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Lesson-workshop "Units of area measurement"

Make up the formula (use the letters suggested on the cards to form a formula)

Guys, we studied a lot of topics: rectangle, square, area of a rectangle, square, units of area. Today we will conduct a generalizing lesson, the goal of our lesson is to summarize and consolidate the acquired knowledge, namely, our task for the lesson is to develop the skill of using formulas to calculate the areas of a rectangle, square, complex figures, converting units of measurement., and also in the lesson you will share your knowledge, show the application of mathematics in a variety of fields and the need to study this important subject

Repair

We very often talked about the practical application of mathematical knowledge in human life. Now we will once again be convinced that mathematics plays a huge role in human life. Look at the objects: a roll of wallpaper, a can of paint, a brush. What do they remind you of? Correct repair. Today we will start planning a classroom renovation.

Work plan

Measuring the length, width and height of the room, door size and window size
Calculation of the area of the surface to be pasted (window area) and the area of one roll of wallpaper
Calculating the ceiling area and counting the amount of paint
Calculating the door area and counting the amount of paint

Well, our plan of action is clear. It remains to determine what mathematical knowledge will help us in our work?

How Calculate the area of a rectangle?

How to calculate the area of a square?

List the units of measurement for areas

mm cm m km ar ha

Necessity forced man already in ancient times to measure not only length, distance, but also area. In ordinary life, we refer to a large open space as a square. But we also know that there is an area near the table top, the notebook, the classroom floor, and the plot of land. That is, area is the space that a figure occupies on a plane.

To measure the area, the Russian people had their own special standards: a shock, a howl, a plow, a tithe. We do not currently use these measures. The student will introduce us to them in more detail with the report “Old Area Units”

Vintage area units

In Kievan Rus there were no area measures as square measures, judging by surviving sources. Although ancient Russian architects and land surveyors had an idea about them. Area measures were needed to determine the size of land plots. The areas were not always clearly demarcated. Used for arable land

PLOW - a piece of land plowed in a day with a plow harnessed by a pair of oxen

QUARTER - The area on which a quarter of rye was sown

PALOW AND VYOT are large measures of land area. The main feature of SOKHI and Vyti was their expression through different numbers of quarters, because the amount of land and the social status of landowners were taken into account, i.e. These measures have had variable meaning.

The area of haymaking areas was estimated by KOPNA - this is the area of the meadow on which a shock of hay can be cut

These measures made it possible to determine the yield, but did not provide information on the shape and size of land plots.

TITHE. Initially, a round tithe was used - a square with a side equal to a tenth of a verst (fathom) - from which the name TITH comes.

Under Peter 1, square measures (sq. verst, sq. fathom, sq. arshin, sq. foot) were firmly established in the system of area units.

In 1916, the Regulations on Weights and Measures were legalized. m, and for land areas are, hectare.

There are various measures of area that people have come up with, but all these units of measurement can be expressed through each other.

The ancient units of area lost their significance due to their inaccuracy and were replaced by units of measurement accepted throughout the world.

Currently, the most common are sq mm, sq cm, sq m, sq km, are, hectare

Vintage area units

KOPNA

PLOW

TITHE

SOHA

HOWL

QUARTER

Vintage area units

Under Peter 1 in the system

units of area firmly

square ones have established themselves

measures (square verst, square fathom,

sq. arshin, sq. foot)

In 1916, the provision on

weights and measures were

legalized

sq. m, and for land

area are, hectares.

If the units are different, then they must be expressed in the same

Ceiling size 4 m 20 cm x 6 m
Wall height 2m 50cm
Wallpaper roll size 100cm x 10m
Door size 2m x 80cm
1 can of paint

designed for 5 m

Size windows 2m x 2m

Answer

To paint the ceiling you will need:

6 cans of paint

To paint the door you will need:

1 can of paint

To wallpaper the walls you will need:

4 rolls of wallpaper

What is the area

Your smile?

Take a ruler and...

smile!

Thank you for the lesson Well done

Used sources:

Textbook “Mathematics 6th grade” Vilenkin N.Ya. And etc.

Images taken from Internet sources .

The presentation, which is called “Units of Measurement. Measuring Instruments” plays an important role in the mathematics course. Moreover, this topic is important. If by some chance this topic is not studied, then the students' memory will be missing the most important link in their knowledge. After all, many sciences are based on the concept of units of measurement. We use many measuring instruments in everyday life. This means that we simply must study this topic.

slides 1-2 (Presentation topic "Units of measurement. Measuring instruments", meter)

So, at the beginning of the presentation, the author offers an introduction to the concept of meter. He defines it as a segment that is approximately equal to one forty-millionth part of the earth's meridian. Further, using an example that illustrates a real metal object and its sketch, it shows what the dimensions of this object are with units of measurement in millimeters.

slides 3-4 (examples)

In addition to the fact that students must know the units of measurement themselves, they must also know and be able to convert one unit of measurement into another and vice versa. The author demonstrates this in the presentation, where it is shown that one meter is equal to one hundred centimeters, and one centimeter is equal to ten millimeters. Here the author draws attention to the fact that there are such units of measurement as millimeters, centimeters and meters. The presentation then emphasizes that there are units of measurement for a large number, such as showing a kilometer and describing that one kilometer is equal to a thousand meters. In addition, the author also draws attention to such concepts as decimeter and nautical mile, which are not encountered so often, but are of great importance. The presentation also states that one decimeter is equal to ten centimeters and a nautical mile is equal to 1852 kilometers.

slides 5-6 (light year, arshin, fathom)

Next, the author suggests getting acquainted with the concept of a light year, which is defined as the path that light travels in one year. But this is not where all the units of measurement end. There are many other units of measurement that were known in ancient times. These include arshin and fathom. The author also gives in the presentation the specific meaning of these quantities. One arshin equals 0.7112 meters, and a fathom equals 2.1336 meters. But besides these quantities, there are also others that relate to national units of measurement.

slide 7 (examples)

But since there are certain units of measurement, they need to be measured with something. For these purposes, measuring instruments were invented. In fact, there are a huge variety of measuring instruments, but this presentation deals with units of length, so the instruments are offered only for measuring length. One of the presentation slides shows three types of such tools that are found quite often in our daily lives. Pictured here are a tape measure, a caliper and a folding ruler. In fact, there are a lot of them.

The presentation can be used in mathematics and geometry lessons by a teacher when explaining new material on the topic “Units of measurement. Measuring instruments". The material will be a good helper in extracurricular or elective mathematics classes. Students can also use the material to independently study the topic.

If the information given in the presentation is not enough for the teacher, he can supplement it at his own discretion.

Description of the presentation by individual slides:

1 slide

Slide description:

RESEARCH WORK “OLD UNITS OF MEASUREMENT” Scientific supervisor Anna Nikolaevna Belousova, mathematics teacher of MAOU “Secondary School No. 42” Ulan-Ude 2016

2 slide

Slide description:

In everyday life, people encounter mathematical quantities every day, without thinking, they make various calculations. Everyone is familiar with modern units of measurement. They are convenient and understandable. I wonder how they measured it in Rus' in the old days? Why are ancient units of measurement not used in our time? Is knowledge of ancient measures necessary in a modern school? These questions served as the basis for choosing the topic of the work. Goal: to study the possibility and feasibility of using ancient Russian measures in modern life. Objectives: 1. Study ancient Russian measures of length, mass, area, volume. 2. Collect and process the material. 3. Select and compose tasks. The object of study is ancient Russian measures. The subject of the study is the use of ancient Russian measures of length, mass, area and volume. Hypothesis - ancient Russian measures are inconvenient to use, but it is necessary to know the relationship between ancient Russian measures and modern units of measurement of quantities, as this will help to more easily understand the content of educational and artistic texts.

3 slide

Slide description:

4 slide

Slide description:

Ancient Units of Length A line is a very small ancient unit of length, equal to 2.54 mm (0.1 in) or the width of a grain of wheat. Tsar Alexei Mikhailovich ordered that pillars with eagles on top be placed along the road leading from the Kaluga outpost of Moscow to the summer palace in the village of Kolomenskoye, at a distance of 700 fathoms from each other. Later they began to talk about a tall and lanky man “as tall as a Kolomna mile” Standard Russian wooden milepost of the early 19th century Naval mile

5 slide

Slide description:

At the end of the 18th century, the French measured the distance overland from the city of Dunkirk on the northern coast of France to Barcelona in southern Spain. The line was drawn through Paris. They decided to consider one ten-millionth of a quarter of the French meridian as a unit of measurement and called it the meter. Along with the meter, the metric system was born. In 1875, it was adopted by 17 countries, including Russia. French revolutionaries saw education of the masses as one of the main tasks of the revolution. Therefore, they placed marble meter standards in frequently visited places in Paris. Two of them have survived to this day.

6 slide

Slide description:

Berkovets = 10 poods Pud = 40 pounds = 16.38 kg Pound = 96 spools = 0.41 kg Lot = 3 spools = 12.797 g Spool = 4.27 g Share = 0.044 g Units of mass measurement BERKOVETS ZOLOTNIK POUND LOT PUD

7 slide

Slide description:

Units of area measurement are 1 square. verst = 250,000 square fathoms = 1.138 sq. kilometers 1 dessiatine = 2400 square fathoms = 1.093 hectares 1 kopn = 0.1 dessiatine 1 sq. fathom = 16 square arshins = 4.552 sq. meters 1 sq. arshin = 0.5058 sq. meters 1 sq. vershok = 19.76 sq. cm 1 sq. ft = 9.29 sq. inches = 0.0929 sq. m 1 sq. inch = 6.452 sq. centimeter 1 sq. line = 6.452 sq. millimeters Volume units Bucket = 1/40 barrel = 10 mugs = 30 pounds of water = 20 vodka bottles = 16 wine bottles = 100 glasses = 200 scales = 12 liters. Barrel = 40 buckets = 492

8 slide

Slide description:

Ancient Russian units of measurement in proverbs and sayings “This is not a pound of raisins for you,” is a humorous expression about some difficult matter. “A pound must yield,” that is, one must have respect for elders, more knowledgeable, experienced. “Two inches from the pot, and already a pointer” - a young man who has no life experience, but arrogantly teaches everyone. “Don’t give in an inch” - don’t give up even the smallest thing. “Seven spans in the forehead” is about a very smart person. “He’s as tall as a fingernail, but with a beard as long as his elbows” - about a person of unenviable appearance, but enjoying authority due to his intelligence, social status or life experience. “Every merchant measures by his own yardstick” - everyone judges any business one-sidedly, based on his own interests. “An arshin's worth of beard, but an inch's worth of intelligence” - about an adult, but stupid person. “Oblique fathoms in the shoulders” is a broad-shouldered, tall man. “He sees three arshins into the ground” - about an attentive, perspicacious person, from whom nothing can be hidden. “If you fall behind by a mile, you will catch up by ten” - even a small gap is very difficult to overcome. “The spool is small, but expensive” - this is what they say about something insignificant in appearance, but very valuable. “Hay is worth pounds, and gold is worth spools” - each thing has its own specific value. “You know a person when you eat a pound of salt with him” - it takes a lot of time to understand another person.

Slide 9

Slide description:

Old Russian units of measurement in literary works The famous Danish storyteller H. C. Andersen wrote the fairy tale “Thumbelina”. Andersen said about her this way: “She was so tender, small, only an inch tall, and they called her Thumbelina.” Pyotr Pavlovich Ershov wrote a fairy tale in verse, in which he also used ancient Russian measures of length. “And what’s more, I’m looking at a horse that’s only three inches tall, with two humps on its back, and ears as big as a yard.” A. S. Pushkin “The Tale of Tsar Saltan...” God gave them a son in arshin, and the queen is over the child, like an eagle over an eaglet; She sends a messenger with a letter to please her father. N. A. Nekrasov “Grandfather Mazai and the Hares” Every minute the water was getting closer to the poor animals; Already under them there was less than an arshin of land in width, less than a fathom in length. S. Ya. Marshak “The Tale of the Goat” Hey, don’t cry, grandma and grandpa! I’ll feed you lunch and bake a mushroom pie two arshins wide.

10 slide

Slide description:

Questioning of 5th grade students of MAOU "Secondary School No. 42" Questionnaire for FI students, grade 1. Are you familiar with modern units of measurement? Yes No 2. Are you familiar with ancient units of measurement? Yes No 3. Is knowledge of ancient measures necessary in the modern world? Yes No Questionnaire for parents 1. Are you familiar with modern units of measurement? Yes No 2. Are you familiar with ancient units of measurement? Yes No 3. Is knowledge of ancient measures necessary in the modern world? Not really

11 slide

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12 slide

Slide description:

1. In 1847, the painter Popov made a wooden icon of the Annunciation of the Blessed Virgin Mary for the Annunciation chapel of the Ilyinskaya Church, based on a drawing of his own composition, 2 arshins high and 1 arshin wide. Find the perimeter of the frame for this icon. Express your answer in meters. Solution: 1) (2+ 1) ∙ 2 = 6 (arshinov) - perimeter 2) 71.12 ∙ 6 = 433.2 (cm) Answer: P = 426.72 cm 2. In 1887, the oil mills of N. N. Botalova and D. S. Grokhotova purchased 500 pounds of flaxseed per year. How many kg of seed will they purchase in 5 years? Solution: 1) 500 x 5 = 2500 (pounds) 2) 16.38 x 2500 = 40.950 (kg) Answer: They will purchase 40.950 kg in 5 years. 3. In 1558, Ivan IV granted Grigory Stroganov “empty” lands from the mouth of the Lysva River down both banks of the Kama to the mouth of Chusovaya and all the rivers flowing into it for 88 miles. According to later estimates, 3,400,000 acres of land. How many hectares of land did Ivan IV grant to Grigory Stroganov? Answer: Ivan IV granted 3,716,200 hectares of land to Grigory Stroganov. 4. 1 jug held 1 bucket. The barrel held 6 times more than the jug. And the tub contains 4 buckets less than the tub. How many liters did 6 buckets hold if 1 bucket held 12 liters? Answer: 144 liters fit into 6 tubs. PROBLEMS WITH OLD UNITS OF MEASUREMENT

Slide 13

Slide description:

Conclusions Having studied the literature and conducted a survey, I found out that many Russian units of measurement originated from units of Western and Eastern countries. In modern Russian, ancient units of measurement and words denoting them have been preserved mainly in the form of proverbs and sayings. Knowledge of ancient measures is necessary for general development. Currently, many countries around the world have a unified international system of units (international system - SI), which facilitates foreign policy, economic and trade relations between countries. The hypothesis put forward was confirmed. Ancient Russian measures are inconvenient to use, but it is necessary to know the relationship between ancient Russian measures and modern units of measurement. Thank you for your attention!