Case background
During the six-week internship, I took two influential classes, one of which was brackets. In my opinion, parenthesis is a very simple course, so I was confident before class, but I found many problems after class, because I couldn't explain the questions raised by students at once. The focus of this lesson is to let students master the operation order after parenthesis. I use persuasion to make students understand. Parentheses are operation symbols, and their function is to indicate the order of operations. Parentheses () were first used by the Dutch mathematician Gilat. The French mathematician Vedas used [] before, but these symbols were not widely used until18th century.
Case description fragment 1: follow suggestions and introduce new knowledge.
Teacher: Calculate 360÷ 12+6×5 in the form of recursive equation on the arithmetic book (written on the blackboard). Who is doing the math problem on the blackboard?
Health: I'll do it.
Teacher: How do you calculate it?
Student 1: first calculate 360÷ 12, then 6×5, and finally add.
Health 2: I have a question. Multiply first, then divide and then add and subtract, so 360÷ 12 and 6×5 can be counted together.
Teacher: Great! To sum up a sentence is to multiply first, then divide and then add and subtract. What should the teacher do first?
Health: You can put a bracket.
Teacher: Oh! Does it count with brackets? Do math problems in your notebook. 360( 12+6)×5 (written on the blackboard)
Student: Yes, sir. I can do math problems on the blackboard.
Teacher: Come on, can you tell the teacher how you calculated it?
Health: I first calculate 12+6 in parentheses, then divide by 360÷ 18, and finally multiply.
Teacher: Do you agree?
Health: I agree.
Teacher: What if the teacher wants to calculate multiplication after brackets?
Health: Put brackets in it.
Teacher: Have you learned brackets before? Today we are going to learn parentheses.
Part II: Thinking and discussing, exploring new knowledge.
Teacher: Now let the students calculate 360÷( 12+6)×5.
Health 1: 360÷( 12+6)×5 Health 2: 360 ÷ (12+6) × 5.
=360÷ 18×5 =360÷( 18×5)
=360÷90 =360÷90
=4 =4
Teacher: Look at the two questions on the blackboard. Do you find any difference?
Health: When you write it down, one is in brackets and the other is in parentheses.
Teacher: Then think about it. Who wrote it right?
Health 1: Parentheses are correct, because parentheses should be counted on the basis of parentheses. If there are no parentheses in the brackets, it is wrong. If there are brackets, there must be brackets in the brackets.
Health 2: It is right to put brackets, because the things in brackets have been counted, so they are in brackets, so writing them down is brackets, not brackets.
The students stopped raising their hands to speak, each said his own words and began to argue.
Teacher: Stop! Now it is found that we have differences in the specification of writing formulas. The teacher can tell you to use parentheses when writing, not parentheses. The reason is that the formula in brackets has been calculated, and then the formula in brackets should be calculated, so write brackets.
Student: Teacher, you can work out what is in brackets directly. If you don't distribute it, you don't have to write brackets, and you can still get the answer.
Teacher: Do you agree with him?
Health 1: agreed.
Health 2: I disagree.
Teacher: Can you tell me the reason why you disagree?
Health: If you don't calculate by parts, you are prone to make mistakes, so it is better to calculate by parts when making recursive equations.
Teacher: Do you understand now? In order to make fewer mistakes, we must work in different parts, ok?
Health: I see.
Teacher: Now let's look at three questions on the blackboard. Do you find any difference between these three questions?
Health: Their symbols are different. One has brackets and the other has brackets.
Teacher: Then why do you always add these symbols?
Health: Because we have to change their calculation order.
Teacher: What is the first formula?
Health (all): multiply first, then divide and then add and subtract.
Teacher: What is the second formula?
Health (all): count the things in brackets first, and then count the things outside brackets.
Teacher: Who can tell us the calculation method after adding brackets?
Health: Count the things in brackets first, and then count the things in brackets.
Teacher: Who can say it completely?
Student: First count what is in brackets, what is in brackets, and finally what is outside brackets.
Teacher: Let's talk about the calculation method with brackets at the same table.
case analysis