1. In our daily life, we often encounter some math problems, such as: it takes 8 minutes to cook one egg, and how long does it take to cook three eggs?

Generate 1 by default: cook one by one, one for 8 minutes, and three 15 minutes.

Default second generation: put three eggs in a pot and cook them together, which takes 8 minutes.

2. Teachers ask questions:

(1) Which method would you choose to cook eggs? (Guide students to compare and optimize strategies without trace here)

(2) Why did you choose this method? Tell me why.

Conclusion: Cooking three eggs together can not only save time, but also save energy through reasonable arrangement. Next, we will study a "pancake problem" that also needs to pay attention to methods. Blackboard: Pancake problem.

Second, explore independently and establish a mathematical model of pancakes.

(1) Read the information and review the pancake rules.

1. Courseware presents a theme diagram to guide students to observe and discover the key mathematical information: only two cakes can be baked at a time, and both sides should be baked for 3 minutes.

2. Teachers ask questions to find out the key mathematical information:

(1) What do you mean you can only bake two cakes at a time? Combine the learning tools on the blackboard and demonstrate that 1 cake, 2 cakes and 3 cakes are baked in the pot in turn. Q: Is this ok? (Let students intuitively feel the maximum resources available in the pot here)

(2) Do you want double branding? Cake should be branded on both sides. ) The teacher stressed: For the convenience of expression, we can call the first brand face positive and the second brand face negative.

(2) Explore the pancake method and establish the optimal pancake strategy model.

1. Define the baking method of 1 cake.

Can you make pancakes? Who can tell you how to bake a cake at the same time?

Combined with the student's report, the blackboard shows the process of making pancakes with a flow chart.

Minimum time of cake counting method (minutes)

1 1 plus → 1 minus 6

2. Construct the first thinking model: study the optimal baking method of two cakes (simultaneous baking).

The teacher asked: What should I do if I bake two cakes? How many minutes at least?

Ask the students to report to the blackboard with their learning tools and demonstrate:

Default value:

① It takes 6 minutes to bake one cake and 12 minutes to bake two cakes.

② You can bake two cakes at the same time. Bake the front side for 3 minutes, then bake the back side for 3 minutes, ***6 minutes.

Combined with the student's report, the process of making pancakes is represented by flow chart.

Supplementary blackboard writing: minimum time for counting cakes (minutes)

1 1 plus → 1 minus 6

2 1 plus 2 plus→1minus 2 minus 2*3=6

(3) Compare and optimize the two schemes.

Doubt: If you want to eat the cake as soon as possible, which method would you choose? Why?

Ask the students to compare two schemes: the second scheme is good because it saves time and makes full use of the resources of the pot. As long as two cakes are baked in the pot at the same time, it can ensure the least time and is the best baking method. (Grasp the key word "at the same time"), and point out that the best way to bake two cakes is to bake them at the same time.

Combinatorial Books on the Chessboard: Minimum Time of the Cake Count Method (Minutes)

1 1 plus → 1 minus 6

2 (simultaneous branding) 1 plus 2 plus→1minus 2 minus 2*3=6

3. Build a second thinking model: discuss the best way to flip three cakes in groups (alternately flip).

1. Show me the question: How many cakes do you need to bake now? (3) How can I eat the cake as soon as possible? How do you brand them?

2, combined with the pre-class research list, ask students to explain under the projection:

Default value:

① It takes 6 minutes to bake 2 cakes first, and 6 minutes to bake 1 cake. Total * * * time 12 minutes.

The teacher asked: whose method is the same as his? Is there a different way?

② Substitute brands. It takes 9 minutes to bake three times.

The teacher asked: whose method is the same as his? Do you know his pancake making method? Please put a pendulum in the group (two people sitting at the same table) with the help of a disc and learn a new method of turning three cakes together.

Invite a group of students (students who didn't think of this method just now) to share the new pancake method with you again. Teachers combined with students' reports: supplementary blackboard writing;

3 (flip alternately) 1 plus 2 plus → 1 minus 3 plus → 2 minus 3 plus 3*3=9.

3. Comparative Optimization: Which of these two methods is more reasonable? Why?

Follow-up: Why is the second method the most time-saving?

Grasp the key words such as "exchange" and "replacement" in students' answers, and point out that the best way to bake three cakes is called "alternate baking" (supplementary blackboard writing). In order to save time and effort as much as possible, it is necessary to bake two cakes in the pot at the same time, using the alternating baking method.

4. Method Review: Students, what experience have we accumulated in making pancakes so far? Who can say something?

Summary of pancake baking methods: According to the different amount of cakes, different optimized baking methods can be selected.

(3) Construct the third mode of thinking: the optimal turnover method of even-numbered cakes.

1, guess: how to bake four cakes quickly?

Learn independently by means of CD or drawing a flow chart, and then communicate in groups.

When they report, they will combine the learning tools on the blackboard, 1 people talk about methods, 1 people demonstrate. First, divide the four cakes into two parts: 2+2. We have just baked two cakes, so we can bake two cakes at the same time and bake the remaining two cakes at the same time.

Query 1: "Why can four cakes be beaten like this?"

Health: Because 4 is a multiple of 2.

Question 2: "How many cakes can be branded as the best branding method of four cakes?" , why?

Health: 6, 8, 10 ..., even-numbered cakes can be baked like this, and two cakes can be baked at the same time, which can bake the cakes as quickly as possible.

Distinguish whether 3+ 1 can be branded like this. From the comparison of the time used, it can be found that this method takes a long time. Don't waste space by leaving 1 cake at the end. )

(4) Construct the third mode of thinking: the optimal turnover method of even-numbered cakes.

Everyone was really amazing just now. From the turning method of four cakes to 6,8 ..., we also summarized the best way to turn even cakes. It's amazing!

(1) However, if you bake five cakes, where five is not a multiple of two, can you find the best baking method? How many minutes at least?

Write and calculate on the exercise paper first. Then share your own methods at the same table.

5=2+3. First scorch at the same time, then alternately scorch. Time: 5*3= 15 (minutes)

(2) "What number of cakes can be branded like the best method of five cakes?" , why?

Health: There are 7, 9 ... that is, an even number of cakes can be baked at the same time, and then the last three are baked alternately. Blackboard writing: singular.

(5) Compare the two methods of turning 6 cakes:

Method 1: Divide into two groups, and bake each group according to the best method of 3 cakes, which takes 18 minutes.

Method 2: Divide into three groups, each group is baked according to the best method of 2 cakes, and the baking time is 18 minutes.

The teacher pointed out: the time of the two methods is the same, but in practice, when baking with the method of three cakes, it is necessary to constantly turn over the pancakes, which increases the difficulty. So we usually choose a simple method to divide 6 into 2, 2, 2.

(6) Application rules:

If you bake a cake for everyone in the class now and need to bake 27 cakes, how would you bake it? How many minutes at least?

Third, explore the law and calculate the minimum time law.

By solving the above problems of pancakes, we have accumulated a lot of experience in pancakes. By carefully observing the formula on the blackboard, can you find out the minimum time for pancakes?

Every time you add 1 cake, it will add 3 minutes.

Minimum time = number of cakes * baking time.

Thinking: According to our rules, how many minutes does it take to bake 1 cake? Three minutes. Think about it, can it be done in three minutes?

Fourth, the class summary:

1. What did you learn from this course?

2. What are your plans for doing things in the future and what do you want to say?

Life can't be separated from optimization thought. It is precisely because people have a sense of optimization that society will continue to progress. I hope the students will continue to surpass themselves and get better and better in the future!

Blackboard Design: Pancake Problem

Minimum time of cake counting method (minutes)

1 1 plus → 1 minus 6

2 (simultaneous branding) 1 plus 2 plus→1minus 2 minus 2*3=6

3 (flip alternately) 1 plus 2 plus → 1 minus 3 plus → 2 minus 3 plus 3*3=9.

(even) 4 2+2 4*3= 12

(singular) 5 2+3 5*3= 15

6 2+2+2 6*3= 18