify that each section is the same length, such as comparing it with two fingers, drawing a mark on a small stick, and measuring it with a piece of string (start with the measurement activity).

Extending one finger on each hand of the left and right hands marks the starting point and end point of the measurement very well, but during the movement, it is difficult to keep the distance between the two fingers constant (tethered in the middle A rope would work). Is there a relatively stable length on our body that can be used as a ruler to measure? Children naturally think of the stroke of a hand or the length of a baby's step. So we explored various rulers on the body to complete the measurement task.

Measurement task: Ask the children to measure the length and width of the classroom. Some of the children are feet long, some are hand-length (Dai Kongran and Ma Qianhua worked together to measure from both ends to the middle, they stretched out their hands to show that their hands were the same length), and some measured with open arms (one fathom, some are the same length). The children used it directly as a meter). As their bodies opened up during the measurement activity, some children even tried to do the splits. (During this process, it was discovered that the children’s concepts of “length” and “width” were not clear, and some children expressed doubts about whether “length” could be used to measure “width”.)

Measurement tasks: How high is the teacher's door? (Height is the third dimension that is relatively difficult to reach.) The children thought of many ways (lowering the door, using shoes, using ropes...), and one child guessed that "the door is as high as two Wang Jinghans." So I tried it. Lift Wang Jinghan up and compare; another child said: "The door is the height of Teacher Huang Min's raised arm." Visual inspection and length comparison help develop the overall perception of length, and it is also an important step in developing the sense of quantity.

I would like to further introduce length units that are easier to communicate and compare. For example, which is higher, the classroom door or the door at home? How many feet long are they? At this time, you need to resort to "measurement" in the true sense. According to the children's suggestions, we first used a rope to measure the height of the door, lowered it to the ground, and then used baby steps to measure it. After that, I asked the children to go home and measure it. How high is the door at home?

Step 2: Make "My Ruler"

? There is a transition from the body to an objective measurement tool: making a "ruler".

During this process, the children felt that the initial measurement methods and measurement units were directly experienced using the body. When an objective "ruler" was made, they slowly became separated from the body. For example, Zhuan-Zhang refers to Chi-Cun; maybe my ruler is made according to Zhuan, which is Zhuanchi, but the names become Chi and Cun. This is the first level of separation and abstraction. The units at this stage can be called "self-made units". The child then uses his own ruler to re-measure what he had previously measured.

When I introduced it in class, I told the story of Zheng Ren buying shoes. Although this fable is taken in the opposite direction - Zheng Guoren would rather believe in the measured size than his own feet, forgetting that the fundamental purpose of measuring data is to make the shoes fit the size of the feet. Without data, the actual Just compare.

If a Zheng person wants to buy a shoe, he should first hold it to his feet and then sit on it. Go to the market and forget to operate it. When he had already taken it, he said, "I forgot to uphold it." Instead, he returned to take it. When he rebelled, he was dismissed from the market and could not carry out his duties. People said: "Why not give it a try?" He said: "It is better to have faith than to have confidence." ("Han Feizi")

From this story, we learned the meaning of "degree" as a verb and a noun. Two meanings. Then I asked the children: When do we need to use a scale instead of just stretching our feet to measure?

We discussed many examples in class. For example, our mother wanted to buy us dance shoes, but we had to go to school and couldn’t go with her. When we couldn’t be there in person, it was very helpful to use an objective ruler. It is necessary; for another example, we reviewed the height of the door yesterday. It is obviously much more convenient to make a foot-long ruler to measure than to remove the door and measure it with your feet; another situation is that if you want to measure The blackboard is several fingers wide, and it is too laborious to move it one by one with your fingers. If we can first make a ruler that is ten or twenty fingers wide, and then use the ruler to measure, it will obviously be much more efficient and more accurate. It will also be more accurate.

How high is the requirement for accuracy in measurement?

Sometimes it is enough to have almost the same measurement results. For example, it's raining today and Teacher Bao wants to teach physical education in the class. If the children raise their arms horizontally, please estimate the width of the classroom. How many people can stand in one row? (The children cooperated and tried on the spot)

Sometimes the measurement needs to be very precise. For example, when we buy audio dance shoes, they must be not too big and not too small to just fit. At this time, the accuracy of measurement is very important.

When the children use their own body scales to measure, the length of my foot is different from the length of your foot, and the results cannot be accurately compared. Because the specific number is uncertain, it can produce a vague sense of quantity, that is, is the measured number reasonable? Conversely, what is the relationship between the units of length I use and the units you use?

We did some oral word problems in the follow-up class. For example: The teacher took one step forward and Xiao Ming was two steps away. From the classroom door to the stairwell, Xiao Ming took 50 steps. What should the teacher do? How many steps does it take? Then this distance is 50 small steps and 25 teacher steps. (Implicit in the conversion relationship between different units).

Homework: 1. Use your ruler to measure the size of your desk and bed.

? 2. Are there other ways you can make a ruler?

Step 3: Discuss "Our Ruler" - the introduction of standard measurement units

Looking back at the production of "My Hand Ruler", we have learned how to use our bodies to measure, how to Make a ruler to measure.

Dramatic scene demonstration: Autumn is the harvest season, there are tall haystacks, and the mother asked the little boy to buy some hemp rope to tie the hay (borrow the big rope from the handicraft/sports equipment room.) The little boy : How long of rope should I buy? Mom: Ask the boss to measure the length of ten arms.

When I went to the first store (looking for the tallest child in the class to be the first grocery store owner), the boss used her arm to measure ten sections, and the mother was very satisfied with the rope she bought. (The children were very into the game. A group of children wanted to act out a haystack to see how many people could be tied up with this long rope.

)

A few days later, I went to the second store (looking for the smallest child in the class to be the owner of the second grocery store). The rope measured this time was too short! Ask the children to discuss why the two results are not the same length?

The live effect of the drama was very good, arousing the children's emotions. Through the scenario display, everyone realized that there must be a "standard ruler" between people to facilitate communication. So I asked the children to discuss in groups to determine "our most common ruler."

Then we talked about how people in history determined a unified unit of length. The King of England used the length from the tip of his nose to the tip of his finger to determine a yard, and the length of his own feet to determine a foot. The rigorous Germans asked the first 16 men to come out of the church to measure their left Add the lengths of the feet together and divide by 16 to get one foot. The children also used the concept of "average foot length" during group discussions, but instead of calculating the arithmetic mean, they took the median of the foot lengths.

On the second day of class, review how "our ruler" is determined? The children mentioned that the length of hands and feet can change, and it would be more reliable to use an objective and unchanging scale. For example, one group of children chose a recorder stick as the fair ruler. However, the recorder sticks made in different batches will have different lengths, so there still needs to be a unified standard. So we looked for things that are common to everyone, easy to measure, and will not change easily - the earth is our common home, and our previous measurements started from the ground beneath our feet. I told the children the story of a French scientist who braved war artillery fire to measure the earth on foot. One meter is officially defined as "one forty-millionth of the earth's circumference." It sounds cool, right? A simple one meter, but behind it lies the truth-seeking spirit of many people who have devoted their lives and persevered in their efforts.

The history of measurement is accompanied by the development of human consciousness. I hope that children will feel more about the encounter between subject and object consciousness from their own experience - how people understand (measure) the world, and how to function in society. to share their knowledge. I deliberately do not talk too much about historical measurement units. Units such as inches, feet, and feet correspond to different lengths in different dynasties. Teacher Shaohua taught the "Huang Zhong Lei Millet Method", using grain (objective natural objects) To make a standardized ruler, there are more cultural connotations in it. I think we can wait until we talk about Chinese history. The focus of this section is still on creating and using a ruler (a ruler that is one arm long and has finger-width scales is easier to make and use, and can also be compared with previous body measurement results.)

Chapter Four steps: Exploring the family of rice - establishing a sense of quantity

After telling the story of rice, the children were all yearning for the "meter ruler" protected by a three-layer cover in the French museum. At this time, I gave each child a "one-meter stick" and asked them to work together to measure the size of the classroom and the phonetic dance classroom. The great advantage of the "one-meter stick" is that it visualizes the length of "one meter" and is a rigid ruler. You can see the measurement process on a larger scale - whether it can be along a straight line. direction, is the starting point of each measurement found correctly?

Next, what if I want to measure the blackboard and table? A one-meter stick is too long, so we need to define smaller units. In the previous body measurement session, the children have experienced that body rulers of different sizes are used for different measurement needs, and when the large unit cannot be used, they can continue to measure with small units.

I was given an IKEA meter ruler to observe how one meter is divided into 100 grids, and each grid can be further subdivided into 10 small grids, which leads to centimeters and millimeters. and the definition of decimeter. With a ruler in hand, we learned the meaning of zero points and scales, and encouraged children to look for decimeters, centimeters, and millimeters in life.

Homework: 1. Use a meter ruler to measure how long and wide your bed is? (Preparing for the study tour)

2. Find family members who use meters in life

After introducing standard units and meter sticks, I hope the children will go through a series of measuring activities , to build a pictorial understanding of these abstract units of length. So I dedicated two main lessons to sort out my understanding of the "family of rice".

At the beginning, I asked the children to draw a one-meter-long line segment on the blackboard and let the children in the audience judge whether it was longer or shorter than one meter. We use the "one-meter stick" to compare and correct the length. Invite several more children to try this process, and compare again after each drawing. In the end, it will continue to approach "one meter", which will have a more dramatic effect and allow all children to focus on this great work. In terms of things, we finally reached the "ideal one meter" together. During this process, children will also spontaneously work hard to draw straight lines and control the direction and length of line segments.

After seeing "one meter", we looked for things close to "one meter" in life. The children found that the length of the arms, excluding the hands, is about one meter; the distance between the door handle and the ground The distance is about one meter; Hao Hongbo sat down, and the height of the tip of his tongue from the ground was about one meter (a genius imagination, we actually measured it). Through these pictures in life, the purpose is to help children have an intuitive feeling about "one meter long".

We used similar procedures to explore "decimeters", "centimeters" and "millimeters". We first tried to draw them, then used a ruler to compare and correct them, and finally looked for corresponding sizes in the surrounding environment. thing. In order to allow each child to fully engage in the work, in addition to asking several children to draw on the blackboard, I asked everyone to try to draw in their own notebooks. Everyone soon fell out of the same rhythm. Some were busy drawing and some were measuring everywhere with rulers. At this time, it was a bit difficult for me to draw the children's attention and look at the presentation on the blackboard together. Moreover, as the scale becomes smaller and smaller, it is difficult to draw "one centimeter" and "one millimeter" things on the big blackboard. The children hold their notebooks and squeeze in front of me to let me see what they have drawn and what they have done. Measure something.

In the chaos, the children measured and discovered many things of one decimeter and one centimeter. For example, the width of a human hand and the outer distance between the left and right eyes are about one decimeter. The thickness of the baby side of the wax block and the table board is close to 1 cm. There were a few boys in the class who liked bugs. They measured the width of the smelly eldest sister's body and the length of the mosquito's legs.

As the end of the measurement activity, I took out the peanuts I prepared in advance and asked everyone to estimate and measure whether the length of the peanuts is close to 1 cm? (The children asked: Can it be eaten? Yes!) In the silence of chewing peanuts, I told the story of the King of England who selected the three largest wheat kernels to determine the "standard legal inch".

In hindsight, giving this group of units all at once was a bit much. Maybe we will only discuss meters and centimeters at the beginning. It will be more valuable to use these two units well and make a lot of estimates and measurements.

The next day, we expanded the family of meters to ten meters, one hundred meters and one thousand meters. First, the children were asked to stand one meter apart in the classroom. This time, the children's perception of one meter was basically very accurate (the distance measurement from the length of the physical object into the space). We went to the small square in the triangle and stood in a 5×5 square array, with 1 meter between the front, back, left and right. There were 26 children in the class, and the extra one (Mou Rongxuan) asked him to hold a one-meter stick in his hand and walk through the square array to see if there was a one-meter gap. Then I asked the children in each group to pass the one-meter stick back and forth to check whether there was a one-meter distance.

With the perception of one meter, I asked the children to estimate how far 10 meters is, and each group worked together to measure the 10-meter finish line from the same starting line with the help of a one-meter stick. location. Wait until the children place the one-meter sticks on the finish line. I took out the measuring tape I used to measure in physical education class and confirmed the length of 10 meters.

This stage does not require each group to measure very accurately, but it is necessary to pay attention to whether the measurement method is correct and understand the reasons that may produce different measurement results (whether it is along the same direction, whether there is any overlap or skipped part when moving the ruler, etc).

Next, I asked each child to walk over at a normal pace to see how many steps he had to take to cover 10 meters. He walked back and forth to see if his steps were stable and consistent. I thought of several ways in advance to let the children measure 100 meters, such as using a one-meter stick to pick up 10 people, using a ten-meter-long hemp rope, and running back and forth alternately to measure... I guess the children started running collectively. It's easy to get too excited, so I decided to use the method of counting steps to estimate 100 meters, and counting steps is very practical in daily life.

I did some research with the teacher of the physical education group before class. The boundary of the football field is 104 meters long and 68 meters wide. The width of each dark green/light green stripe is 4 meters, and one circle of the track is 350 meters. meters (to be confirmed). Because there is a ready-made length of nearly 100 meters, I asked the children to go to the football field and use their own steps to measure the distance from one end of the football field to the other.

This task is really difficult for third-grade children. They need to keep a steady pace, count correctly, and finally be able to do division. Wang Yixin ran back and forth and told me firmly: "160 meters." He introduced his calculation process in detail. Some of the other children calculated it to be very close to 100 meters, while others only told me how many steps they had taken. It is still a bit of a test to convert it into meters. ——If this task is changed to, use your own steps to measure a distance of 100 meters. Wouldn't it be simpler? Or borrow some cones and mark them every 10 meters.

At this time, the children discovered that the dark and light green stripes on the football field were the same width. Really? I asked the children to measure it with steps, and it turned out to be the same! Then use a measuring tape to measure, each section is 4 meters long. The boys were very interested in the big measuring tape I brought, and Chen Junshi simply took it and put it outside. So everyone pulled the tape measure all the way on the playground, and then chased to see the length of each stripe: 4, 8, 12, 16, 20! Unfortunately, the tape measure is only 20 meters long, but it is enough for children to feel the multiple relationship. Some clever children have already run to count the stripes. After Li Yumo finished counting, he ran over and told me: "There are 25 sections, 100 meters!"

An accident happened in this class. While most of the children were following me in the front to measure, there were children behind who climbed on the football. The goal, a child pulled the goal down and hit his leg. Other children were content to lie on the grass and bask in the sun. After counting a round of steps, they lay down and enjoyed the sun. The subsequent discussion and thinking process were not too intrusive. At that moment, I complied with the psychological needs of the children, and at the same time, I was thinking, how can the organization more fully mobilize each child in the overall activities? It is of course best to be fully immersed in the field. Review and summary after returning to the classroom are also essential.

Step 5: Length Diary and Unit Test

The following week we went to Tianfuyuan Farming Study Tour. Work on the farm also involves some knowledge of measurement, such as choosing the distance and distance to dig a tree pit when building a fence, the length of branches, and keeping two trenches equally spaced when planting winter wheat. The children used body measurements freely and also inserted a row of small tree sticks to assist in the measurement.

After returning from the study tour, there are only three days of classes before the National Day holiday. I also have to review the study tour, prepare for the sports meeting and the Mid-Autumn Festival celebration. I decided not to add new content, but reviewed and summarized the length measurement part and conducted a small unit test.

I focused my review on the "sense of quantity" and "summary of measurement methods" of length units.

Riding on the enthusiasm of writing a diary during the study tour, I read a "Diary" to the children, describing the length in daily life. I deliberately used exaggeration and mixed length units, such as: " In the morning, I got up from the 2-centimeter-long bed, wore 2-meter-long slippers, went to the bathroom, and started brushing my teeth with a 15-centimeter-long toothbrush. "The children were very happy after hearing it and strongly urged me to read it again.

I said: "You can read it again, but you have to help me correct my mistakes and fill in the correct units of length, so as not to tell others and be laughed at." I read slowly, and most of the children helped me fill in the units very seriously. . Finally, they said: "I want to listen to the original version again!" Then I'll say the original version, and you can help me correct it, okay?

The children carefully used their hands or rulers to mark the imaginary length. Combining life situations, we reviewed the different length units of the "meter family" again. Everyone still remembers the "Length Diary" at the beginning, so as the day's homework, each child was asked to go back and write a short length diary.

After the unit quiz, on the occasion of the Mid-Autumn Festival, I told the children the story of "Wu Gang Cutting the Osmanthus": "The osmanthus tree in the Moon Palace is more than 500 feet high. For thousands of years, it has been Who is Wu Gang? Why does he keep chopping down trees? "My intention in telling this story is to let the children experience concentration and perseverance." The Chinese character "Zhang" and its corresponding measurement unit. After telling the story, we read Li Bai's poem "If you want to cut the laurel in the moon, hold on to the salary of those who are cold".

The children said: "If Li Bai goes to the Moon Palace to chop down the sweet-scented osmanthus tree, he will definitely be able to chop it down." Why? Because he is not doing it for himself, but for other people who are frozen. A great career can bring a greater sense of accomplishment and meaning, and therefore be more able to transcend one's own limitations.

After being touched, I thought: In future measurement activities, we should more consciously introduce the big picture (big story), stir up the power of the heart and soul, and embrace great things.