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

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

Default Generation 2: Put three eggs into the 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.

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

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

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

1.Courseware presents a theme map 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? Combined with the learning tools on the blackboard, demonstrate the baking of 1 cake, 2 cakes and 3 cakes in the pot in turn, and ask: Is this ok? (Let students intuitively feel the maximum resources available in the pot here)

(2) Do you want to brand both sides? A cake should be branded on the front and the back. ) The teacher stressed: For the convenience of expression, we can call the first branded side positive and the second branded side negative.

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

1. Define the method of baking1piece of cake.

Can you make pancakes? Who can tell you how to bake a cake while baking it?

Combined with the students' report, the blackboard uses the flow chart to show the pancake making process.

Minimum time for the number of cakes 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 if you want to bake two cakes? How many minutes at least?

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

Default:

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. It takes 3 minutes to bake the front side first, then 3 minutes to bake the back side, and ***6 minutes.

Combined with students' report, the process of pancake making is represented by flow chart.

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

1 1 plus → 1 minus 6

2 1 plus 2 plus → 1 minus 2 minus 2*3=6

(3) Compare and optimize the two schemes.

Doubt: Which method would you choose if you want to eat cakes as soon as possible? Why?

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

Combining Books on the Board: Minimum Time for the Method of Number of Cakes (Minutes)

1 1 plus → 1 minus 6

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

3. Construct the second thinking model: discuss the best method of flipping three cakes in groups (alternating flipping).

1.Show me the question: How many cakes do I need to bake now? (3) How can I eat cakes 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:

① It takes 6 minutes to bake two cakes first, and then it takes 6 minutes to bake 1 cake. Total * * * takes 12 minutes.

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

② Alternate branding. It takes 9 minutes to bake for 3 times.

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

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

3 (alternately branded) 1 positive 2 positive → 1 anti 3 positive → 2 anti 3 anti 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 "alternating baking" (supplementary blackboard writing). In order to save time and energy as much as possible, it is necessary to bake two cakes in the pot at the same time, and the alternating baking method is used.

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

Summary of pancake baking methods: According to different quantities of cakes, we can choose different optimized baking methods.

(3) Constructing the third thinking model: the optimal flipping method of even number of cakes.

1, Guess: How can I bake 4 cakes quickly?

Study independently with the help of discs or by drawing flowcharts, and then communicate in groups.

When they report, they will combine the learning tools on the blackboard, 1 person will tell the method, and 1 person will 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 the remaining two cakes at the same time.

Ask 1: "Why can four cakes be branded like this?"

Health: Because 4 is a multiple of 2.

Questioning 2: "What number of cakes can also be branded like the optimal branding method of four cakes?" , why?

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

Discriminate 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. (Make sure not to leave 1 piece of cake at the end, which will waste space. )

(4) Constructing the third thinking model: the optimal flipping method of even number of cakes.

Just now, everyone was really amazing. From the flipping method of four cakes to 6, 8 ..., we also summed up the best method of flipping even-numbered cakes. That's amazing!

(1) However, if you bake 5 cakes, where 5 is not a multiple of 2, can you find the best way to bake it? 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 sear at the same time, then sear alternately. Time: 5*3= 15 (minutes)

(2) "What number of cakes can also be branded like the optimal method of 5 cakes?" , why?

Health: There are 7, 9 ..., that is, even the odd 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 flipping 6 cakes:

Method 1: Divide into two groups, each group is baked according to the best method of 3 cakes, * * * to be baked 18 minutes.

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

The teacher pointed out: the time of the two methods is the same, but in practice, when using the method of three cakes to bake, it is necessary to constantly turn over the pancakes, which increases the difficulty. So we usually choose an easy method to divide 6 into 2, 2 and 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 law of minimum time.

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 what the minimum time for pancakes is?

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

Minimum time = number of cakes * time to bake once.

Thinking: According to our law, how many minutes does it take to bake 1 piece of cake? Three minutes. Think about it, can it be cooked in 3 minutes?

Fourth, the whole class summary:

1. What did you get from this class?

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

Life is inseparable from optimization thought. It is precisely because people have a sense of optimization that society will continue to progress. I hope that students will continue to surpass themselves and become better and better in the future!

Blackboard design: pancake problem

Minimum time for the number of cakes method (minutes)

1 1 plus → 1 minus 6

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

3 (alternately branded) 1 positive 2 positive → 1 anti 3 positive → 2 anti 3 anti 3*3=9.

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

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

6 2+2+2 6*3= 18