1, the idea of "equivalent substitution"
Everyone knows the story of Cao Chong's elephant calling. In fact, let the elephant go to the boat first, look at the position of the flooded boat and mark it. Then, drive the elephant off the boat and put stones on the boat to achieve the same mark. Weigh the stone, and the elephant's weight can be changed into the same amount.
After the teacher sent out a video explaining "equivalent replacement", many lovely people talked to the teacher privately about many other ways to weigh elephants. A lovely person told the teacher that there is no need to use stones, because people need manpower to move them, so that people can walk directly to the boat, and then everyone can report their own weight, and then add them up to get the weight of the elephant. This not only does not require people to move stones, but also does not require weighing stones, so that everyone on board can directly report their own weight. The teacher is really pleased to see that the little cute people can have such a good idea. It can also be seen from this example that the little lovelies really understand the idea of equal substitution.
2. "Equivalent replacement to find the bridge"
The core idea of equivalent substitution is to find a bridge. For example, like Cao Chong weighing an elephant, we have to calculate the weight of the elephant, but we can't, so we use stones as "substitutes" and then calculate the weight of the elephant. We just need to understand that when calculating the equivalent substitution problem, we must find a quantifiable bridge, so that we can easily solve the equivalent substitution problem. Let's look at the following question: What is a bridge?
In fact, for this problem, we can draw an equivalent substitution diagram first. From the equivalent substitution diagram, we can clearly see that chickens and ducks are related, ducks and geese are related, and finally find the genetic relationship of chickens and geese. Then the middle bridge is the duck, and we just need to take the duck as the middle bridge and unify it into the same number.
3. Advanced questions
In fact, the answer to the above question is very fast, because we only need to multiply the number of ducks under the condition of 1 by 2, but in fact, when doing the problem, the magnification may not be able to get the answer directly. For example, the following problem just needs to be solved with more math problems, and the little darlings can try to solve it first.
In this problem, we know that 6 chickens can be exchanged for 10 ducks, and we want to exchange 9 chickens for some geese. So it can't be calculated by direct magnification like the above problem. How should I calculate it? Actually, the idea is the same. Our aim is to unify the bridge and draw an equal sign on it before calculation. So no matter what the topic asks us, you can ask us this question. We should find the bridge first, then draw an equal sign on the bridge, and then ask questions to get the answer.
In fact, the idea of equivalent substitution has not changed, but we have found a unified bridge. For the students in the second and third grades of primary school, we have used a lot of multiplication and division operations, which puts high demands on the students' computing ability, including the fourth step, from 12 chickens to 15 geese, to how many geese are 20 chickens, which is actually very large. First of all, cut the point. We tangent points on 12 and 15 to get 12÷3, 15÷3, and four chickens are equal to five geese. Then, we convert 4 chickens into 20 chickens and multiply them by 5 respectively, and get that 20 chickens are equal to 25 geese.