The basic requirement of this element is to know cuboids and cubes, and to find the sum of sides, surface areas and volumes of cuboids and cubes. Here we will teach six independent formulas, plus the unified formula of volume V=sh. Then, it is also required to use what you have learned to solve practical problems in class.
To learn this unit well, students should break through three mountains-the sum of side length, surface area and volume. Recite the formula according to the students' usual learning methods, and then calculate. However, there are too many formulas and they are easy to be confused. What shall we do? My practice is to make students understand first and then remember. The sum of sides is "12 sides" in students' words, and students can remember it well. What is more troublesome is the surface area. Look at its formula:
The surface area of a cuboid = (length× width+length× height+width× height) ×2.
This long formula makes me dizzy. I finally memorized it. The topic is tested like this again:
It is known that the length, width and height of a cuboid are 2dm, 3dm and 4dm respectively. Find the area of its front and top.
It is known that the classroom is a cuboid with the length, width and height of 8m, 6m and 4m respectively, and the door and window area of the classroom is 10m? If you want to paint this classroom, how many square meters should you paint?
The formula just now is to find the areas of six faces of a cuboid. What should I do if the formula doesn't work if I find the area of one face alone or less than six faces?
Analyzing the reasons, the most important thing is that most students have poor spatial imagination. If the topic is not given a picture, they will have no way to start. I thought of a way to teach students to draw a "three-line diagram", that is, draw three lines "one horizontal, one vertical and one oblique" and mark them with length, width and height respectively. This kind of painting is not difficult to learn, and it is easy for students to master.
With this "three-line diagram", with a little guidance, it is not difficult for students to find that the area in front (back) = length× height, the area above (bottom) = length× width, and the area on the left (right) = height× width. In this way, even if the formula is forgotten, the surface area of a cuboid can be calculated smoothly as long as a "three-line diagram" is drawn. For some practical problems, such as painting the classroom, as long as the perimeter and ceiling are painted well, the floor need not be painted. Some students like to work out the area of all six faces with formulas first, and then subtract the area of the "bottom". Some students like to calculate the areas of five faces separately and then sum them up. I am sure of all these methods. According to the student's thinking, he can use whatever method he likes or is used to, and does not force a routine to solve the problem.
Another difficulty in this unit teaching is "finding the volume of irregular objects", and the method exemplified in the textbook is drainage method. For example, to measure the volume of a potato, you can put it in a cuboid or cube container filled with water, measure the rising height of the water, and then calculate the added volume of water, which is the volume of the potato. This kind of problem is difficult for students, and many students can't imagine how to find the volume. At first, the method I taught students was to calculate the rising height of water, and then multiply it by the bottom area of the container to find out the volume of the object. I think this is the fastest and best way. But the students' homework tells me that only a few students can accept and master this method, and most students are still confused, unable to start, and take a ride at will. What shall we do? Finally, once, when I was a student in a remedial class, I asked, "How do you think we can find out the volume of irregular objects?" He said, "Subtract the front volume from the back volume to get the volume of that object." .
I had an epiphany. My previous teaching method, though simple, required jumping thinking. For students who are a little slow-witted, I may not accept how I came up with this formula for a while. So, I tried to figure out the students' thinking: put potatoes in a container and the water level will rise. At this time, I calculated the volume of water (including potatoes) in the container, that is, the raised water level x the bottom area of the container. Then, subtract the original water volume from this volume to get the potato volume. After I taught this method in class, some students understood it. Slowly, combining these two methods to train problems, most students in the class have mastered the solutions to these problems.
The teaching of this unit makes me deeply realize the disunity of students' thinking mode. For a topic, students will think in different directions. We can guide students to think in many ways, let them express their ideas in class, and then summarize the methods to solve problems according to their own thinking direction. In this way, it is better than the best way to teach students directly by ourselves. Respect the "letting a hundred flowers blossom" of students' thinking, so that students can walk better on the road of learning.