# Based on the source, grasp the law

Time：2022-5-5

“Multiplication distribution law” is an important operation law in primary school, which is used in the solution of many problems. “Multiplication distribution law” is the knowledge basis for learning algebraic simplification and formula induction in the future, which has important value and position in mathematics learning. Its biggest difference from multiplication exchange law and combination law is that multiplication exchange law and combination law are only the internal law of multiplication, while multiplication distribution law is a law between multiplication and addition, which communicates the relationship between multiplication and addition, and has special significance.

Because of its many variant exercises, students are most likely to make mistakes and confusion when splitting the formula according to the “multiplication distribution law”. How to make students understand the internal theory of the law while mastering the form of the operation law is a key point of teaching. After listening to the special grade teacher Liu Song, I have some new inspiration.

1、 The relationship between the law of transfer and distribution in the expression of words

In the conversation before class, Mr. Liu introduced two students and said: Xiao Xu is my good friend and Xiao He is my good friend. How to turn these two sentences into one sentence. Then turn one sentence into two sentences. Feel the magic and beauty of Chinese language. This implies the form of multiplication distribution law. Therefore, Mr. Liu is easily connected to mathematics: there are so magical and wonderful things in the mathematical world.

2、 Understanding the arithmetic theory of distribution law from the meaning of multiplication

In this lesson, Mr. Liu focuses on the significance of multiplication and launches the teaching of the arithmetic theory of multiplication distribution law.

What is the essence of multiplication distribution law? What Mr. Liu explained to us is the combination of addition and multiplication. Show me how to add six 3’s, five 3’s and one 3’s and use multiplication to communicate the essential relationship between multiplication and addition, and then combine five 3’s and one 3’s to be 3’s × 5+3 × 1. Let students understand 3 × 6=3 × 5+3 × 1. Highlight that 6 in the left formula is (5 + 1) in the right formula, that is, 3 × （5+1）=3 × 5+3 × 1。 Then guide the students to observe and compare, find the differences between the formulas on both sides of the equal sign, guide the students to formally model the “multiplication distribution law”, emphasize that 3 should be multiplied by 5 and 1 in brackets, and understand the calculation theory from the meaning of multiplication. On this basis, please try to find the same formula by yourself. It is easier for students to understand the multiplication distribution law from the meaning of multiplication, and the introduction is also relatively simple and clear. The formula must be regular like this. (separation law, students become discoverers and researchers.)

3、 A model of rich distribution law in the connection of old and new knowledge

In fact, students have no foundation for the application of multiplication distribution law, such as multiplication oral arithmetic 12 × 3. Calculate 10 first × 3 = 30, then calculate 2 × 3=6，30+6=36。

Area formula of rectangle: (a + b) × c=a × c+b × c。 Wall map of Tiling: how many red tiles (square) and yellow tiles (rectangle) are there in total? I will change: use other symbols to represent the multiplication distribution law without letters. Cultivate a sense of conformity. The sum of Pentagram multiplied by square and triangle. Talk about the law of distribution in your own words.

4、 Structure of clear distribution law in comprehensive application

1. Complete the formula according to the multiplication distribution law.

Mr. Liu pays attention to making students understand the mathematical theory of multiplication distribution law from multiple angles.  Students understand the laws of operation in different ways of solving problems.

5、 In the summary, the significance of distribution law is combed

Can you dictate 67 × 88？ sixty-seven × What about 12? But can you work out the sum of these two formulas? Why can the number of calculation steps increase, but it can be calculated?

Multiplication distribution law: make the calculation simple.

Especially worth learning:

1. Students take action to read equation: 3 × （5+1）=3 × 5+3 × 1, (the sum of 3 times 5 plus 1 is equal to the product of 3 times 5 plus the product of 3 times 1). Although the action is a little exaggerated, it focuses on the different operation sequences on both sides of the equation: first sum and then product on the left, and first product and then sum on the right. Read through the equation to promote students’ overall perception of the operation form of multiplication distribution law, and cooperate with the action to help students break through the cognitive inflection point and deepen their impression in the humorous atmosphere.

2. Try to encourage students. Call the children “Sir, teacher, fairy” and so on. When the students make a wonderful speech, let the whole class look at the student with adoring eyes and ask him to announce the end of class.

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