Romantic stage: the division of numbers within 10 thousand
With the previous splitting experience, 4000 was split into two thousand digits, and the small shell did a good job. It also expressed its own splitting process with the addition and subtraction formula. What is the result of 2000+2000? The little shell answered in one bite-4000. But why 4000? The little shell was speechless. Is it? Why? Children vaguely feel that the method of 1 1 is no longer desirable, but 2000,2000! Count one by one. When does it count? But what about the result of 4000?
It seems that it is time to awaken their existing ideas about the number "thousand" in their minds. How much is two thousand plus two thousand? The child suddenly understood that 2000 can be regarded as two thousand, and it is much clearer to explain it with thousands.
There is a restless little guy who wants to challenge the split of non-integer thousandths.
Divide 4000 into 1005 and 2095, right? This time, the little shell was stumped. Check it with addition! The calculation process of 1005+2095 is operated on the counter. No! One digit is ten into one, and ten digits are ten into one. The result is 3 100, which is 900 less. 4000 should be divided into numbers 1005 and 2995!
To break 4000 into 1000 digits and 10 digits, the little shells seem to be in trouble again!
This time, we not only learned to use counters to check whether division is correct, but also learned to try to describe the calculation process of addition and subtraction from the perspective of value system. The calculation process of 3090+ 10 is: 9+1 10 = 10 = 1 100; Three thousands+1 a hundred =3 100. There seems to be nine "hundred" missing.
When it comes to the discussion of splitting 4000 into thousands and single digits, the little shells can already describe themselves in the language of value system to verify their guesses. Of course, this process is still inseparable from the operation of the counter.
If you give a multiplication of thousands of digits, can you still solve it?
If 3242 is regarded as 3242, it is really too difficult, but if analyzed according to the value system, this formula doesn't look so terrible, but it is fun!
In this way, in the romantic stage, I constantly encounter problems, constantly feel the "full ten into one" of the larger numbers in the counter operation, and try to analyze the problems with the number "thousand" in the language description. The door to thousands of people has been gently knocked open by us.
Accurate stage: constructing the concept of large numbers within 10 thousand
With the operation experience in the romantic stage, the little shells can easily find that the number of thousands is 10 after ten thousand. At this time, we can dial a bead on the number of thousands to represent a million, and 10 thousand equals a million. At the same time, a particularly interesting question is raised-how many representations of the number 10000 are there on the counter?
At first, the small shell thought that there were only two paths-1 0000 bits1bead or 1000 bits 10 bead.
But someone didn't give up. Haha, I have-nine beads on a thousand, and 10 beads on a hundred can also represent the number 10000.
This time, the children immediately thought that it could also be represented by thousands of 9 beads, hundreds of 9 numbers and tens of 10 beads; Of course, you can also use the beads on the unit: thousands of 9 beads, hundreds of 9 beads, ten of 9 beads, and 10 beads on the unit. In this way, we use five methods to represent the number 10000 on the counter. The surprise of this number made the little shell ecstatic. It turns out that the number 10000 can be so fun.
With the operation experience of the counter, we began to try to communicate in written language, symbolic language and graphic language, and to express numbers within 10 thousand in various ways.
Some small shells began to challenge to express large numbers with various skipping shafts. In this process, the concepts of decimal and numerical system in children's minds became more flexible.
What if this number contains 0? How to express in four languages? When children first encounter this problem, they begin to understand that any kind of expression is not only to convey information accurately, but also to be concise and efficient.
At this point, after a series of game activities, the decimal relationship of one, ten, hundred, thousand and ten thousand has taken root in children's minds. But what does any number of digits matter? We first communicate from the intuitive model diagram.
But this is not enough. Children need a more intuitive, operational and interactive model to help them reflect and abstract in their minds, so as to build a digital concept within 10,000. This model is the number axis.
One big cell means 1 thousand. What about the cell? Small shells can easily answer 1 100. So what else can this little box represent? Children have rich experience in the life and operation of 100, and they will immediately find that this cell can also represent 10 tens and 100 ones. So with the help of the number axis model, we jump forward from 0, one grid at a time, which can represent 100 tens, 100 hundreds, 1000 thousands. So we jumped to the position of the number 10000, and we jumped a total of 1000 tens.
In fact, this game can really be played in class, but during the epidemic, we have to use the sliding of the little finger instead of the moving of the little foot, and the language description process is definitely indispensable. This language description process will help them really understand the conversion relationship between arbitrary numbers.
Welcome to click on the link and watch your child "jump a few axes" at home.
The relationship between "10,000" and "100"
After understanding the relationship between different numbers, it becomes more comfortable for children to represent big numbers on the number axis!
Remember the rice game we played in winter vacation? Do you want to know how much 10000 grains of rice are? Then play!
I especially like to know 10000. How do you count such a big number? Can you count them one by one?
Two small shells found a small container that could hold about 100 grains of rice at home, and then they filled 100 times, that is, 1000 grains of rice, which was about 10000 grains of rice. Haha, that's how the idea of value system is used.
Others think that counting 100 and 100 times is too much trouble. Look, the little guy first made a small container that can hold 100 grains of rice, counted about 1000 grains of rice, that is, 100 grains of rice, then made a container that can hold 1000 grains of rice, and loaded it.
Isn't this the practical application of measurement thought? Invent suitable units of measurement as needed. If you want to calculate a bigger number, it's not enough. Then invent a larger counting unit, in the words of small shells, to make a larger container.
Comprehensive part: the application of the concept of number within ten thousand years
1. Specific size
With the expansion of numbers, numbers become more and more complicated. Can small shells compare the sizes of numbers smoothly?
Xun actually used two methods to compare the size of numbers: subtraction calculation and number axis. This little guy is trying to make the process of drawing conclusions reasonable. The addition and subtraction of large numbers and the number axis he has been using before have become his tools to solve problems. In fact, the comparison of large numbers can be much simpler than you think: the number of digits is different, and the number with more digits is larger; The numbers are the same, and it is more convenient to go from a high place. But the children's leading performance makes me believe that the concept of large numbers in their minds is flexible and can grow.
Step 2 operate
When we combine a specific situation, the existing operational concepts in their minds are fully activated. What wonderful chemical reaction will happen when addition, subtraction, multiplication and division (division has not been formally learned) encounter large numbers? How much does it cost to buy four TV sets and a refrigerator?
The children listed the formulas easily, and some children who spoke quickly even reported the answer of 10000 yuan. The teacher asked you how to calculate? The little guys are quite confident: because 4× 1=4, 3×2=6, 4+6 = 10, the result is 10000 yuan! I gave it a push and it came out.
Haha, this description is so irresponsible! Children also realize that although 4× 1 and 4× 1000 have some similarities, there is no way to describe them in words. At this time, the essential meaning of multiplication and the concept of value system were activated in class discussion!
After that, the language of the small shell was much more rigorous. They know that mathematics cannot be "pushed" by feelings, but "truth". The "truth" we want to talk about in this unit is the application of the concept of value system of large numbers in operation.
For the formula of 9000-3000 = 6000, which obviously needs to be explained clearly, we have tried many methods, which can be calculated by thousands, hundreds and tens.
Finally, the children agreed that it is the simplest to calculate according to the counting unit of "thousands", that is, 9000 is regarded as 9000, 3000 as 3000, and 9000-3000 =6000.
When the value system can really become a tool for children to solve problems, they dare to challenge more complex multi-digit calculation. Every child sent their own process of dialing the counter-
Looking at the vivid language expressions of the children, my heart is melting-
Calculation of large numbers
Counter representation
There are actually four different calculation methods-
Others try to describe their own computing process in three languages-written language, graphic language and symbolic language.
We are not only fully prepared for a larger number of calculations, but also strive to make our language more rigorous. Translation between three languages is gradually becoming a tool for children to think.
estimate
In the evaluation game, we had another heated discussion: the price of a refrigerator is 3 198 yuan. If I want to buy this refrigerator, how much money can I bring? It is estimated that the price of refrigerators ranges from 3 198 yuan to 10000 yuan. Do you agree?
If you want to estimate it as 10000 (the author should want to express 10000, but write it as 10000. ) Do you agree? The children immediately raised their own objections, and the estimated value should not be too far from the accurate value, but should be as accurate as possible. Then what about the estimate of 3000 yuan?
Someone immediately disagreed: if we want to buy this refrigerator, it is estimated that 3000 yuan is not enough! It is estimated that 3200 yuan is more appropriate. It is meaningful to estimate that children's understanding is in the scene.
Have to admit, during the epidemic, we walked in this chapter for a long time. Have a clear brain map. Under the guidance of the teacher, Little Shell tried to make a brain map for the first time this semester.
I believe that at the end of this semester, the brain map will really become a thinking tool for children to organize a unit learning process.
So what will you study in the future? Look what these little shells say-
Larger counting units, more complicated calculations ... this is really a wider world!