After school in the afternoon, the class teacher gave us a homework assignment, asking everyone to find a way to measure the volume of disposable chopsticks and record the measurement process in the form of math diary. On the surface, this assignment is a mathematical practice, but in fact it may have a deeper meaning, because the use of disposable chopsticks is related to environmental protection.

As soon as I got home, I sat quietly at my desk and thought about it. Disposable chopsticks are irregular three-dimensional figures. How do we measure its volume? I reasoned, scratching my head for a while, shaking my head for a while ... finally, I got something. I can put disposable chopsticks in a container full of water, so that the water in the container will overflow. Isn't the amount of splashing water as big as chopsticks? But chopsticks are lighter than water and will float on the water. What shall we do? Can you fix chopsticks with stones or tape or something? I think it should be possible, but these methods are too troublesome to measure. If only there were a simpler way! After thinking hard, I finally smiled proudly.

June 10 will be fine on Tuesday.

I went to the restaurant to buy a box lunch at noon today, and specially asked for several pairs of disposable chopsticks to prepare for the experiment.

When I got home, I was really excited at the thought of doing the experiment, but I was a little scared. I don't want the first plan to be eliminated as soon as it comes out. In order to verify the correctness of the experimental scheme, I specially measured the length (20cm), thickness (0.35cm) and width (1.6cm and 0.8cm respectively) at both ends of chopsticks. Because disposable chopsticks are similar to trapezoid, I use the formula to calculate the volume of trapezoid to calculate the volume of chopsticks. According to the calculation results, the volume of disposable chopsticks is about 8.4 cubic centimeters. If the results measured in the experiment are similar to those calculated by me, it means that my experiment has been successful, otherwise, I have to find another way. I'm about to start the experiment, but the experimental equipment is not enough, so I can only wait until tomorrow.

June 1 1 Wednesday is fine.

The moment of hope has finally arrived. After school, I trotted home and put down my schoolbag. I can't wait to pick up the beaker my father borrowed from the company. After being filled with water, carefully put the beaker into the basin to ensure that the water in the beaker does not leak. Then, I carved a mark on the chopsticks with a knife and divided it into two parts. This mark is the dividing line between the two parts of chopsticks. I want to measure the chopsticks twice.

When the experiment started, my heart was pounding with nervousness, and my hands holding chopsticks were shaking from time to time, but I tried my best to control this excitement. I slowly inserted the chopsticks into the beaker, trying not to shake them, otherwise the water would overflow too much and the measurement result would be inaccurate. After inserting a part of chopsticks into the beaker for the first time, I saw that some of the water in the beaker overflowed into the basin. After the beaker is filled with water, another part of the chopsticks is inserted into it. Finally, I poured the water overflowing from the basin into another beaker with scales twice, thus obtaining the volume of chopsticks.

As a result, I failed. The size of chopsticks measured in the experiment is only 3 cubic centimeters, which is far from the size of chopsticks calculated by me. At first, I still didn't believe it. After repeated thinking, I finally understood the reason for my failure. It turns out that the diameter of the beaker is too large, even if the beaker is not filled with water, people's vision will think it is full, while the size of chopsticks is too small and the scale of the beaker is too large, which leads to the deviation of the experimental results. Therefore, I must improve my experimental method. Believe that I will succeed. Isn't failure the mother of success?

June 12 Thursday is fine.

Since the first experiment failed, I have been trying to improve it, but I just can't think of a simple and feasible way. At noon that day, mom and dad didn't cook, so we decided to eat out.

After ordering in the restaurant, in order not to disturb my waiting, my mother specially ordered a glass of juice. As soon as the juice came, I took a few swigs. My mother told me to drink less juice for fear that I would lose my appetite after drinking it. Before the food was served, I felt that I had nothing to do, so I thought of blowing bubbles, so I picked up the straw in the juice bottle and blew a few breaths at the water. For a moment, I thought that when I took the straw in the cup just now, the water level dropped a little, and suddenly I had an idea. I was so happy that my appetite increased greatly. I ate several bowls of rice today, which is not enough.

It will be fine on Friday, June 13.

At noon today, in order to measure the size of chopsticks more accurately, I asked my father to take a slender measuring cylinder from the chemistry room. The scale unit is smaller, and each unit is only 1 cubic centimeter. At this point, I seem to feel victory beckoning to me. I really have everything except hands-on experiments.

First of all, I drew a dividing line on disposable chopsticks with a pencil, divided the chopsticks into two sections evenly, and soaked them in water to avoid washing them when measuring. Then, insert the chopsticks into the measuring cylinder, drop water into the measuring cylinder with a dropper, let the water in the measuring cylinder rise to the dividing line of the chopsticks, take the chopsticks out of the measuring cylinder after recording the water level scale (38 ml), and then record the water level scale (34.5 ml) in the measuring cylinder. The difference between the two water level gauges is the volume of this part of chopsticks, which is 3.5 cubic centimeters. In the same way, I measured the volume of the other part of the chopsticks to be 5 cubic centimeters. When the two measurements are added together, the volume of the chopsticks is 8.5 cubic centimeters. When I got the result, I cried excitedly. How proud and proud I am at this time!

Then, according to the situation that each person uses three pairs every day, I calculated the disposable chopsticks consumption of our school (1500 people) and the whole country (1200 million people) for one year, which are 13.96 cubic meters and169000 cubic meters respectively. The result surprised me. What a pity to waste so many wooden disposable chopsticks every year! I hereby appeal to the students at school, no! It is the people of the whole country, and it is not! Everyone in the world should stop using disposable chopsticks. Only in this way can we protect our forest resources, make our earth environment better and let everyone on the earth breathe clean and fresh air.

Math diary I

Tuesday, June 28th

At noon today, I was doing my math summer homework. Writing, unfortunately, I have a problem. I thought about it for a long time, but I couldn't figure out a way. The question is this:

There is a cuboid, the product of the front and the upper two areas is 209 square centimeters, and the length, width and height are prime numbers. Find its volume.

I saw it and thought: this question is really difficult! Only knowing the product of two surface areas, the volume must also know the length, width and height, but there is no hint at all. How does this start?

Just as I was scratching my head, a colleague of my mother came. He taught me to use the idea of equation to solve it first, but I am not very familiar with this method of equation. So, he taught me another way: list the numbers first, and then exclude them one by one. First, we listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1, and then we began to exclude them, and then we found that only1and 19 were left. At this time, I thought: one of these two numbers is the length of the common side of the front of the cuboid in the question; One is the front of the cuboid, and the other is the division of the previous one.

Sum of side lengths (all lengths are prime numbers). So, I began to tell which number these two numbers were.

Finally I got the result, which is 374 cubic centimeters. My formula is: 209 =119 = 2+171× 2×17 = 374 (cubic centimeter).

Later, I checked this problem with what I learned this semester: prime factor decomposition, and the results are exactly the same.

I am happier than anyone to solve this problem. I also understand the truth that mathematics is full of mysteries, waiting for us to explore.

Math diary 2

Saturday, August 6th

I saw a puzzling math problem tonight. The topic is: 37 students want to cross the river. There is an empty boat at the ferry that can only take five people. How many times must they cross the river with this boat at least?

Careless people often