Like Share 1002 Views
Magic decimals. 5th grade project. INTRODUCTION On a typical day after school, two best friends, fifth grade students Annika and Lilya, were doing their math homework. They opened the textbook and saw decimal fractions ...
Download Presentation
Grade 5 project
E N D - - - - - - - - - - - - - - - - - - - - - - - - - - - -
No related presentations.
Presentation Transcript
Decimals Grade 5 Project
On a typical day after school, two best friends, fifth grade students Annika and Lilya, were doing their math homework. They opened the textbook and saw decimal fractions ... I don't understand! What? These ... like their ... ah ... decimals. We did not pass them! - Lily was indignant. Solve the problem with decimal fractions - reads Annika. - In the spring we sowed 0.9 fields, and harvested only from 0.6 fields. How much crop has not been harvested from the field?
Lily asked. Maybe you need to add 9 to 0? Annika suggested. No, we should probably choose 0 or 9 ourselves! Annika agreed. And as soon as the girls wanted to write it down, the textbooks began to dance and sang: Decimal fractions We really need it. What kind of letter is the curve? Or is it a comma? But what does the comma have to do with it? Fairy Maya will tell us!
Please to my kingdom! I found out that you don't know what decimal fractions are? And having visited my castles, you will learn all about decimal fractions. We agree! - the girls said in unison and ended up in the kingdom.
1st castle, in which you will be introduced to the history of decimal fractions 3rd castle, in which you will be taught how to perform actions with decimal fractions 5th castle, in which they will tell you a fairy tale about decimal fractions Exit from the kingdom 4th castle, where you meet exciting problems with decimal fractions 2nd lock, in which you will learn interesting facts with decimal fractions
Decimal fractions appeared in the works of Arab mathematicians in the Middle Ages and independently in ancient China. But even earlier, in ancient Babylon, they used fractions of the same type, but of course sixties. Later, the scientist Hartmann Beyer (1563-1625) Published the essay "Decimal Logistics" where he wrote: "... I drew attention to the fact that technicians and artisans, when they measure any length, they very rarely and only in exceptional cases express it in whole numbers of one name; usually they have to either take small measures, or turn to fractions, in the same way astronomers measure values not only in degrees, but also in fractions of a degree, i.e. minutes, seconds, etc., but it seems to me that dividing them into 60 parts is not as convenient as dividing by 10, into 100 parts, etc., because in the latter case it is much easier to add, subtract and generally perform arithmetic operations ; It seems to me that decimal fractions, if introduced instead of sexagesimal, would be useful not only for astronomy, but also for all kinds of calculations. " In the European practice, decimal fractions were introduced by Simon Stevin. Until then, anyone who came across non-integers had to tinker with numerators and denominators. (Material provided by Egor Gorokhov)
Why did people switch from ordinary fractions to decimals? Yes, because operations with them are simpler, especially addition and subtraction. Add the fractions 3/50 and 7/40. First, you need to find the smallest common multiple of their denominators (this is the number 200), then divide it by 50 and multiply the result (number 4) by the numerator and the denominator of the first fraction. It turns out 12/200. Then you need to divide 200 by 40 and the quotient (number 5) multiplied by the numerator and denominator of the second fraction. It turns out 35/200. We have brought the fractions to a common denominator. Only now can we add the numerators and get the answer: 47/200. And if these fractions are presented in the form of decimal notation: 3/50 = 0.06; 7/40 = 0.175, the amount is found instantly - this is 0.235. Of course, the number 1/7 has to be written down only with some precision, 0.143 or 0.14287, but everything in life has its limits of accuracy. Only in the first quarter of the 18th century. fractional numbers began to be written using a simple decimal point. In some countries, and in particular in Russia, a comma is used instead of a period. It was introduced by the German mathematician Georg Andreas Böckler in 1661.
5 3 4 1 S. Stevin 0 I II III IV 3. 1 4 1 5 4 3 1 0 2 J. H. Beyer 3 1415 A. Girard From the history of decimal fractions Today we use decimal fractions naturally and freely. However, what seems natural to us was a real stumbling block for the scientists of the Middle Ages. In Western Europe, 16th century. along with the widespread decimal system for representing whole numbers, sexagesimal fractions, dating back to the ancient tradition of the Babylonians, were used everywhere in calculations. It took the bright mind of the Dutch mathematician Simon Stevin to bring the notation of both integers and fractional numbers into a single system. Apparently, the impetus for the creation of decimal fractions was the tables of compound percent compiled by him. In 1585 he published a book tithe, in which he explained decimal fractions. Stevin's designations were not perfect, as were the designations of his colleagues and followers. Here's how they would write down the number 3.1415: (Material provided by Dmitry Kruglikov)
We've heard a lot about air. Air is 99.96% composed of three gases: nitrogen, oxygen and argon. Carbon dioxide contains 0.03%, the rest is 0.01%.
The problem of the numerical relationship between the atoms of various elements is of great importance for understanding the world. If we compare the available on the whole Earth, iron, cobalt and nickel, it turns out that the globe consists of: Iron 92% Cobalt 0.5% Nickel 7.5% Accurate chemical analyzes of a huge number of meteorites that fell to Earth gave remarkable results. It turned out that in iron meteorites the percentage of iron, cobalt and nickel is strikingly the same as their content on our planet. (Material provided by Ivshin Gleb)
Ask her how to add and subtract. She will answer: "Memorize the algorithm for adding or subtracting decimal fractions." To begin with, the number of decimal places, you equalize, Write them down in a column and of course, know that the comma should be under the comma, And then just decide. First do the addition or subtraction without paying any attention to the comma. Well, in the answer, you, of course, put a comma under the comma in these fractions. You will remember these rules forever, so that in your memory, they remain, like two and two! You can tell me a lot, About what decimal fractions are, About what can be at the end of the fractional part, On the right, discard or insert zeros. Well, tell me how to compare them. Well, this is, of course, as easy as shelling pears. Compare the whole parts of the decimal fraction, And the one that has more of it, of course, will be more. Well, if those parts are exactly equal, Tell me what to do, you tell me. If two decimal fractions have integer parts equal, You look at the first of the non-coinciding digits, And the one with more of it, of course, will be more. Did you remember everything, tell me? If not, ask Galina Vasilievna, (Verse provided by Christina Nichiporuk)
Vasya found sunken treasures in the river and brought them home. He decided to sell them to a rich man. But the rich man deceived him for 1,234,567 rubles. How much is the treasure really worth if 0.5 gram of treasure costs $ 120.5 and their weight is 564.67 grams?
Katya) A cabbage butterfly caterpillar eats 10g per month. cabbage. The titmouse eats 100 caterpillars daily. Calculate how much cabbage "saves" for 1 month (30 days) a family of tits consisting of a female, a male and 4 chicks, assuming that the chick eats 2 times less than an adult tit.
Biyanova Masha) Kolya dreamed of a chocolate bar, which is 3.7 m long and 2.1 m wide. Tolya dreamed of a chocolate bar of the same length, but three times larger than Kolya's. How many meters is the width of the chocolate that Tolya dreamed of longer than the width of which Kolya dreamed of? Fractions? Authors: Volkova Masha, Vasilyeva Liza In the city where fractions lived, such as 1 2/10, 2 98/100, 1872/10000, 5/100 and generally with denominators 10, 100, 1000, etc., everyone lived very amicably. Nobody beat or hurt anyone and nobody argued. There were beautiful houses in this city, and beautiful flowers stood on the windows. Each shot had its own house and garden. The garden was full of apples, cherries, pears, and also different flowers. There were also schools there. There were such small fractions with a denominator of 10. There were also adult fractions with denominators from 100 to 100,000 and very old ones with a denominator from 100,000 to infinity. Adult fractions ran to work.
During the day they sat in rocking chairs and read books, and sometimes they spanked on the asses of the little ones for disobedience or pranks, or read fairy tales to them.But once the city was attacked by Shtrikh with his army. He mercilessly killed everyone, burned houses, robbed them. The war lasted ten years. One or the other won, but no one could win the war. But one kind Wizard helped the helpless fractions. He put out the burning houses, returned the loot and drove the strokes away. Only one question worried the Wizard: "How can the injured fractions be cured?" He thought for a long time, and finally came up with. Instead of a fractional bar, he gave commas to fractions, removed the denominators, and to such fractions as 1/100, 32/1000, etc. added after the whole part on the right 1, 2, 3, etc. zeros, depending on how many were in the denominator.
Girls over the kingdom of decimals. On this journey, they learned a lot, and now they can handle any problem with decimal fractions!
Slide 1
Slide 2
INTRODUCTION On a typical day after school, two best friends, fifth grade students Anna and Tanya, were doing their math homework. They opened the textbook and saw decimal fractions ... I don't understand! What? These ... like their ... ah ... decimals. We did not pass them! - Tanya was indignant. Solve the problem with decimal fractions - reads Anna. - In the spring we sowed 0.9 fields, and harvested only from 0.6 fields. How much crop has not been harvested from the field?
Slide 3
All the same, sowed 0 or 9? - asked Tanya. Maybe you need to add 9 to 0? - suggested Anna. No, we should probably choose 0 or 9 ourselves! Anna agreed. And as soon as the girls wanted to write it down, the textbooks began to dance and sang: Decimal fractions We really need it. What kind of letter is the curve? Or is it a comma? But what does the comma have to do with it? Fairy Maya will tell us!
Slide 5
Kingdom of decimal fractions 1st castle, in which you will be introduced to the history of decimal fractions 2nd castle, in which you will learn interesting facts with decimal fractions 3rd castle, in which you will be taught how to perform actions with decimal fractions 4th castle, where you will meet exciting problems in which there are decimal fractions 5th castle, in which you will be told a fairy tale about decimal fractions Exit from the Kingdom
Slide 6
From the history of decimal fractions Decimal fractions appeared in the works of Arab mathematicians in the Middle Ages and independently in ancient China. But even earlier, in ancient Babylon, they used fractions of the same type, but of course sixties. Later, the scientist Hartmann Beyer (1563-1625) Published the essay "Decimal Logistics" where he wrote: "... I drew attention to the fact that technicians and artisans, when they measure any length, they very rarely and only in exceptional cases express it in whole numbers of one name; usually they have to either take small measures, or turn to fractions, in the same way astronomers measure values not only in degrees, but also in fractions of a degree, i.e. minutes, seconds, etc., but it seems to me that dividing them into 60 parts is not as convenient as dividing by 10, into 100 parts, etc., because in the latter case it is much easier to add, subtract and generally perform arithmetic operations ; It seems to me that decimal fractions, if introduced instead of sexagesimal, would be useful not only for astronomy, but also for all kinds of calculations. " In the European practice, decimal fractions were introduced by Simon Stevin. Until then, anyone who came across non-integers had to tinker with numerators and denominators.
Slide 7
From the history of decimal fractions Why did people switch from ordinary fractions to decimals? Yes, because operations with them are simpler, especially addition and subtraction. Add the fractions 3/50 and 7/40. First, you need to find the smallest common multiple of their denominators (this is the number 200), then divide it by 50 and multiply the result (number 4) by the numerator and the denominator of the first fraction. It turns out 12/200. Then you need to divide 200 by 40 and the quotient (number 5) multiplied by the numerator and denominator of the second fraction. It turns out 35/200. We have brought the fractions to a common denominator. Only now can we add the numerators and get the answer: 47/200. And if these fractions are presented in the form of decimal notation: 3/50 = 0.06; 7/40 = 0.175, the amount is found instantly - this is 0.235. Of course, the number 1/7 has to be written down only with some precision, 0.143 or 0.14287, but after all, everything in life has its limits of accuracy. Only in the first quarter of the 18th century. fractional numbers began to be written using a simple decimal point. In some countries, and in particular in Russia, a comma is used instead of a period. It was introduced by the German mathematician Georg Andreas Böckler in 1661.
Slide 8
From the history of decimal fractions Today we use decimal fractions naturally and freely. However, what seems natural to us was a real stumbling block for the scientists of the Middle Ages. In Western Europe, 16th century. together with the widespread decimal system for representing whole numbers, sexagesimal fractions were used everywhere in calculations, dating back to the ancient tradition of the Babylonians. It took the bright mind of the Dutch mathematician Simon Stevin to bring the notation of both integers and fractional numbers into a single system. Apparently, the impetus for the creation of decimal fractions was the tables of compound percent compiled by him. In 1585 he published the book tithe, in which he explained the decimal fractions. Stevin's designations were not perfect, as were the designations of his colleagues and followers. Here's how they would write the number 3.1415:
Slide 9
It's interesting. We've heard a lot about air. Air is 99.96% composed of three gases: nitrogen, oxygen and argon. Carbon dioxide contains 0.03%, the rest is 0.01%. Substance Content in air (vol%) dry wet N2 O2 H2O Ar CO2 Others 78.08 20.95 --- 0.93 0.03 0.01 76.28 20.47 2.31 0.98 0.03 0 , 01
Slide 10
This is interesting The problem of the numerical ratio between the atoms of various elements is of great importance for the understanding of the world. If we compare the available on the whole Earth, iron, cobalt and nickel, it turns out that the globe consists of: Iron 92% Cobalt 0.5% Nickel 7.5% Accurate chemical analyzes of a huge number of meteorites that fell to Earth gave remarkable results. It turned out that in iron meteorites, the percentage of iron, cobalt and nickel is strikingly the same as their content on our planet.
Slide 11
A verse about decimal fractions You can tell me a lot, About what decimal fractions are, About what can be at the end of the fractional part, On the right, discard or insert zeros. Well, tell me how to compare them. Well, this is, of course, as easy as shelling pears. Compare the whole parts of the decimal fraction, And the one that will have more, Of course, there will be more. Well, if those parts are exactly equal, Tell me what to do, you tell me. If two decimal fractions have integer parts equal, You look at the first of the mismatched digits, And the one with more of it, of course, will be more. Did you remember everything, tell me? How to add and subtract ?. Remember the algorithm for adding or subtracting decimal fractions. To begin with, the number of decimal places, you equalize, Write them down in a column and, of course, know that the comma should be under the comma, And then just decide. First do the addition or subtraction without paying any attention to the comma. Well, in the answer, you, of course, put a comma under the comma in these fractions. You will remember these rules forever, so that in your memory, they remain, like two and two!
Slide 12
Problem 1 Vasya found sunken treasures in the river and brought them home. He decided to sell them to a rich man. But the rich man deceived him for 1,234,567 rubles. How much is the treasure really worth if 0.5 gram of treasure costs $ 120.5 and their weight is 564.67 grams?
Slide 13
Problem 2 A cabbage butterfly caterpillar eats 10g per month. cabbage. The titmouse eats 100 caterpillars daily. Calculate how much cabbage "saves" for 1 month (30 days) a family of tits consisting of a female, a male and 4 chicks, assuming that the chick eats 2 times less than an adult tit.
Slide 14
Problem 3 Kolya dreamed of a chocolate bar, which is 3.7 m long and 2.1 m wide. Tolya dreamed of a chocolate bar of the same length, but three times larger than Kolya's. How many meters is the width of the chocolate that Tolya dreamed of longer than the width of which Kolya dreamed of?
Slide 15
Problem 4 The inscription on the empty container is preserved: GROSS - 21.8 kg, NET - 20.6 kg. They put 19.9 kg of butter in it. What do you need to write on the container now?
Slide 16
Problem 5 Donna Duck the duck decided to make an apple pie. To do this, she took: 0.57 kg of apples, 2 glasses of flour, 0.25 kg each, 0.01 kg of butter, 2 glasses of milk and 2 eggs. How much will the pie weigh when Donna Duck pulls it out of the oven? How much will the pie weigh when Donna Duck's nephews eat 1/3 of the pie?
Slide 17
Loading...
