"Finding Defective Products" Mathematics Wide Angle PPT Courseware

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"Finding Defective Products" Mathematics Wide Angle PPT Courseware

Part One: Introduction to the topic

1. There are 3 bottles of calcium tablets, and one bottle is missing 3 tablets. Can you use any method to find it?

[Reference method] 1. Open the bottle and count. 2. Weigh it with your hands.

Finding defective products PPT, part 2: new teaching knowledge

Example 1: There is 1 defective product among the 9 parts (the defective product is heavier). How many times can you weigh it with a balance to ensure that the defective product can be found?

[Conclusion] Divide the item to be tested into 3 parts; if it can be divided into 3 parts equally, divide it into 3 parts, such as 3 (1, 1, 1). If it cannot be divided into 3 parts equally, try to make each part even.

Refer to the previous question and think:

There are 13 boxes of candies, 12 of which have the same quality, and one box is missing a few candies. If you use a scale to weigh it, how many times can you find this box of candies? Please write down the process.

[Reference answer] Divide 13 boxes of candies into 3 parts, take out 8 bottles, put 4 bottles on each side of the scale, balance, one of the remaining 5 bottles is defective, then divide the 5 bottles into 3 parts, take Remove 4 of the bottles and put 2 bottles on each side of the balance. If it is balanced, the rest is defective. If it is unbalanced, one of the bottles on the high end is defective. Divide these 4 bottles into 3 points and place them on both sides of the balance. 1 bottle, if balanced, one of the remaining 2 bottles is defective. Finally, put the two bottles on the scale and weigh them. The higher end is the defective product. If it is unbalanced, one of the bottles at the high end is defective. Divide the 4 bottles into 3 points and put 1 bottle on each side of the balance. If it is balanced, one of the remaining 2 bottles is defective. Finally, put these two bottles on Weigh on a scale, and the higher end is the defective product. It takes at least 3 weighings to find defective products.

Example 2: There are 7 bottles of pills, and one bottle is missing 2 pills. Can you try to find it?

[Reference answer] 1. Divide 7 bottles of pills into 3 parts, take out 6 bottles, put 3 bottles on each side of the scale, balance, the remaining bottle is a defective product, if it is not balanced, put 3 bottles on the high end, and then Divide it into 3 parts, take out two of the bottles and place them on both sides of the scale. If it is balanced, the remaining bottle is a defective product. If it is unbalanced, the higher end is a defective product. It must be weighed at least twice to ensure that defective products are found.

Knowledge points

Divide the item to be tested into 3 parts; if it can be divided into 3 parts equally, divide it into 3 parts. If it cannot be divided into 3 parts equally, try to make each part even.

Finding defective products PPT, the third part: knowledge sorting

Knowledge point 1: Use optimization strategies to find defective products.

1. Divide the items to be tested into 3 parts.

2. If it can be divided into 3 equal parts, divide it into 3 parts, such as 3 (1, 1, 1). If it cannot be divided into 3 parts equally, try to make each part even.

Example 1: There are 5 beads with the same appearance, 4 of which are pearls and one is a fake bead, and the fake bead is heavier than the pearl. Use a scale (without weights) to weigh it. How many times can you find out the fake beads? Use a diagram to show hypersymmetry.

Example 2: There are 7 bottles of pills, one of which is missing 2 pills. Can you try to find it?

[Analysis] Divide 7 bottles of pills into 3 parts, take out 6 bottles, put 3 bottles on each side of the scale, balance, the remaining bottle is a defective product, if it is not balanced, put 3 bottles on the high end, and divide it into 3 parts , take out two of the bottles and place them on both sides of the scale. If they are balanced, the remaining bottle is a defective product. If it is unbalanced, the higher end is a defective product. It must be weighed at least twice to ensure that defective products are found.

Finding defective products PPT, Part 4: Classroom exercises

1. There are 5 hoops, 4 of which are equally heavy and the other is heavier. How many times should you weigh it to ensure that you find the hoop?

2. Find one defective item among the 9 items. It is more appropriate to divide the 9 items into ( ) parts.

3. There are 5 bottles of multivitamins, one of which is missing 4 tablets. If you use a balance to weigh one bottle at a time, it will take at least ( ) times to find the bottle with fewer pills; if you weigh two bottles at a time, it will take at least ( ) times to find it.

Comment: There are 5 bottles of multivitamins, one of which is missing 4 tablets. If you use a scale to weigh one bottle at a time, you need to weigh it at least 4 times to find the bottle with fewer pills. When you weigh the fourth bottle, you can find the bottle with fewer pills. If two bottles are weighed each time and they are balanced, the remaining bottles are defective and unbalanced. Weigh the two lighter bottles again. So weigh it at least twice to find it.

Finding defective products PPT, Part 5: After-class exercises

1. fill in the blank.

(1) There are 5 packages of peanuts, one of which is lighter and the other 4 packages are equally heavy. Use a balance to weigh them. The method is as follows: place ( ) packages of peanuts on each side of the balance. If the balance is balanced, the remaining package is ( ); If the balance is unbalanced, divide the two packages on the side ( ) into two parts and place them on the left and right sides of the balance before weighing. To ensure that you can find the lighter bag of peanuts, weigh it at least ( ) times.

(2) Among 9 products with the same appearance, it is more appropriate to find one defective product and divide the 9 products into ( ) parts.

(3) There are 15 bottles of iced black tea, 14 of which have the same quality, and one bottle contains sugar water, which is slightly heavier than the others. Weighing at least ( ) times can ensure that this bottle of sugar water is found.

2. Calculate each of the following questions.

3. There are 10 screw heads, one of which is a defective product and is lighter in weight. Now I use a balance. Please find this defective product and write down your own method.

[Analysis] Divide 10 screw heads into 3 parts (3, 3, 4), put 3 on each side of the balance, if balanced, the defective product will be in the remaining 4 screw heads, then divide it into 3 parts ( 1, 1, 2), put a screw nut on each side of the balance. If it is unbalanced, the light end will be the defective product. To balance it, put the remaining 2 screws on each side of the balance, and the light end will be the inferior product. Taste. When weighing for the first time, if it is unbalanced and there is a defective product in the light end, divide the 3 defective products in the light end into (1, 1, 1), put 1 on each side of the balance, balance, and the remaining The lighter end is a defective product and is unbalanced.

Keywords: free download of PPT courseware for mathematics in the second volume of the fifth grade of the People's Education Press, download of defective PPT, download of wide-angle mathematics PPT, .PPT format;

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"Finding Defective Products" Mathematical Wide Angle PPT:

"Finding Defective Products" Mathematical Wide-angle PPT Part One Content: Exciting Introduction There are 3 bottles of calcium tablets, one of which is missing 3 tablets. Can you manage to find it out? I weighed it with my hands but couldn't get it out. ... ... ... Find defective products PPT, part 2 content: knowledge explanation, there are 3...

"Finding Defective Products" Discovery Park Flash Animation Courseware 2:

"Looking for Defective Products" Flash Animation Courseware for Discovery Park 2 This courseware is part of the Hebei Education Edition's Sixth Grade Mathematics Volume 1 Unit 8 Teaching Materials for Finding Defective Products Flash Animation Courseware for Discovery Park. The content is vivid and vivid. Please download it! Keywords: Explore the paradise teaching courseware, find defective teaching...

"Finding Defective Products" Discovery Park Flash Animation Courseware:

"Looking for Defective Products" Flash Animation Courseware for Discovery Park. This courseware is part of the Hebei Education Edition's Sixth Grade Mathematics Volume 1 Unit 8 Teaching Materials for Finding Defective Products Flash Animation Courseware for Discovery Park. The content is vivid and vivid, please download it! Keywords: Explore the paradise teaching courseware, find defective teaching materials..

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Update Time: 2024-09-08

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