In teaching practice, I designed a table of fractional lines according to the "division and combination" of one-year series, and discussed it with the teacher:

First, the intention of formal design

The division of numbers is the focus of the first semester of senior one. Many students are used to using hand index. The main reason is that these children have no foundation before school, abstract thinking is in the primary stage, and they are still thinking figuratively, so they can't completely get rid of physical calculation. Without a certain foundation, it is difficult to recite division in a short time. You may not be proficient in calculation without memorizing division, but you may not be proficient in calculation without memorizing division. It obviously takes a long time for children to complete the obstacle transition from concrete objects to abstract numbers by counting their fingers, which will also greatly reduce our classroom efficiency. Children's skillful recitation of division can help them to calculate numbers by means other than fingers, and quickly complete this thinking transition. Therefore, we should pay attention to mastering the division of numbers and find a reliable way for children to remember division.

When dividing the number of teaching, we generally take the form of "number can be divided into number and number", which is relatively complete, but it is more complicated to read, and it takes time to express it with the habitual drawling of junior children; Too long expression also affects children's memory efficiency. How to simplify and simplify, let children remember pure mathematics and improve memory efficiency? I tried to design a table (figure 1)? .

(Figure 1)

Second, the perfect design form

This is a complete 2-9 division table with ***45 division formulas, which can be called a big division table. The main feature is to get rid of Chinese interlanguage ("can be divided into" and "he") and only keep pure mathematical keywords (number combination). There are 20 pairs of duplicate exchange numbers, such as (10=3+7, 10=7+3). Remove these pairs of repeatedly exchanged numbers to reduce the child's memory burden as much as possible, and it becomes this small table (Figure 2):

This is a positive sequence division table starting from decimals. After simplification, there are only 25 pairs of numbers left. You can also make a division table in reverse order (starting from large numbers) (Figure 3), as follows:

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People's Education Edition arranges the division of numbers (addition formulas within 10) in this way (Figure 4), and arranges the addition formulas within 10 in an orderly way according to the vertical and horizontal dimensions, requiring students to explore and discover the arrangement rules of formulas. This kind of processing is helpful for students to discover the rules and test the proficiency of calculation, but it is not helpful for students to remember.

Third, the use of forms.

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? Because the number of horizontal lines is the same, you can read the number first (for example, the last line), which can be read as "10 equals19,28,37,46,55" or "10:19,28,37,46". This table is different from the multiplication table. The multiplication formula table can only be memorized by mechanical memory and then used. Reciting is difficult to remember the division form of numbers. The process of reciting is actually a disguised understanding process, which helps children to complete the transition from concrete image thinking to abstract thinking in a short time. This table can also be used for many purposes. For example, the combination of numbers can be said first, and the numbers can be said quickly. For example, the first column of the number combination can be used vertically, so that children can look at the number pairs and say the numbers: one, two (one, one, two), one, two, three, one, three, four and so on. , thus changing the way children master, but also gradually understand that one addend is unchanged, while the other addend is constantly changing, or even changing with it.

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Fourth, the function and reflection of form.

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? Through my own teaching practice, this watch can really facilitate communication, memory and understanding. It takes less than 20 seconds to read it from beginning to end, and you can master it several times in each class. It takes a week or so for children to master it.

So will the memory of this table have a negative impact on the multiplication table? I don't think it has much impact. First of all, because this division table adopts the expression of "flashback", it is opposite to the multiplication formula table. In addition, when students learn multiplication formula, children's division has been understood and familiar, and the obstacle transition from concrete objects to abstract numbers has been completed. Children no longer need to memorize division tables to calculate. During my trial, I found that it can simplify the language, improve efficiency, promote thinking and stimulate interest. I hope all colleagues can learn from it, explore it, criticize it and correct it.